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An investigation into the upward transport of uranium-series radionuclides in soils and uptake by plants

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Society for Radiological Protection J. Radiol. Prot. 34 (2014) 545–573

Journal of Radiological Protection doi:10.1088/0952-4746/34/3/545

An investigation into the upward transport of uranium-series radionuclides in soils and uptake by plants D Pérez-Sánchez1 and M C Thorne2 1

  Radiological Protection of the Public and Environment, CIEMAT, Avenida ­Complutense 40, 28040, Madrid, Spain 2   Mike Thorne and Associates Limited, Quarry C ­ ottage, Hamsterley, Bishop Auckland, County Durham, DL13 3NJ, UK E-mail: [email protected] Received 3 September 2013, revised 3 March 2014 Accepted for publication 30 May 2014 Published 1 July 2014 Abstract

The upward migration of radionuclides in the 238U decay series in soils and their uptake by plants is of interest in various contexts, including the geological disposal of radioactive waste and the remediation of former sites of uranium mining and milling. In order to investigate the likely patterns of behaviour of 238 U-series radionuclides being transported upward through the soil column, a detailed soil–plant model originally developed for studying the behaviour of 79 Se in soil–plant systems has been adapted to make it applicable to the 238U series. By undertaking a reference case simulation and a series of sensitivity studies, it has been found that a wide variety of behaviour can be exhibited by radionuclides in the 238U decay chain in soils, even when the source term is limited to being a constant flux of either 238U or 226Ra. Hydrological conditions are a primary factor, both in respect of the overall advective flow deeper in the soil, which controls the rate of upward migration, and in the influence of seasonally changing flow directions closer to the soil surface, which can result in the accumulation of radionuclides at specific depths irrespective of changes in sorption between the oxic and anoxic regions of the soil. However, such changes in sorption can also be significant in controlling the degree of accumulation that occurs. This importance of seasonally varying factors in controlling radionuclide transport in soils even in very long-term simulations is a strong argument against the use of annually averaged parameters in long-term assessment models. With a water table  that was simulated to fluctuate seasonally from a substantial depth in soil to the surface soil layer, the timing of such variations in relation to the period of plant growth was found to have a major impact on the degree of uptake of radionuclides by plant roots. 0952-4746/14/030545+29$33.00  © 2014 IOP Publishing Ltd  Printed in the UK

545

D Pérez-Sánchez and M C Thorne

J. Radiol. Prot. 34 (2014) 545

In long-term safety assessment studies it has sometimes been the practice to model the transport of 226Ra in soil, but to assume that both 210Pb and 210Po can be treated as being present in secular equilibrium with the 226Ra. This simplification is not always appropriate. Where geochemical conditions are such that the 226Ra migrates upward in the soil column faster than 210Pb and 210 Po, disequilibrium is not a significant issue, as the 226Ra supports 210Pb and 210Po at concentrations somewhat below those estimated on the basis of assumed secular equilibrium. However, for low, but realistic, values of the distribution coefficients for 210Pb and 210Po and high, but realistic, distribution coefficients for 226Ra, the 210Pb and 210Po can reach the surface soil in high concentrations that are not locally supported by 226Ra. This means that models based on the assumption of secular equilibrium should not be employed without a careful consideration of the hydrological and hydrochemical situation of interest. Keywords: 238U decay chain, transport in soil, plant uptake, hydrology, sensitivity study (Some figures may appear in colour only in the online journal)

1. Introduction The upward migration of radionuclides in the 238U decay series in soils and their uptake by plants is of interest in various contexts, including the geological disposal of radioactive waste and the remediation of former sites of uranium mining and milling. However, there is only a limited literature on such upward transport. Furthermore, information on the sorption of these radionuclides to soils and their availability for plant uptake has recently been reviewed (Mitchell et al 2013), providing an updated source of information relevant to modelling the transport and uptake of 238U-series radionuclides. In order to investigate the likely patterns of behaviour of 238U-series radionuclides being transported upward through the soil column, a detailed soil–plant model originally developed for studying the behaviour of 79Se in soil–plant systems (Pérez-Sánchez et  al 2012) has been adapted to make it applicable to the 238U series. An initial version of the adapted model and some illustrative results obtained from it in the case of downward migration of 238U series radionuclides in soils has been described elsewhere (Pérez-Sánchez and Thorne 2014). However, subsequently that model has been modified to include the effects of bioturbation, based on the approach described by Klos et al (2014). In this paper, a brief account is given of the mathematical basis of the updated model. Key parameters are identified and ranges of values for those parameters are then estimated, based on the information included in the recently published review by Mitchell et al (2013). Hydrological data appropriate to a situation in which upwelling groundwater interacts with meteoric water in the soil zone are also selected, using meteorological data from a former uranium mining site in Spain as a key input. On this basis, a reference calculation case and a set of variant sensitivity cases are defined. Each of these cases is run for a unit input rate of either 238 U or 226Ra at the base of the soil column and for a simulation period of 5000 years. Results from these cases are then used to comment on potential long-term patterns of behaviour of 238 U-series radionuclides in soils and their uptake by plants. 546

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J. Radiol. Prot. 34 (2014) 545

2.  Form of the updated mathematical model 2.1.  Extension of the 79Se model to the 238U decay chain

The mathematical structure of the model is essentially identical to that described previously for 79Se (Pérez-Sánchez et al 2012), except in respect of the inclusion of bioturbation, which is discussed separately below. That model was implemented in the AMBER 5.4 simulation system (Quintessa 2012) that provides a simple method for encoding decay chains of any length. This meant that extending from the single-member decay for 79Se to the full decay chain for 238 U did not require any structural changes to the model. The decay chain that is represented is:  238 U  →234 Th  →234 U  →230 Th  →226 Ra  →222 Rn →210 Pb  →210 Po. Shorter-lived progeny of these radionuclides, notably the several generations of short-lived progeny of 222Rn, are considered to be present in secular equilibrium with their most immediate ancestor in the modelled chain. The quantities that were generalised to be contaminant dependent were:

• Distribution coefficients (Kd values); • Volatilisation rates from soil; • Plant uptake rates from soil; • Volatilisation rates from plants; • Mineralisation rates of organic matter in soil.

