Proceedings of ICEM ‘03:
The 9th International Conference on Radioactive Waste Management and Environmental Remediation
September 21 – 25, 2003, Examination School, Oxford, England

icem03-4632
MODELLING 226RA, 222RN, AND 210PB MIGRATION IN A PROPOSED SURFACE REPOSITORYOF VERY LOW-LEVEL LONG-LIVED RADIOACTIVE WASTE
Dirk Mallants, Diederik Jacques, and Theo Zeevaert
Belgian Nuclear Research Centre, SCK•CEN, Boeretang 200, B-2400 Mol, Belgium

ABSTRACT
A generic concept for disposal of very low-level long-lived
radioactive waste is currently being evaluated for radium
bearing wastes that originated from a historical radium
extraction plant at Olen, Belgium. A total volume of
approximately 217 000 m3 of waste with an average radium
content of 7 Bq/g has to be disposed of. Upon request by the
Belgian National Agency for Management of Radioactive
Waste and Nuclear Fuels, NIRAS/ONDRAF, a generic disposal
concept was evaluated for the purpose of identifying theminimum disposal concept which guarantees long term safety.
Such an analysis would provide useful input to the final designof the disposal concept, as the contribution of the different
engineered barriers to the overall safety will have beenassessed. The analysis focussed on the migration of 226Ra,
222
Rn, and 210Pb to groundwater owing to infiltration of
rainwater and the diffusive radon transport via the gas phase to
the atmosphere. The generic design considered a waste dumpwith the contaminated material completely enclosed by a clay
barrier. To protect the low-permeability clay from degradation
by water and wind erosion, frost and desiccation, burrowing
animals, and plant roots, among others, a multi-layer cap was
designed to meet these requirements. In the performanceassessment calculations, various cases were considered inwhich one component of the disposal concept was changed at
the time. Cases considered included absence of clay layers,
effects of hot spots, lower adsorption capacity of various
materials, and the effect of separating the radium contaminatedmaterial from nearly uncontaminated material. Unsaturated
flow calculations were done first to estimate the steady-statewater content profile. Knowledge on the degree of water
saturation is of paramount importance for radon transport
through the gas phase. Based on the steady-state water content
profile, advective dispersive transport calculations were done
considering the decay chain reaction of 226Ra. In addition to theradon gas flux to the atmosphere, fluxes of 226Ra, 222Rn, and210

Pb to groundwater were also produced. Groundwater flow
and transport calculations yielded radionuclide concentrations
in a hypothetical well nearby the planned disposal site, whereas
biosphere modelling provided the annual doses to the publicconsidering the groundwater pathway and direct inhalation ofradon in case of the atmospheric pathway. On the basis of thecalculated radionuclide fluxes and doses the importance of thevarious model parameters and concept components will be
evaluated and discussed.
INTRODUCTION
From the early 1920's to the mid 1970's the industrial
activities of Metallurgie Hoboken-Overpelt (MHO) at Olen,
now Umicore, were known world wide for the radium anduranium production [1]. During several decades, MHO was oneof the most important radium production plants and contributed
significantly to the widespread use of radium in medical andindustrial applications. These industrial activities resulted in avariety of waste products, including mill tailings, dismantlingand decontamination materials, contaminated soil, residues
from radium extraction, etc. An impact assessment analysis forthe most radioactive radium bearing wastes that are presently
stored in a heavily engineered facility was reported by [2]. In
the present paper we discuss the preliminary impact assessment
for a proposed surface disposal facility for very low-level
radium bearing waste. The impact assessment will focus on two
major exposure pathways, i.e., the groundwater pathway andthe atmospheric pathway. Human intrusion is not discussed
here. The objective of the paper is to assess the long-term
radionuclide behaviour in response to changes in disposal
concept, and transport related parameters. For this purpose aseries of scoping calculations were carried out, focussing on theradionuclide fluxes to groundwater and atmosphere. Suchcalculations may help define the minimum disposal concept
which guarantees long term safety.
1