Distribution coefficients are defined in terms of the maximum and minimum Kd values (m3 kg−1) applicable to each contaminant and interpolated between them using the fractional water content, θ, of each layer. Thus: (1a) ⎧ Kd−min θ ≤ θ low  ⎪ K (1b) d = ⎨ K d−min + ( K d−max − K d−min ) ( θ − θ low ) / ( θ high − θ low ) θ low < θ < θ high ⎪  θ high ≤ θ. ⎩ Kd−max (1c)

Note that Kd−min can be smaller or larger than Kd−max, so that Kd values that either increase or decrease with increasing water content can be represented. The only restriction is that the Kd behaviour occurs over the same vertical extent for all members of the decay series. This is a minor restriction, as the detailed behaviour across the capillary fringe is not known precisely. For volatilisation from soil, there are three volatilisation rates (above, within and below the capillary fringe) with linear interpolation between those regions (see figure  2 of ­Pérez-Sánchez et al 2012). The three rates, k1, k2 and k3, have been made contaminant dependent (they can, therefore, be set high for 222Rn to simulate its loss from soil). The plant uptake rate from soil layer i is given by: λi p ( t )  = Gi ( t ) di f ( θi ) (2) −1

Only G (m y ), the root uptake efficiency per unit soil depth in the presence of sufficient water, is dependent upon the contaminant and the biogeochemical characteristics of the soil (see also section  2.3 of Pérez-Sánchez et  al 2012). It has been generalised accordingly. In  practice, values of G are calculated from empirical observations of the behaviour of the contaminant of interest in soil–plant systems, as discussed in section 3.7. The other quantities are the depth 547

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J. Radiol. Prot. 34 (2014) 545

Table 1.  Mass transfer rates by bioturbation.

Parameter

Value (kg m−2 y−1)

Parameter

Value (kg m−2 y−1)

M1,2 M2,3 M3,4 M4,5 M5,6 M6,7 M7,8 M8,9 M9,10

0.54 0.42 0.30 0.18 0.06 0.0 0.0 0.0 0.0

M2,1 M3,2 M4,3 M5,4 M6,5 M7,6 M8,7 M9,8 M10,9

0.54 0.42 0.30 0.18 0.06 0.0 0.0 0.0 0.0

Note: The soil layer thicknesses are each 0.2 m and layer 1 is the surface soil layer.

of each soil layer, d (m) and a dimensionless function f (θ) that reflects the consideration that root uptake becomes less efficient as the soil becomes anoxic, for which degree of saturation is here used as a surrogate measure. The value of f (θ) would also decrease at very low soil moisture contents and would be zero at soil moisture contents below the wilting point. This has not been represented in the model, as it is assumed that precipitation plus irrigation would be adequate to maintain crop viability throughout the growing season. The volatilisation rate from plants has been generalised to a single value for each contaminant (in practice, volatilisation is not a significant factor for any of the radionuclides in the 238 U decay chain, except for 222Rn, for which the process is substantially different than it is for 79Se, see sections 3.3 and 3.4). Similarly, the mineralisation rate of organic matter in soil (or more strictly the rate of release of a contaminant from organic matter back to soil solution) has been made contaminant dependent. In practice, 222Rn lost from the soil by volatilisation may be taken up by plants through the stomata. This effect is not included in the model, but the potential implications of stomatal uptake of 222Rn have been explored by Vives i Batlle et al (2011). They show that plants trap 222Rn rather inefficiently by diffusion and permeation, and that its progeny, including 210 Pb and 210Po, are taken up more efficiently through deposition and translocation. Such deposition and translocation are included in conventional models of radionuclide behaviour in plants following atmospheric deposition and are not addressed within the modelling study described herein. 2.2.  Inclusion of bioturbation

Following Klos et al (2014), the rate coefficients between the soil layers have been augmented by adding a term Mi, j/ρidi, where Mi, j (kg m−2 y−1) is the rate at which soil is moved from layer i to layer j by bioturbation (expressed on a dry weight basis), ρi (kg m−3) is the dry bulk density of soil in layer and di (m) is the depth of layer i. Both i and j lie on the range [1, 10] and j = i ± 1. In general, mass balance considerations dictate that Mi, j = Mj,i for any i and j. For the purpose of this study, values of Mi, j have been taken from Klos et al (2014). They are listed in table 1. It is noted that Klos et al (2014) include bioturbation in the top five layers of the soil. This is broadly compatible with the hydrological situation simulated in this study, since the top four layers of the soil system become unsaturated from September through to November (see tables 4 and 9). In practice, very limited bioturbation would be expected in the saturated region of the soil. A more comprehensive model would make the depth and intensity of bioturbation a function of the seasonally changing soil moisture content, but it is doubtful whether adequate data currently exist to parameterise such a model. 548

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J. Radiol. Prot. 34 (2014) 545

Table 2.  Mean monthly meteorological data used in the model simulations.

Month

Month number

Monthly precipitation (mm)

Monthly potential evapotranspiration (mm)

Precipitation rate, R (m y−1)

Potential evapotranspiration rate, PE (m y−1)

January February March April May June July August September October November December

1 2 3 4 5 6 7 8 9 10 11 12

91.4 75.8 55.0 61.4 47.1 25.9 5.4 4.7 30.3 74.5 92.3 92.5

13.7 17.7 34.1 46.4 80.2 122.3 160.7 149.5 104.4 60.3 27.3 14.8

1.097 0.910 0.660 0.737 0.565 0.311 0.065 0.056 0.364 0.894 1.108 1.110

0.164 0.212 0.409 0.557 0.962 1.468 1.928 1.794 1.253 0.724 0.328 0.178

3.  Parameter values for the reference case 3.1. Hydrology

The meteorological data used are those appropriate to the Los Ratones former uranium mine, which is located in the Autonomous Region of Extremadura in the south-west of Spain. The mine was in use from 1960 to 1974, and restoration work on the tailings pile was undertaken in 1998 and 1999. The site has been subject to environmental sampling and characterisation during and after completion of the site remediation process. Meteorological, chemical, physical, and radiological data relating to the site have been obtained over a series of discrete sampling campaigns since the site remediation was undertaken (e.g. Vera Tomé et al 2002, 2003). Mean monthly meteorological data are required for the model. The values adopted are held by CIEMAT and are listed in table 2. Note that this standard annual cycle was repeated for each year of the simulations, i.e. the effects of inter-annual variation were not taken into account. The lower boundary condition of the hydrological model is set to an upward flux of 0.1 m y−1 (i.e. 0.1 m3 m−2 y−1). This value is arbitrary and is used to represent a discharge zone for deep groundwater carrying a flux of radionuclides upward from a repository for radioactive wastes. Because this value is arbitrary, a sensitivity study was undertaken in which the value used was reduced to 0.02 m y−1 (see section 4.1). Also, the ratio of actual evapotranspiration to potential evapotranspiration is set to 0.7, which is typical of agricultural land. This gives the vertical water fluxes shown in table 3 and the water contents of the model layers shown in table 4. It is emphasised that the ratio of actual to potential evapotranspiration varies seasonally and with the type of land use (see, e.g. table C44 of BIOMASS 2003). Exploration of the effects of such variations was beyond the scope of this study, but is an important topic for future investigation. It is also emphasised that the model formulation deliberately includes only a simplified representation of soil hydrology. In particular, water uptake from the soil by plants is not represented explicitly. Instead, water losses by evapotranspiration are uniformly distributed across the unsaturated zone. It would be of interest, in future studies, to compare the soil moisture regime simulated with this simplified assessment model with that simulated with a physically based model such as HYDRUS (see, e.g. Šimůnek et al 1998, 2011) or the Richards equationbased model developed by Imperial College for Nirex (Wheater et al 2007). 549

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J. Radiol. Prot. 34 (2014) 545

Table 3.   Water fluxes (m y−1) between layers in the reference case.

Layer 1 to 2 Layer 2 to 3 Layer 3 to 4 Layer 4 to 5 Layer 5 to 6 Layer 6 to 7 Layer 7 to 8 Layer 8 to 9 Layer 9 to 10 Layer 10 to sink

Jan.

Feb. March April May June July Aug.

Sept.

Oct. Nov. Dec.

−0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1

−0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1

0.07 −0.21 −0.5 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1

0.75 0.6 0.45 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1

−0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1

−0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1

−0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1

−0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1

−0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1

−0.61 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1

1.03 0.95 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1

1.05 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1 −0.1

Note: Positive fluxes are directed downward and negative fluxes upward. Each layer is 0.2 m thick and Layer 1 is the superficial soil layer. Table 4.  Fractional volumetric content of soil layers in the reference case.

Layer

Jan.

Feb.

March

April

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

1 2 3 4 5 6 7 8 9 10

0.44 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.46 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.22 0.42 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.1 0.19 0.39 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.1 0.13 0.31 0.48 0.5 0.5 0.5 0.5 0.5 0.5

0.1 0.21 0.41 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.21 0.41 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

Note: Each layer is 0.2 m thick and Layer 1 is the superficial soil layer.

3.2.  Distribution coefficients

The hydrology model calculates Kd values on a normalised range of [0, 1] based on the water content of the soil. The actual Kd values are estimated in the transport model by scaling these normalised values to the specified Kd for each radionuclide in the decay chain. The values used for the reference case are listed in table 5. It is emphasised that, amongst the elements modelled, only in the case of uranium is there strong evidence for a dependence of Kd value on redox conditions and hence on soil moisture content. Furthermore, there are a wide variety of other soil characteristics that can affect Kd values. For members of the 238U decay series these factors are discussed in detail in Mitchell et al (2013) and the reader is referred to that review for detailed information. In practice, interpretation of the Kd values for uranium reported in the literature can be difficult, as the redox conditions and/or chemical speciation of the uranium are not always recorded. A simplification of the model is that it uses the water content of the soil as a surrogate measure of whether conditions are oxidising or reducing. However, if the soil is saturated to the surface or close to it, there will be a limited degree of penetration of oxygen by diffusion into the saturated zone within the superficial soil layer. This effect is not taken into account in the model. It could be addressed through detailed experimental and modelling studies of the diffusion of oxygen through a variably saturated soil column (MacKay 1997, Aachib et al 2004), with the results used to parameterise an extension of the simplified approach used in this study. 3.3.  Volatilisation from soil

The volatilisation rates k1, k2 and k3 apply at fractional water contents of θd, respectively, with values in the ranges θa–θb and θc–θd obtained by linear interpolation. In the 550

D Pérez-Sánchez and M C Thorne

J. Radiol. Prot. 34 (2014) 545

Table 5.  Distribution coefficients used in the reference case.

Element

Kd−min – oxic conditions (m3 kg−1)

Kd−max – anoxic conditions (m3 kg−1)

U

0.1

1.0

Th

3.3

3.3

Ra

2.5

2.5

Rn Pb

0 2.0

0 2.0

Po

0.2

0.2

Comment Illustrative values based on table 2 of Mitchell et al (2013), assuming that lower values apply in oxic conditions than in anoxic conditions because U(VI) is more soluble and less well adsorbed than U(IV), see Mitchell et al (2013), section 2.2 Table 3 of Mitchell et al (2013). Geometric mean value for mineral soils of near-neutral pH Table 4 of Mitchell et al (2013). Geometric mean value for all soils Inert gas Table 6 of Mitchell et al (2013). Geometric mean value for all soils Rounded geometric mean value for all soils from table 7 of Mitchell et al (2013)

original model (Pérez-Sánchez et al 2012) and as applied here, the values are for a total soil porosity of 0.5. The values of θa, θb, θc and θd used are 0.30, 0.40, 0.48 and 0.50, respectively. The three parameters k1, k2 and k3 are set to zero for all 238U series radionuclides except for 222Rn. For 222Rn, rapid losses from the unsaturated zone are expected, due to diffusion and pressure pumping, but little loss is expected from the saturated zone. On this basis, k1 is set to 1000 y−1, k2 to 500 y−1 and k3 to zero. The value of 1000 y−1 implies a mean residence time for 222Rn in superficial soil of 8.8 h. For comparison, a representative diffusion coefficient for 222Rn in soil is 5 × 10−7 m2 s−1 (table 19 of Annex A of UNSCEAR 1993). Therefore, the characteristic time for loss from a 0.2 m thick soil layer is about 2 × 104 s or 6 h. Thus, k1 and k2 have been set consistent with observations of 222Rn loss from soils. As values of k1 to k3 are very uncertain for 222Rn, there would be merit in investigating the effects of changes in these values in sensitivity studies. This has not been done in the current analysis, but from the results obtained for the reference case for 226Ra (section 6.2), it is clear that the main effects would occur within the first few hundred years of a chronic release when the 226Ra is localised towards the bottom of the soil column, but both 210Pb and 210Po are produced higher up the soil column. Increasing k1 and k2 would increase the rate of loss of 222Rn from the soil and would tend to reduce the degree of disequilibrium occurring in the upper soil layers, since less 222Rn, 210 Pb and 210Po would be available for upward transport in soil water. 3.4.  Volatilisation from plants

The volatilisation rates from plants (V) are taken as zero for all members of the 238U chain except for 222Rn. For 222Rn, a rate of 1000 y−1 is adopted, to ensure that 222Rn produced in plant tissues is lost from them on a timescale of a few hours. This rate is not well known, but the value adopted is thought likely to over-estimate 222Rn retention in plant tissues, bearing in mind the rapidity of loss observed from mammalian soft tissues (ICRP 1979). 3.5.  Soil density

As quartz has a particle density of approximately 2650 kg m−3 and the total porosity of the soil is 0.5, the dry bulk density of the soil is set to 1325 kg m−3. 551

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J. Radiol. Prot. 34 (2014) 545

Table 6.  Standing biomass and biomass production rate.

Month

Standing biomass (kg d.w. m−2)

Production rate (kg d.w. m−2 y−1)

January February March April May June July August September October November December

0.0500 0.0500 0.0500 0.0708 0.1250 0.2208 0.3667 0.5750 0.7833 0.4583 0.0500 0.0500

0.0 0.0 0.0 0.5 0.8 1.5 2.0 3.0 2.0 0.0 0.0 0.0

Note: The standing biomass is obtained by adding the standing biomass at the mid-point of the month to the production through to the mid-point of the next month. Thus, the standing biomass at the end of March is 0.0500 kg d.w. m−2 and the average production rate between mid-March and mid-April is (0.0 + 0.5) = 0.25 kg d.w. m−2 y−1. Thus, the standing biomass in mid-April is 0.0500 + 0.25/12 = 0.0708 kg d.w. m−2. The value for October is obtained by estimating the value at the end of September (0.7833 + 2/24) = 0.8667 kg d.w. m−2 then averaging with the post-harvest value of 0.05 kg d.w. m−2.