Copyright © 2003 by ASMEMATERIALS AND METHODS
Site Characteristics
An extensive hydrogeological characterization has been
carried out in the vicinity of the proposed disposal site. The
uppermost layer (0-8 m) is composed of well sorted sands,
known as Kasterlee Sands. Between 3 and 5 m depth the sandlayer has a typical green color owing to the presence of a small
amount of glauconite. At the eastern boundary of the site thesand layer contains a fairly thin clay layer, known as Kasterlee
Clay. At some locations the latter is only present as a series offairly thin clay lenses. A second sand layer, known as Diest
Sands, extends from 8 to approximately 90 m depth andcontains about 25-30 weight % glauconite. The groundwater at
the site is very close to the soil surface. The hydraulicconductivity varies between approximately 10-6 m/s for theupper and lower sands and about 10-7 m/s for the clay-richlayer. Further details can be found in [2].

the van Genuchten-Mualem soil hydraulic functions [5] were
estimated for each soil layer [6]. The steady-state water
redistribution together with the appropriate initial and boundary
conditions were imposed to model steady-state water
redistribution in the multi-layer cap. A long term average net
rainfall of 10-8 m/s was used as top boundary.

Top soil (1,5 m)interface foratmospheric flux

Sand-gravel mix (0,3 m)
Coarse gravel (0,5 m)
Compacted sand (0,5 m)
Clay-1 (0,5 m, K=10-8 m/s)
Clay-2 (0,5 m, K=10-9 m/s)
Sand (2,25 m)

22.3 mDisposal Characteristics
A preliminary concept for surface disposal of
approximately 217 000 m3 of very low-level radioactive waste
was recently designed. The waste was mainly composed ofcontaminated soil, ironhydroxides and calcium sulphate as
major residues from cobalt production, and residues fromradium extraction [3]. Waste is composed of 135 000 m3 ofradium bearing material at an average concentration of 7 Bq/g
226
Ra, whereas approximately 82 000 m3 of material has anegligible radium content. The total radium inventory is
estimated at 2×1012 Bq.
The waste material will be isolated from the geosphere bymeans of clay layers that enclose the waste at the bottom and at
the top of the disposal dump. A schematic view of the various
layers that comprise the repository, including a multi-layer
protective cap, is given in Fig.1. Protection of the 1-m-thickclay layer (clay-1 and clay-2) against burrowing animals,
drying, freeze-thaw cycles, etc. is secured by means of a 2.8-mthick layer composed of several materials, including a loamy
top soil, sand, and gravel. Total maximum depth of radioactive
waste material is 14.5 m. At the bottom of the repository, a 0.5m-thick clay layer (clay-3) together with a High Density
Polyethylene (HDPE) foil separates the waste from theunderlying groundwater.
Numerical Models
Calculation of the migration of radium and its daughter
nuclides to geosphere and biosphere requires several models.
Each of the models used here will be briefly discussed.
Flow model for multi-layer cap
Prior to the modelling of radium leaching to groundwater,
the water flux through the waste material has to be known. The
magnitude of this flux is determined by the capacity of themulti-layer cap to divert the infiltrating rainwater. The twodimensional variably saturated flow and transport code
HYDRUS-2D [4] was used for this purpose. The 2D flow
model included the first six layers of the profile shown in Fig.
1, i.e., from top soil to the clay-2 layer. Appropriate values for

Waste (14.5 m)

Clay-3 (0,5 m, K=10-9 m/s)

interface for flux
to groundwater

Sand (1,25 m)