3.6.  Plant growth and harvesting

Plants were taken to have a growth period starting at the beginning of April (month 4) and finishing in September (month 9). The standing biomass and biomass production rates adopted are listed in table 6. These values are simplified illustrative data and do not correspond to a specific crop. Note that harvesting occurs at the beginning of October. The standing biomass after harvest represents roots and stubble. These degrade to soil organic matter over the winter months. As 0.05 kg dry weight (d.w.) out of 0.7833 kg d.w. remains after harvest (table 6), FC, the fraction removed by cropping, is calculated as 0.7333/0.7833 = 0.936. The fraction 1−FC is transferred to soil organic matter. To ensure that harvesting is rapid, the harvesting rate (Br*FC/Y), where Y is the standing biomass (kg (d.w.)), is modelled setting the user-supplied removal rate Br to 100 kg(d.w.) y−1. The transfer to organic matter in soil has a rate Br*(1−FC)/Y, so the total loss rate is Br/Y = 100/0.7833 = 127.7 y−1. Thus, the characteristic harvesting period is 365.25/127.7 = 2.9 d. As harvesting a particular crop would generally occur within a few days, a period of 2.9 d seems appropriate. 3.7.  Root uptake

As the water table is close to ground surface throughout much of the year (table 4), plant roots will be shallow. Thus, G values (see section 2.1) are set to zero for all soil layers except for soil layer 1 (0–0.2 m below the soil surface). For the surface layer, the relationship used is (Pérez-Sánchez et al 2012): G = YR / ρs d 2T (3)

where Y (kg d.w. m−2) is the standing biomass, R the plant:soil concentration ratio, ρs (kg m−3) the soil bulk density, d (m) the depth of the soil and T (y) the growing period. Parameter values are selected appropriate to pot experiments, since these are the conditions under which most of the plant:soil concentration ratios used were measured. For 79Se, the following values were taken 552

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J. Radiol. Prot. 34 (2014) 545

238 U decay chain (comments are from section 3.2 of Mitchell et al (2013); R and G are defined in section 3.7).

Table 7.   R and G values for elements in the

Element

R

G (y−1 m−1)

Comment

Uranium

0.02

0.001

Thorium

0.0035

0.0002

Radium

0.1

0.005

Radon Lead

0 0.03

0 0.0015

Polonium

0.01

0.0005

Fodder, pasture and herbs have the highest values of R (0.023 to 0.065), with legumes, tuber and cereals having the lowest values (0.0022–0.0065) The R value (0.0035 for all crops) is typically an order of magnitude lower than that observed for uranium (0.023 for all crops) There are two clear groups of R values, with the highest values being for pasture, leafy vegetables root crops, herbs and fodder (0.06–0.6) Inert gas There were few significant differences between crop groups with the largest R values occurring for pasture (0.14) and leafy vegetable crops (0.08) and the lowest for tubers (0.0015) An analysis of the IAEA data set found significantly larger R values for pasture, but no differences between other crops. Typical values were of the order 0.01

Y = 0.25, R = 1, ρs = 1325, d = 0.2, T = 0.1. This gave G = 0.047 which was rounded to G = 0.05 (Pérez-Sánchez et al 2012). Here, the same approach is used. Thus, G = 0.05 R, where R is the element-specific plant:soil concentration ratio. Values of R were taken from a recent review by Mitchell et al (2013) and are given in table 7. These values are typical best estimates for mineral agricultural soils and are rounded to the most appropriate half order of magnitude in order to avoid any suggestion of undue precision. It is emphasised that plant:soil concentration ratios are sometimes measured for whole plants and sometimes only for the edible component. In the case of 238U-series radionuclides, the main distinction is between accumulation in roots and accumulation in above-ground parts of the plants, with accumulation in roots dominating over accumulation in above-ground parts for uranium and thorium (Mitchell et al 2013). However, concentration factors for root crops are not increased relative to those for other crop types (see table 7). For the purpose of this study, the R values used are broad averages over different crop types and are taken to be applicable to all plant tissues. Thus, they are appropriately used in conjunction with the total rate of biomass production and the total standing biomass as given in table 6. The value of G is multiplied by a factor (PA) that reflects the rate of plant growth, but is not simply proportional to it. PA values are set consistent with the growth profile set out in table 6, i.e. they are constant during the main active period of growth but allow for a degree of reduction in uptake in the maturation period immediately before harvest. Therefore, PA values for the twelve months are specified by the vector {0, 0, 0, 1, 1, 1, 1, 1, 0.4, 0, 0, 0}. It is emphasised that there would be considerable merit in undertaking sensitivity studies for different hydrological conditions with drier near-surface soils. This would give rise to several competing effects. First, root penetration would be to greater depths, so radionuclides would be taken up from deeper contaminated layers. Second, there would likely be less upward water flow into the upper part of the soil, so upward migration of radionuclides might be reduced. However, this could be compensated by deeper and more intense bioturbation in the drier upper layers of the soil. Investigation of the combined influence of these various factors is a matter for future simulations using the model. 553

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Table 8.  Water fluxes (m y−1) between layers in the sensitivity case.

Layer 1 to 2 Layer 2 to 3 Layer 3 to 4 Layer 4 to 5 Layer 5 to 6 Layer 6 to 7 Layer 7 to 8 Layer 8 to 9 Layer 9 to 10 Layer 10 to sink

Jan.

Feb.

March April

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

1.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02

−0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02

−0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02

−0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02

−0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02

−0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02

−0.53 −1.12 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02

0.1 −0.16 −0.42 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02

0.76 0.63 0.5 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02

1.04 0.98 0.91 −0.02 −0.02 -0.02 −0.02 −0.02 −0.02 −0.02

1.06 1.01 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02

−0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02 −0.02

Note: Positive fluxes are directed downward and negative fluxes upward. Each layer is 0.2 m thick and Layer 1 is the superficial soil layer. Table 9.  Fractional volumetric content of soil layers in the sensitivity case.

Layer

Jan.

Feb.

March

April

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

1 2 3 4 5 6 7 8 9 10

0.31 0.48 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.48 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.43 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.17 0.37 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.1 0.14 0.33 0.49 0.5 0.5 0.5 0.5 0.5 0.5

0.1 0.1 0.22 0.42 0.5 0.5 0.5 0.5 0.5 0.5

0.1 0.13 0.31 0.48 0.5 0.5 0.5 0.5 0.5 0.5

0.12 0.3 0.47 0.5 0.5 0.5 0.5 0.5 0.5 0.5

Note: Each layer is 0.2 m thick and Layer 1 is the superficial soil layer.

4.  Parameter values for sensitivity studies In this study, sensitivities have been investigated in respect of three aspects: • The hydrological context; • Distribution coefficients for the various members of the 238U decay chain; • Plant:soil concentration ratios for the various members of the 238U decay chain. These distinct aspects are expanded upon below. 4.1.  Hydrological context

In the reference case, a high rate of groundwater upwelling is adopted (0.1 m y−1). For the variant case, a much lower rate (0.02 m y−1) is used. The variant case gives rise to the water fluxes shown in table 8 and the water contents shown in table 9. All other parameter values are identical to those in the reference case. This sensitivity case is denoted H1, to distinguish it from the reference case, R1. 4.2.  Distribution coefficients

Based on the information included in Mitchell et al (2013), various combinations of Kd values were selected for use in the sensitivity studies. These are listed in table 10. In each case, all parameter values other than Kd values are the same as in the reference case. Cases were selected to explore both the effects of low and high Kd values, and the effects of maximised 554

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Table 10.  Sensitivity cases varying the distribution coefficients.

Distribution coefficient (m3 kg−1) Case

Uranium– Uranium– Oxic Anoxic

Thorium Radium

Radon

Lead Polonium Comment

R1 D1 D2 D3

0.1 0.01 1.0 0.1

1.0 0.1 10 1.0

3.3 0.1 10 3.3

2.5 0.1 10 10

0.0 0.0 0.0 0.0

2.0 0.1 10 0.1

0.2 0.1 10 0.1

D4

0.1

1.0

3.3

0.1

0.0

10

10

Reference case All decreased All increased High radium, low lead and polonium to maximise differential transport Low radium, high lead and polonium, to contrast with Case D3

Table 11.   Sensitivity case varying plant:soil concentration ratios.

Concentration ratio (R) Element

Reference case R1

Sensitivity case P1

Sensitivity case P2

Uranium Thorium Radium Radon Lead Polonium

0.02 0.0035 0.1 0.0 0.03 0.01

0.005 0.0005 0.03 0.0 0.001 0.001

0.05 0.05 0.3 0.0 0.1 0.1

contrasts in Kd values between successive members of the decay chain, so as to emphasise differential transport and hence disturbance of secular equilibrium. 4.3.  Plant uptake

It was anticipated that plant uptake would have little effect on radionuclide concentrations in the soil column. This was investigated in a two sensitivity studies, P1 and P2, in which all the concentration ratios were either decreased or increased. The values used are listed in table 11. The ranges are estimated from information in Mitchell et al (2013). 5.  Source term Two alternative source terms were used. These were a flux of 1 mol m−2 y−1 of 238U to the base of the soil column or 1 mol m−2 y−1 of 226Ra to the base of the soil column. It is emphasised that the inputs are treated by the model as tracers that do not perturb the system, so the results scale proportionately with the input flux. A value of 1 mol m−2 y−1 was selected solely for convenience of normalisation. The 238U source was primarily of interest in the context of uranium migration through the soil column, as there is little in-growth of long-lived progeny of 238U within the 5000 year simulation period. In contrast, the 226Ra case is associated both with substantial decay of the 226Ra and substantial in-growth of its progeny. 555

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6.  Results from the reference case 6.1.  U-238 source term

In this case, there is little in-growth of progeny, so attention is appropriately focused on the behaviour of the 238U. The upward migration of the 238U through the soil column is illustrated in figure 1. As expected, the concentration in soil layer 10 increases most rapidly and reaches the highest concentration. Further up the column, the concentration increases more slowly and the maximum concentration that is reached is progressively lower. However, even after 5000 years in a soil system with a strong advective upward flow of groundwater (see table 3), there remains a strong concentration gradient between the uppermost soil layer and the lowermost, with 238U concentrations in those two layers differing by almost four orders of magnitude. This, in itself, is sufficient to demonstrate the difficulty of using one or two compartments to represent deep soil systems, as is often done in assessment models. In the absence of bioturbation, virtually no 238U penetrates above soil layer 4 (results not shown), emphasising the importance of interactions between upward groundwater flow in the saturated zone and soil-mixing processes in the unsaturated zone. The long timescale for migration is readily explained by noting that the upward flux of groundwater is typically 0.1 m y−1 and that most of the migration takes place through a zone that remains fully saturated throughout the year (tables 3 and 4). As the water-filled porosity in saturated conditions is 0.5, the upward velocity of the groundwater is 0.2 m y−1. However, in the fully saturated zone, the 238U is taken to have a Kd value of 1.0 m3 kg−1. As bioturbation applies only in the upper soil layers, its effects can be neglected in this approximate calculation. The retardation factor is 1 + ρKd/θS, where ρ (kg m−3) is the dry bulk density of the soil and θS is the water-filled porosity at saturation. Thus, the retardation factor for 238U in the region below the water table is 1 + 1325 × 1/0.5 = 2651. Hence the vertical velocity of 238U is 7.5 10−5 m y−1 and the characteristic time to cross a layer of 0.2 m thickness is 2651 years. Thus, as expected, most of the 238U is localised in the lowermost three soil layers after 5000 years of simulation. To some degree, migration further up the soil column reflects the numerical dispersion that arises from discretising the soil column into layers of finite thickness rather than treating it as a continuous system. Over the 5000 year simulation period, the total amount of 238U entering the soil column is 5000 mol. As 238U is very long lived, radioactive decay can be neglected, so the total amount present in the soil column plus plants at 5000 years should also be 5000 mol. Based on the concentrations shown in figure 1 and using a dry bulk density of soil of 1 325 kg m−3 together with layer thicknesses of 0.2 m, the total amount present is determined to be 5000.49 mol. This confirms the accuracy of the numerical solution method over the extended simulation period adopted. Although relatively little 238U reaches the uppermost soil layer, there is sufficient to compute the plant:soil concentration ratio (i.e. the ratio of the plant concentration expressed on a dry mass basis to the concentration in the top 0.2 m of soil expressed on a dry mass basis). Results are calculated at the end of June, i.e. part way through the growing season. Variations in the concentration ratio during the growing season are discussed elsewhere using a case in which the contamination is by irrigation (Pérez-Sánchez and Thorne 2014). Values of the concentration ratio as a function of the simulation time are shown in figure 2. The lower concentration ratios recorded in the first few years of the simulation reflect the fact that the plant concentration lags the soil concentration (being determined by uptake throughout the preceding part of the growth period). As the soil concentration is increasing with time, this means that the plant ‘sees’ a somewhat lower soil concentration than that 556

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Figure 1. Concentrations of 238U in soils and plants in the reference case.

Figure 2. Plant:soil concentration ratios for 238U in the reference case.

existing at the time the concentration ratio is calculated. Beyond about ten years, this lag effect becomes negligible, as the fractional rate at which the soil concentration changes decreases. Thus, a constant ratio of 3.6 × 10−4 is established. From table 7, the corresponding R value is 0.02. This is about a factor of fifty higher than the simulated value. This arises because the soil is saturated to the surface in the early part of the growing period (see table 4) and this strongly suppresses uranium uptake by the roots. For comparison, in year 90 of the simulation, the concentration ratio increases from 3.6 × 10−4 at the end of June to 1.46 × 10−2 at the end of September, as the soil dries from a moisture content of 0.5 to a moisture content of 0.1. 557

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Figure 3. Ratios of mass concentrations of 234U to 238U in the reference case.