Figure 1 Vertical profile of waste material and protective
layers.
Source term model
Leaching of 226Ra and its most important decay products
222
Rn and 210Pb was calculated using the one-dimensionalvariably-saturated flow and transport code HYDRUS-1D [7]. A
conceptual model for the migration of the three radionuclides
considered here is given in Fig. 2. The source term model
calculates fluxes of dissolved radionuclides at the bottom of therepository, in addition to the flux of radon gas at the interfaceof the clay-1 layer and the overlying sand layer (see Fig. 1).
The 1D computational domain excludes the first six soil layers,
as they were treated in a separate 2D calculation. The
calculated water flux at the bottom of the clay-2 layer will be
used as top boundary for the 1D model.
Not including the first six soil layers implies that the effectof the first 2.8 m soil is not accounted for in calculating radon
migration. This assumption is conservative as long as these
protective layers are intact (i.e., during the institutional control
period). However, the assumed condition becomes realistic
when long term assessment is of concern. In such case, various

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Copyright © 2003 by ASME

degradation processes may have lead to a partial removal of
those layers.

Total concentration of the porous medium, CT (Bq/m3 porous
medium), of each radionuclide is calculated from [8]:


a



1-

Water flux

Raw

Rng

Ras

Rnw

CT    C w   b  C s  a  C g

where ρb = dry bulk density (kg/m3), and all other parameters
are as defined previously.
The partial differential equations governing onedimensional transport of radionuclides involved in a sequential
first-order decay chain during steady-state water flow in avariably saturated porous medium were solved using
HYDRUS-1D. We assume radionuclides are transported byconvection and dispersion in the liquid phase and by diffusionin the gaseous phase. Additional parameters for advectivedispersive transport in the liquid phase are pore-water diffusion
coefficient, Dp (m2/d), and dispersivity, λ (m). Best estimateparameter values for Dp are given in Table 1. For λ a uniform
value of 0.03 m was considered for the entire soil profile.
Transport in the gas phase requires estimates of the
diffusion coefficient for the soil gas phase, Dp,g (m2/d) [8]:D p , g   g  Do , g

Pbw

Pbs

Gas phase Water phase

Solid phase

Figure 2 Partitioning of 226Ra, 222Rn, and 210Pb between threephases of the porous medium. Soil parameters are: η = total
porosity, θ = volumetric water content, a = η - θ = volumetric
air content.
The presence of the radon gas requires that three phases are
considered in the modelling, i.e. solid, liquid, and gaseous
phase. If we conservatively assume radon (as a gas or
dissolved) is not sorbed on the solid phase, partitioning
between solid and liquid phase applies to radium and lead,
whereas partitioning between liquid and gaseous phase applies
to radon. The solid-liquid partitioning relationship is [8]:Cs  kd  Cw

(1)
where Cs is solid phase concentration (Bq/kg soil), Cw is liquid
phase concentration (Bq/m3), Kd is solid-liquid distribution
coefficient (m3/kg soil). Partitioning between liquid andgaseous phase is defined in a similar way [8]:(2)Cw  k  C g
where Cg is concentration in the gas phase (Bq/m3 soil air), andk is Ostwald constant (-). The latter parameter may be
calculated from the Henry constant, KH [9]:(3)k  KH  R T
where R is universal gas constant and T absolute temperature (°Kelvin). The product RT is 0.0244 atmm3/mol. At 10 °C, KH= 14.6 mol/atmm3, hence k = 0.356. At 20 °C, KH = 10.7 and k= 0.26 [10]. We assumed k = 0.26.

(4)

(5)

where Do,g is free air diffusion coefficient (m2/d), and ξg is
tortuosity factor for the gas phase, defined as ξg = a7/3/θs2 [11].
A value of 0.864 m2/d was considered for Do,g and was takenfrom [12].
Modelling of the flux to the atmosphere requires a different
type of soil boundary condition for volatile chemicals. A thirdtype (Cauchy) boundary condition was invoked, with anadditional term that accounts for gas diffusion through astagnant boundary layer of thickness d. The gas flux is
proportional to the difference in gas concentrations below andabove the boundary layer [13]. A value of 0.5 cm for d for baresoil was suggested by [13].
Table 1 Radionuclide specific parameter values.
Material
Dp
Kd(m2/d)(m3/kg)
Ra
Clay
0.014
6.210-5
Waste
2.7
6.210-5
0/0.65Sand
6.210-5Rn0Clay8.6510-50
Waste
8.6510-50Sand8.6510-5
Pb
20
Clay
6.210-5
0.27
Waste
6.210-5
0Sand
6.210-5