Finally, brief consideration has to be given to the limited in-growth of progeny of 238U. This is illustrated by the ratio of mass concentrations of 234U to 238U in various soil layers as a function of simulation time (figure 3). For comparison, the ratio (η) for a pure initial source of 238U not subject to any transport is also shown. This is calculated using: η(4) =  { λU−238 / λU−234 } { 1 – exp( − λU−234t ) }

where λ is the decay constant of the radionuclide (y−1) and t (y) is the simulation time. The ratios in the soil layers are always lower than in an un-transported source because the 238 U in the soil is younger than the total simulation time. The effect is most marked in soil layer 10. This is the lowermost layer and hence immediately ‘sees’ fresh 238U entering the soil system. In contrast, 238U in soil layers 5 and 1 has been progressively resident longer in the soil column and has thus had more opportunity to give rise to 234U by in-growth. 6.2.  Ra-226 source term

As was found with 238U, concentrations of 226Ra increase rapidly in the lowermost soil layer, but increase successively more slowly in the higher soil layers (figure 4). Also, by the end of the simulation period the concentration of 226Ra in the uppermost soil layer is more than four orders of magnitude lower than the concentration in the lowermost soil layer. This follows from the high Kd value of 2.5 m3 kg−1 associated with 226Ra (table 5). After 5000 years of simulation, the total inventory of 226Ra present in the soil is 2 040 mol. The total input is 5000 mol, but 226Ra has a radioactive half-life of 1600 years, so the decay corrected inventory is 2043 mol, in good agreement with the simulation. In the case of 226Ra, the build-up of its shorter-lived progeny is of particular interest. This is shown for soil layers 1, 5 and 10 in figure 5. It is immediately clear that the build up of the progeny follows similar kinetics to the build up of 226Ra. This can be brought out further by plotting the mass ratios of the four radionuclides. This is done in figure 6. Note that times of less than 100 years have been excluded, because these mass ratios are very high at such early times for the reason discussed below. 558

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Figure 4. Concentrations of 226Ra in the reference case.

From figure 6, it will be observed that the mass ratios tend to asymptotic constant values at long times. However, in the cases of soil layers 1 and 5, these constant values are approached from above, whereas for soil layer 10, the constant values are approached much more rapidly and from below. The reason for this difference is that 222Rn is transported rapidly up the soil column giving rise to 210Pb and 210Po in the upper soil layers. Conversely, the 222Rn concentration is somewhat decreased in the lowermost soil layer due to this rapid upward migration. This effect is of greatest importance at early times when little 226Ra has been transported into the upper soil layers from the lowermost layer, i.e. the 222Rn, 210Pb and 210Po in the upper soil layers are unsupported. At late times, 226Ra migrates up the soil column and the 226Ra in each soil layer becomes the predominant source of 222Rn in that layer. At 5000 years, the mass ratios of 222Rn, 210Pb and 210Po to 226Ra are as listed in table 12. Also listed are the mass ratios expected under conditions of secular equilibrium. As expected, secular equilibrium is closely approached in soil layer 10, though the values remain slightly low because of the upward migration of 222Rn. Conversely, in soil layer 5, the values are slightly high, because of transport of 222Rn to that layer from below. In soil layer 1, the values are depressed below secular equilibrium, due to loss of 222Rn generated in that layer to the overlying atmosphere. Note that 222Rn transport in the saturated zone is solely in groundwater, whereas in the unsaturated zone it is mainly transported in the gas phase, as parameterised in the volatilisation model. Concentration ratios in this case are illustrated in figure 7. These rapidly reach a longterm plateau. The concentration ratios at 5000 years are found to be 1.81 × 10−3, 1.08 × 10−4, 5.38 × 10−4 and 2.52 × 10−4 for 226Ra, 222Rn, 210Pb and 210Po, respectively. The corresponding R values (table 7) are 1 × 10−1, 0.0, 3 × 10−2 and 1 × 10−2, respectively. The non-zero value for 222Rn arises due to production in the plant from 226Ra present in plant tissues. Although this 222Rn is rapidly lost by volatilisation, the process is not assumed to be instantaneous (section 3.4). The concentration ratios are lower than the R values because root uptake is suppressed due to the waterlogged condition of the soil early in the growing season, as discussed for 238U (section 6.1). 559

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Figure 5. Concentrations of 226Ra and its progeny in three soil layers for the reference case in which 226Ra enters the base of the soil. 560

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Figure 6. Mass ratios in three soil layers for the reference case in which

the base of the soil.

561

226

Ra enters

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Table 12.   Mass ratios of 222Rn, 210Pb and 210Po to 226Ra at 5000  in the reference case

in which 226Ra enters the base of the soil.

Mass ratio to 226Ra Basis

222

210

Soil layer 1 Soil layer 5 Soil layer 10 Secular equilibrium

6.75 × 7.03 × 6.46 × 6.54 × 10

Rn 10−6 10−6 10−6 −6

210

Pb

6.84 × 1.52 × 1.36 × 1.39 × 10

10−3 10−2 10−2 −2

Po

1.16 × 10−4 2.61 × 10−4 2.31 × 10−4 2.37 × 10−4

Figure 7. Plant:soil concentration ratios for the reference case in which 226Ra enters the

base of the soil.

7.  Results for sensitivity cases 7.1.  Decreased upward groundwater flow

As expected, the main result of decreased upward groundwater flow (Case H1) is that radionuclides migrate more slowly up the soil column. This is illustrated for 238U in figure 8 and for 226Ra in figure 9. The 238U concentration in soil layer 1 is more than 1 × 10−3 mol kg−1 in the reference case but only marginally more than 1 × 10−6 mol kg−1 in sensitivity case H1. A similar degree of difference applies in the case of 226Ra (compare figures 9 and 4). 7.2.  Effects of altered Kd values

The effects of altered Kd values is also to change the degree of migration up the soil column. This is illustrated for 238U in figure 10. This applies to case D1 with 238U as the source and is for the minimum applicable Kd values. In this case, the effects of changes in saturation in the upper soil layers are readily apparent. Concentrations in soil layers 10 to 6 exhibit a value of around 1 mol kg−1. However, in soil layers 5 and 4, which are the lowest layers to become unsaturated for part of the year, the concentrations increase. Above this transition region, 562

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Figure 8. Concentrations of the source.

238

U in soils and plants in sensitivity case H1 for

238

U as

Figure 9. Concentrations of 226Ra in soils and plants in sensitivity case H1 for 226Ra as the source.

in soil layers 3 to 1, concentrations again decrease. This is well illustrated in the soil profile at 5000 years shown in figure 11. The effect arises because of reversals in the flow direction in soil layers 4 and 5 in different months of the year coupled with changes in the applicable Kd value as the soil dries and resaturates. This case provides a convenient illustration of how the plant:soil concentration ratio varies throughout the year. Figure 12 provides a plot of variations in the concentration ratio for 238U between years 90 and 100 of the simulation and an expanded view of the variations during 563

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Figure 10. Concentrations of

the source.

238

U in soil and plants in sensitivity case D1 for 238U as

Figure 11. Soil profile of 238U at 5000 years in sensitivity case D1 for 238U as the source.

year 90. The consistency of results between years is well illustrated, as is the increase toward the end of the growing season as the soil dries out. Results for 226Ra in case D1 with 226Ra as the source are illustrated in figure  13. This demonstrates that the accumulation of a radionuclide at the boundary between upwardly moving groundwater and variable direction flows due to the interaction of downwardly moving meteoric water with upwardly moving groundwater can occur even if the radionuclide does not exhibit different Kd values in the saturated and unsaturated zones (see also figure 14). This should serve as a warning against interpreting concentration fronts as evidence for the effects 564

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Figure 12. Concentration ratios between 90 and 100 years and in year 90 in sensitivity case D1 for 238U as the source.

of hydrogeochemical changes, as they can be solely hydrological in origin. In this case, the peak is imposed on a smoothly decreasing profile of 226Ra concentration. Plant:soil concentration ratios for this case (not shown) are almost identical to those for the reference case. Case D2 is of less interest than case D1, because the degree of retardation is increased relative to the reference case. The calculations were performed only for 238U as the source and results are shown in figure 15. As expected, the degree of penetration of the 238U up the soil column is extremely limited (compare figure 15 with figure 1). This is further illustrated by the soil profile at 5000 years shown in figure 16. In the two further cases studied (D3 and D4) only 226Ra as a source term was simulated, as these two cases were designed to investigate the effects of adopting contrasting Kd values 565

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Figure 13. Concentrations of as the source.

Figure 14. Soil profile of

source.

226

226

Ra in soil and plants in sensitivity case D1 for

Ra at 5000 years in sensitivity case D1 for

226

226

Ra

Ra as the

for the various members of the 226Ra subseries (see table 10). The key distinctions between the results are well illustrated by soil profiles at 100, 500, 1000 and 5000 years, as illustrated in figures 17 and 18. In the simulation illustrated in figure 18, 226Ra moves more rapidly than either 210Pb or 210 Po. In consequence, these progeny have the opportunity to grow in to close to secular equilibrium below the upwardly advancing 226Ra. Thus, their profiles are similar to that of 226 Ra at all times. Also, as the simulation time increases, the 226Ra distributes further up the 566

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Figure 15. Concentrations of

the source.

238

U in soil and plants in sensitivity case D1 for 238U as

Figure 16. Soil profile of 238U at 5000 years in sensitivity case D2 for 238U as the source

(note that a logarithmic y-axis is used in contrast to a linear y-axis in figures 11 and 14).

soil column and its profile flattens. Note that the concentrations in these profiles are shown on a logarithmic scale. Thus, the slight peak at 0.7 m depth in the 5000 year profile shown in figure 18 is similar to the pronounced profile shown on a linear scale in figure 14. In the simulation shown in figure 17, the situation is very different. In this case, the 226Ra is retarded relative to the 210Pb and 210Po that move more rapidly up the soil column. Thus, by 500 years the mass concentration of 210Pb is higher than the mass concentration of 226Ra in the soil column at all depths from 0.1 to 1.3 m. As 210Po has a short radioactive half-life and 567

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Figure 17. Soil profiles of 226Ra and its progeny in sensitivity case D3 for 226Ra as the source (note that a logarithmic y-axis is used).

is retarded to the same degree as 210Pb, it is approximately in equilibrium with the 210Pb at all times and depths. Departures from secular equilibrium for soil layer 1 are listed in table 13. This soil layer was selected, since it gives the largest distance over which differential transport can be exhibited. In D4, 222Rn initially exhibits a ratio slightly higher than would be expected at secular equilibrium, due to its upward migration from deeper soil layers in which the 226Ra concentration is higher than at the surface. However, this effect has largely disappeared within a few hundred years. In D4, both 210Pb and 210Po exhibit concentrations that reach about 40% of the secular equilibrium values. This is because 226Ra from below continues to accumulate in the soil layer during the period of in-growth of these radionuclides and this 226Ra is associated with limited influx of 210Pb and 210Po due to their much higher retardation. In D3, the 210Pb and 210Po move toward the surface soil layer much more rapidly than the 226Ra, giving very high mass ratios relative to secular equilibrium. The mass ratio of 222 Rn is initially higher than in D4 not because the 222Rn moves any faster, but because the 226 Ra moves more slowly. At longer times in D3, 226Ra reaches the surface soil in appreciable amounts and the mass ratios approach those expected at secular equilibrium.

7.3.  Effects of altered plant uptake

The two sensitivity studies of altered plant uptake were undertaken both for 238U as the source and for 226Ra as the source. As migration through the soil column was unaltered from the 568

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Figure 18. Soil profiles of 226Ra and its progeny in sensitivity case D4 for 226Ra as the source (note that a logarithmic y-axis is used).

reference case, attention is here concentrated on estimates of plant uptake. The comparison is made for uptake in year 90 of the simulation and at 5000.5 years, i.e. the final time of the simulation, which occurs part way through the growing season. Plant:soil concentration ratios from the reference case for 238U and the associated two sensitivity studies during year 90 of the simulation are shown in figure 19. As expected, the concentration ratios for 238U scale in direct proportion to the concentration ratios adopted as input (table 11). The plant uptake is too limited to significantly affect the soil concentrations, which differ by no more than 1.0% between the three simulations. At 5000.5 years, the plant:soil concentration ratios are 3.61 × 10−4 in the reference case, 9.02 × 10−5 in case P1 and 9.02 × 10−4 in case P2. These plant:soil concentration ratios are themselves in the ratio 1: 0.25: 2.5, as expected from the input data specified in table 11. Plant:soil concentration ratios from the reference case for 226Ra and the associated two sensitivity studies for year 90 of the simulation are shown in figure  20. The intra-annual profiles for the three cases are virtually identical, except for scale factors reflecting the concentration ratios adopted for input (table 11). This is well illustrated by the concentration ratios at 5000.5 years. These are listed in table 14. Note that the values for cases P1 and P2 differ by almost exactly one order of magnitude for 226Ra and two orders of magnitude for 210 Pb and 210Po, as would be expected from the two sets of R values adopted (table 11). In this case, the soil concentrations differ by rather more than in the 238U case. For 226Ra, they are increased in P1 relative to R1 by about 2.5% at 5000.5 years. In P2 they are decreased relative to R1 by about 12.5%. This reflects the relatively large plant:soil concentration ratio for 226Ra in P2 (table 11). 569

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Table 13.  Mass ratios of 222Rn, 210Pb and 210Po to 226Ra in soil layer 1 for cases D3 and

D4 in which 226Ra enters the base of the soil.