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In the scoping calculations, several source term parameters will
be given alternative values such that the effect of eachparameter on the radionuclide behaviour can be assessed.
Variations in the following parameters will be discussed:
 Clay layers: in the reference scenario, all three layers
are present. Calculations will also be made with all
three clay layers being degraded. Such a model
presumably is more representative for the very longterm, when natural processes and/or human actions
have resulted in a deterioration of the protective clay
layers.
 Presence of hot spots: several hot spots have been
detected in the waste material. A field survey revealed
radium concentrations in excess of 40 Bq/g in 15% of
the samples [14]. Therefore, calculations with thesource term model were carried out assuming auniform concentration in the 14.5-m-thick waste zoneof 40 Bq/g 226Ra rather than 7 Bq/g. Since the 1D
calculations provide fluxes per m2 of surface area, theresults can be extrapolated for any quantity (i.e.
surface area) of hot spots (from 0 to 100 %). In thefollowing discussion we assume 100% hot spots, i.e.
the whole waste dump has 40 Bq/g radium as initialconcentration.
 Reduced sorption capacity of waste material. Given
the large variety in waste materials, a high level ofsorption heterogeneity may be expected. Therefore, a
Kd value 10 smaller than the best estimate given in
Table 1 was used for all materials.
In addition to the above alternative cases, several otherparameters have been considered. These include degree ofwater saturation of the waste material at the time of waste
emplacement (i.e., very dry or very wet), less permeable wastematerial, etc. [6]. Discussion of these cases was beyond thescope of the present paper. Therefore, only six cases will be
discussed. A summary of calculation cases is shown in Table 2.
Best estimate parameter values were used for the reference case
(case 1) and case 4, but the effect of degraded clay layers was
also investigated for the latter parameter set. For eachalternative parameter set, calculations considered both intact
and degraded clay layers.
Table 2 Cases considered in scoping calculations
Parameter
Intact clay
Degraded clay
layerslayersReference
1
4
Hot spots
2
5Reduced sorption
3
6
Hydrogeological model
Radionuclide transport through groundwater is an
important pathway for human exposure. In our assessment weconservatively assume the presence of a small well in thevicinity of the repository, say at 100 from the disposal facility.
The well capacity is assumed small enough to have little or noeffect on groundwater flow.
All groundwater flow calculations were done using the
GMS-Modflow 96 software package [15]. Concentrations of

226

Ra, 222Rn, and 210Pb in the hypothetical well were calculatedusing a dilution factor. The latter was obtained by assuming
transport of a non-adsorbing and non-decaying chemical fromthe bottom of the repository to the well. In this way, only
dilution and dispersion in the aquifer is accounted for, while
sorption has been neglected. As a result, calculated
concentrations are conservative. Transport calculations weredone using the MT3DMS software package [16].
Biosphere model
In the last step the annual dose for each radionuclide for awater well pathway is obtained by applying a biosphere model.
The well pathway assumes that a self-sustaining farmer
community uses water from the well as drinking water, forirrigation of crops, etc. The biosphere model accounts for all
major exposure pathways, including ingestion of contaminatedfood or water, direct irradiation by contaminated soil orsediment, etc. [17].
Exposure to radon gas escaping through the degraded
protective cap may also contribute to the total annual dose. The
methodology for calculating the annual dose (Sv/y) for anindividual that is staying for a given time on top of therepository is based on the approach described by [18]:Dose  exhalation rate  dose factor(6)
 radon concentration in air
where exhalation rate is total radon flux density to atmosphere(atoms/cm2/s), dose factor is 3.1 (nSv/h)/(Bq/m3), and radon
concentration in air per unit of exhalation rate (Bq/m3)/(
atoms/cm2/s) at 1.5 m above soil surface is depending on thestability of the atmospheric layers close to the soil surface. For
weak mixing and normal mixing a value of 20, respectively 4
Bq/m3 per unit of exhalation was proposed [18]. We assumed
an intermediate value of 8 Bq/m3 per unit of exhalation rate.
The average exposure time for an individual from the referencegroup, i.e., a self-sustaining farmer community, was taken as
100 h/y. For example, an exhalation rate of 4.6×106 Bq/m2/y =6.95 atoms/cm2/s would result in an annual dose of
approximately 17 µSv.
The time history of the total annual dose will be based on
the contribution from the groundwater pathway and theatmospheric pathway. Only the maximum value and the time it
occurs will be reported here.

RESULTS AND DISCUSSION
The 1D calculations using the source term model resulted
in three types of output, notably (1) depth profiles ofradionuclide concentrations in the relevant phases (water andsolid phase for radium and lead and water and gas phase forradon) at selected time intervals, (2) radionuclide fluxes at theinterface repository/groundwater, and (3) radon flux at theinterface between clay-1 and the overlying sand (Fig. 1).
Depth profiles for various cases are given in Fig. 3. Only
concentrations in water or gas phase are discussed.
Concentrations on the solid phase may be easily calculatedusing Eq. (1). A comparison of 226Ra concentrations for case 1,
3, 4, and 6 reveals that reduced sorption (case 3 and 6) results

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Copyright © 2003 by ASME

in a higher pore water concentration in the waste zone andbelow and a faster leaching compared to the reference
parameter set. Hence, fluxes for case 3 and 6 will besignificantly higher than those for the other cases (see further).
The effect of degraded clay layers, i.e. compare cases 1 with 4
and 3 with 6, has a much smaller effect on the downward
movement of radium. Therefore, regarding radium fluxes togroundwater, the effect of reduced sorption (based on theassumptions used here) is expected to be much more important
than the effect of degraded clay layers (see further).
Case 5 (t = 100 y)
C ase 5 (t = 1000 y)
Case 6 (t = 100 y)
Case 6 (t = 1000 y)

Case 1 (t = 100 y)
Case 1 (t = 1000 y)
Case 3 (t = 100 y)
Case 3 (t = 1000 y)
Case 4 (t = 100 y)
Case 4 (t = 1000 y)

0
(a)

0

(c)

clay

clay

-4

-4
sand

-8

-12

-12

-16

-16

-20

-20

-24
1E+002226

0

1E+003

1E+004-24
1E+005 1E-002

Ra concentration in pore water (Bq m-3)

210

0

(b)

1E-001

1E+000

1E+001

Pb concentration in pore water (Bq m-3)

(d)

clay

clay
-4

-4
sand

-8

-12

-12

Waste zone

-8

-16

-16

-20

-20

Waste zone

sand

Depth below surface (m)Waste zone

-8

Waste zone

Depth below surface (m)

sand

-24
-24
0E+000 1E+007 2E+007 3E+007 4E+007 5E+007 0.0E+000 5.0E+007 1.0E+008 1.5E+008 2.0E+008
222

Rn concentration in pore water (Bq m-3)

222

Rn concentration in air phase, Ca (Bq m-3 air)Figure 3 Calculated depth-profiles for (a) dissolved 226Ra
concentrations, (b) dissolved 222Rn concentrations, (c) dissolved
210
Pb concentrations, and (d) 222Rn concentrations in gas phase.
For explanation of cases, see main text.