Mass ratio Simulation D3

Time (y)

Rn-222

Pb-210

100 500 1000 5000

D4

100 500 1000 5000 Secular equilibrium

Po-210

8.62 × 7.76 × 7.16 × 6.75 × 10

107 104 101 −2

3.38 × 1.69 × 9.82 × 1.03 × 10

5.87 × 105 2.94 × 102 1.70 × 100 1.75 × 10−4

9.45 × 10−6 7.02 × 10−6 6.78 × 10−6 6.63 × 10−6 6.54 × 10−6

3.69 × 10−3 4.99 × 10−3 5.23 × 10−3 5.38 × 10−3 1.39 × 10−2

6.03 × 10−5 8.38 × 10−5 8.81 × 10−5 9.07 × 10−5 2.37 × 10−4

10−4 10−7 10−6 −6

Figure 19. Plant:soil concentration ratios for 238U in year 90 for the reference case (R1)

and the two sensitivity studies in which plant uptake was varied (P1 and P2).

8.  Discussion and conclusions The various simulations reported in this study illustrate the wide variety of behaviour that can be exhibited by radionuclides in the 238U decay chain in soils, even when the source term is limited to being a constant flux of either 238U or 226Ra. Hydrological conditions are a primary factor, both in respect of the overall advective flow deeper in the soil, which controls the rate of upward migration, and in the influence of seasonally changing flow directions closer to the soil surface, which can result in the accumulation of radionuclides at specific depths irrespective of changes in sorption between the oxic and anoxic regions of the soil. However, such changes in sorption can also be significant in controlling the degree of accumulation that occurs, so there is a need to take both factors into account simultaneously when evaluating radionuclide transport in soils. This importance of seasonally varying factors in controlling radionuclide transport in soils even in very long-term simulations is a strong argument against the use of annually averaged parameters in long-term assessment models, unless those 570

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J. Radiol. Prot. 34 (2014) 545

226 Ra and its progeny in year 90 for the reference case (R1) and the two sensitivity studies in which plant uptake was varied (P1 and P2).

Figure 20. Plant:soil concentration ratios for

Table 14.  Plant:soil concentration ratios at 5000.5 years for cases R1, P1 and P2 and for 226Ra as the source.

Plant:soil concentration ratio Case

Ra-226

Rn-222

Pb-210

Po-210

R1 P1 P2

1.81 × 10−3 5.42 × 10−4 5.42 × 10−3

1.08 × 10−4 3.25 × 10−5 3.25 × 10−4

5.38 × 10−4 1.82 × 10−5 1.79 × 10−3

2.52 × 10−4 1.81 × 10−5 1.80 × 10−3

annually averaged parameters have been suitably calibrated against a more detailed model in which seasonal variations are taken into account. One caveat should be noted. The simulations reported here used a single annual hydrological cycle that was repeated throughout the simulation period. In practice, the hydrological cycle will vary somewhat from year-to-year. In ­particular, the depth of the water table will vary both seasonally and inter-annually. The effect of inter-annual variation may be to smear out to some degree the sharp accumulation fronts simulated in this study. The effects of such inter-annual variations should be a priority for further investigation. It is also noted that the model makes a variety of other simplifications, e.g. a homogeneous soil column and a simplified plant growth profile. These will not always be applicable, but have been adopted in order to illustrate a number of aspects of soilplant behaviour that are seldom addressed in simpler models of the soil–plant system. With a water table that fluctuates from a substantial depth in soil to the surface soil layer, the seasonality of such variations in relation to the period of plant growth has a major impact on the degree of uptake of radionuclides by plant roots. In this study, it has been shown that high water content in the rooting zone early in the growth season can strongly suppress plant uptake of radionuclides, with the uptake occurring mainly later in the growth season as the soil dries out. It is emphasised that this result arises as a result of the particular way in which the model characterises the effects of soil water content on plant root activity. In practice, the 571

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effects of water content on root uptake are likely to be affected by the type of plant under consideration. Again, this is a topic that should be a priority for further investigation. In long-term safety assessment studies it has sometimes been the practice to model the transport of 226Ra in soil, but to assume that both 210Pb and 210Po can be treated as being present in secular equilibrium with the 226Ra. This study illustrates that this simplification is not always appropriate. Where geochemical conditions are such that the 226Ra migrates upward in the soil column faster than 210Pb and 210Po, disequilibrium is not a significant issue, as the 226 Ra supports 210Pb and 210Po at concentrations somewhat below those estimated on the basis of assumed secular equilibrium. However, for low, but realistic, values of the distribution coefficients for 210Pb and 210Po and high, but realistic, distribution coefficients for 226Ra, the 210 Pb and 210Po can reach the surface soil in high concentrations that are not locally supported by 226Ra. This means that models based on the assumption of secular equilibrium should not be employed without a careful consideration of the hydrological and hydrochemical situation of interest. It is emphasised that the direct application in post-closure assessments of models of the type described here is likely to be acceptable in terms of resource requirements. Each 5000 year simulation required less than two hours computing on a standard single core PC operating in the background while the machine was in use for other purposes. However, if there was a requirement to undertake large uncertainty and sensitivity analyses, with extensive parameter value variation, it might be appropriate to move to a parallel-processing arrangement, or to simplify the model structure, as discussed by Klos et al (2014). It is emphasised that assessment modelling is always likely to be a compromise between the need to achieve a detailed physically based representation of the system of interest and the requirement to undertake a substantial number of long-term assessment simulations. The model described here is thought to be a useful compromise for assessment purposes, but it is recognised that it is likely to need to be underpinned by more detailed physically based modelling, and that it may need to be augmented or simplified to satisfy assessment requirements at specific sites. A further consideration in undertaking assessment-level modelling is that the hydrological conditions, and soil and crop characteristics, may be defined only in very broad terms. Therefore, it may be appropriate to substantially simplify the assessment-level model relative to physically based models of specific present-day situations. Acknowledgements This work has been financially supported by the Empresa Nacional de Residuos Radiactivos (ENRESA) under agreement CIEMAT/ENRESA. However, the opinions expressed are those of the authors and do not necessarily represent those of CIEMAT or ENRESA. References Aachib M, Mbonimpa M and Aubertin M 2004 Measurement and prediction of the oxygen diffusion coefficient in unsaturated media, with applications to soil covers Water Air Soil Pollut. 156 163–93 BIOMASS 2003 ‘Reference biospheres’ for solid radioactive waste disposal Report of BIOMASS Theme 1 of the BIOsphere Modelling and ASSessment (BIOMASS) Programme IAEA-BIOMASS-6 International Atomic Energy Agency, Vienna, Austria ICRP 1979 ICRP publication 30, limits for intakes of radionuclides by workers—part 1 Ann. ICRP 2(3/4) Klos R, Limer L, Shaw G, Pérez-Sánchez D and Xu S 2014 Advanced spatio-temporal modelling in long-term radiological assessment models—radionuclides in the soil column J. Radiol. Prot. 34 31–50

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