For an analysis of radon concentrations in pore water, also
the radon concentrations in the gas phase has to be considered.
In the waste zone, dissolved radon is determined by theconcentrations of its parent, 226Ra, whereas gaseous radon isdetermined by the partitioning law between water and gas
phase (Eq. (2)). Above the waste zone, presence of gaseousradon is the result of upward diffusive transport via the airphase. When the clay layers are intact, gas transport is limited
to the unsaturated sand, as no gas pathway exists in thesaturated clay. When the clay has degraded to some more
permeable and therefore unsaturated material, radon transportalso takes place through the latter layer. We conservatively
assumed the top of this layer coincides with the interface
between soil and atmosphere (Fig. 1), hence exhalation ofradon gas occurs.
Based on theoretical considerations, the diffusion length inunsaturated media is at most 2 m [12]. Our calculations indicate
a diffusion length that is nearly twice as large. This is mostprobably due to the large concentration gradient above thewaste zone.
Concentration profiles for 222Rn are shown for cases 4, 5,
and 6, i.e. the only cases for which upward transport throughthe gas phase may occur. Cases 4 and 6 display a very similar
concentration profile, as a result of the assumption that radon is
not adsorbed, and hence Kd parameters for radon are identicalfor case 4 and 6. Intuitively, one would expect 222Rn to have
10× higher pore water concentrations, as does its parent 226Ra.
However, 222Rn is generated by decay of both dissolved andsorbed 226Ra, and total radium activity has not changed. Hence,with no differences in Kd between case 4 and 6, radon
concentration profiles are nearly identical. Evidently, whentotal initial radium increases by a factor of 40/7 (case 5), decay
products will increase the same amount.
A fairly uniform 210Pb concentration profile is observed
within the waste zone, where it is generated due to decay of
222
Rn in both water and gas phase. In the sand layer above thewaste zone, the presence of 210Pb is due entirely to decay of
222
Rn in the gas phase. Because we assumed lead is not sorbedon the sand (see Table 1), higher concentrations exist in thesand compared to the underlying waste material, where sorption
is considered important. Although radon gas diffuses throughthe degraded clay layer, lead concentrations in the degradedclay are very small owing to the high sorption onto the clay.
Note that we assume that the clay is only physically degraded,
but not chemically. In other words, its hydraulic conductivity
has increased considerably, but its sorption capacity is still at its
initial value.
Analysis of concentration profiles for 210Pb based on cases
1, 3, and 4 demonstrate a higher sensitivity with respect to thesorption parameter than to absence of clay layers. In the sandlayer above the waste zone, lowest concentrations exist for case4, whereas cases 1 and 3 have similar values. Lower
concentrations for case 4 (degraded clay) are due to the lower
accumulation of its parent 222Rn in the sand layer, as aconsiderable amount of the radon gas will diffuse through thedegraded layer to the atmosphere.
An analysis of the effect of variations in model parameters
on radionuclide fluxes is based on Fig. 4. When all clay layers
are intact, i.e. cases 1-2-3, largest effect is due to a reduced
sorption (case 3). For the latter case, maximum 226Ra flux isnearly three orders of magnitude larger than case 1 (also see

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1x10

8

Case 1Case 2
Case 3
Case 4
Case 5
Case 6

7

1x106

1x10

5

1x10

4

1x10

3

226

Ra flux (Bq y-1) in drainage water

1x10

10

100

1000

10000

1000

10000

1000

10000

Time (y)111x1010

1x109

1x10

8

1x10

7

222

Rn flux (Bq y-1) in drainage water

1x10

1x106
10

100
Time (y)1x10

5

Pb flux (Bq y-1) in drainage water

1x104

1x103

1x10

2

1x10

1

1x10

0

210

Table 3). Also note that the maximum flux for case 3 occurs
considerably earlier than that for case 1 and 2, i.e., between
1000 and 2000 y for the former and 10000 y for the latter two.
Fluxes for case 2 are only 40/7 times larger than case 1,
because of the linearity between flux and source concentration.
In other words, when the source concentration is increased by afactor of 40/7, fluxes increase likewise. When clay layers havedegraded, fluxes increase by a factor of approximately 50 forcase 4 and 5 compared to case 1 and 2, and nearly a factor of 10
for case 6 (compared to case 3). The effect of degraded clay
layers is thus larger when best estimate sorption parameters areused than when a ten times smaller sorption is used. In the latter
case, transport time smaller than half-life of 226Ra (T1/2 = 1600y), hence decay of 226Ra is not yet influencing the flux values,
whereas for the former case transport time is much longer andhence significantly affected by decay.
The flux history for 222Rn under the condition of intact clay
layers is determined in part by that of its parent 226Ra and inpart by the faster transport velocity of radon compared toradium. Owing to the assumed zero sorption of dissolved radon,
its mobility in the water phase will be orders of magnitude
higher than that of radium, especially in the lower clay-3 whichisolates the waste at the bottom from groundwater. The peak
flux appears around 2000 years, whereas that for radium it
appeared around 10000 years (Fig. 4). When all clay layers
have degraded, the radon flux is observed very soon after
repository closure. This behaviour is due to the presence of afree gas phase between the bottom of the waste material and thegroundwater table, in the absence of a low permeable clay
layer. In other words, diffusion of radon through the gas phase
is now determining the flux history, rather than diffusivetransport through the water phase. There is one exception,
however. Fig. 4 shows that case 6 has a maximum flux at a latertime than that of case 4 and 5, although the initial flux for case
4 and 6 is identical, illustrating the same initial transport
process, i.e., diffusion through the gas phase. However, sinceradium is 10 times less retarded compared to case 4 and 5, thecontribution of the radon flux in the water phase to the total
flux is not negligible anymore.
Flux history for 210Pb is very similar to that of 222Rn, bothin the presence and absence of clay layers (Fig. 4). Whentransport in the water phase dominates the mobility of lead andits parent radon, i.e. in the presence of the clay layers, both
radionuclides migrate at the same rate because we assumed
zero sorption for both in the lowest sand layer (see Table 1). In
the absence of clay layers, lead history is determined by that ofits volatile parent radon.
A summary of maximum fluxes and doses is given in
Table 3. Total dose for groundwater pathway includes
contributions from all three radionuclides considered. However,in all cases the contribution of 226Ra is far more important thanthat of 222Rn and 210Pb.

10100
Time (y)Figure 4 Calculated total radionuclide fluxes at the bottom of
the repository. For explanation of cases, see main text.

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Table 3 Maximum fluxes (Fmax) and dose (Hmax) for
groundwater and atmospheric pathway, and combined total
dose (Htot) from both pathways.
Case

Groundwater pathway

226

1
2
3
4
5
6

Fmax (Bq/y)Ra 222Rn 210Pb

2.7E4
1.5E5
1.3E7
1.3E6
7.6E6
9.3E7

2.7E8
1.5E9
2.7E9
2.7E9
1.5E101.2E10

6.9E2
3.9E3
5.5E3
2.5E3
1.5E4
7.7E3

Hmax

Fmax

Hmax

(Sv/y)

Total
dose
Htot
(Sv/y)

1.1E-6
6.0E-6
6.5E-44.8E-5
2.7E-4
2.3E-3

6.9E103.9E11
6.9E101.9E-5
1.1E-4
1.9E-5

1.1E-6
6.0E-6
6.5E-44.8E-5
2.7E-4
2.3E-3(Sv/y)

Atmosphericpathway(Bq/y)The maximum total dose was calculated as the sum of thedoses due to the groundwater and atmospheric pathway. It is
important to note that the time of the maximum flux, and hence
also the dose, does not occur at the same time for both
pathways. As is demonstrated in Fig. 4, the maximum 226Ra
flux to groundwater occurs between 4000 and 5000 y (case 4
and 5). The maximum dose due to the atmospheric pathway
occurs during the first 100 years after repository closure.
Between 100 and 1000 y, the dose drops by almost a factor of
2. Between 1000 and 5000 y, the dose further drops by at least
one order of magnitude. Case 6 is an exception, with the
maximum 226Ra flux around 500 y. This means that the
maximum dose for both pathways occurs almost at the sametime. However, the maximum dose due to the atmosphericpathway is two orders of magnitude smaller than that of thegroundwater pathway.
Compared to the background dose of 2-3 mSv/y, nearly all
calculated doses are smaller. The only exception is case 6, forwhich the dose has the same order of magnitude as the
background value. All other cases have a maximum dose that is
one to three orders of magnitude smaller than the annual
background dose.
The results clearly demonstrate that the dose contribution
via the groundwater pathway is more important than that via
the atmospheric pathway. Although the gaseous radon
concentrations in the waste zone are quite high, the thickness ofthe soil layers considered in the calculations (3.25 m) was large
enough to reduce the fluxes at the assumed interface
soil/atmosphere to acceptable levels.

CONCLUSIONSLong-term safety was investigated for a proposed surface
disposal facility for very low-level radium bearing waste.
Exposure pathways investigated were leaching to groundwaterand exhalation to the atmosphere. For this purpose, a source
term model, a groundwater flow and transport model, and abiosphere model were adopted. These models were run for ageneric disposal concept and a set of best estimate model
parameters. To assess the sensitivity of the model outcome withrespect to some key parameters, alternative runs were carriedout which included the following modifications: (1) the initial
radium concentration in the waste zone was increased from 7(best estimate) to 40 Bq/g, assumed uniformly distributed overthe entire repository depth, to address the issue of waste
heterogeneity (2) the sorption of radium and its daughter

nuclides was decreased by a factor of 10 to address the issue ofsorption heterogeneity, and (3) waste confining clay layers
were assumed to be degraded, in order to address the issue ofincreased leaching and radon exhalation. Parameters for the
groundwater flow and transport model and biosphere model
were kept constant.
Results show that the proposed design using the best
estimate parameter set leads to an annual dose of nearly 10-6 Sv,
which is approximately three orders of magnitude smaller thanthe background dose. When early degradation of the clay layers
is accounted for, i.e. immediately after repository closure, themaximum dose using best estimate parameters increases about
40 times. However, the dose is still about two orders ofmagnitude below the background.
The effect of a higher initial radium concentration will
depend on the fraction of the waste that contains hot spots. As
an extreme case, we assumed 100% hot spots with a uniform
concentration of 40 Bq/g. As expected, the increase in dosefrom 1.1×10-6 to 6×10-6 Sv was proportional to the increase inconcentration. For smaller fractions of hot spots resulting doses
can be easily derived.
The results further showed that reducing the sorption ten
times increases the dose nearly 500 times. Such a dose would
still be smaller than the background dose if clay layers areintact.
An important conclusion of this study is related to thesignificance of the atmospheric pathway. Radon exhalation
happens only if clay layers have degraded. Under suchconditions, doses are negligible compared to the doses due toleaching of radium and its daughter nuclides to groundwater.
The issue of degraded engineered barriers is an importantone. In reality, as soon as institutional control has ended, thesoil cover will degrade gradually to a condition where the least
permeable clay layer becomes permeable also for radon gas.
Because it is difficult if not impossible to predict when this will
occur, we conservatively assumed it happens very soon after
repository closure. Our calculations demonstrate that evenunder such highly unlikely situation doses due to radon
exhalation are negligible. Furthermore, the accelerated leachingof radium and its daughter nuclides to groundwater owing toincreased infiltration when the clay has degraded, does not leadto a dose that is higher than the annual background dose of 2-3
mSv.

ACKNOWLEDGMENTS
This study was financially supported by the Belgian
National Agency for Radioactive Waste and Nuclear Fuels(NIRAS/ONDRAF).

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