Graduate School of Nuclear and Allied Sciences, University of Ghana, P.O. Box AE 1, Atomic Energy, Legon, Ghana
National Radioactive Waste Management Centre, National Nuclear Research Institute, Ghana Atomic Energy Commission, Box LG 80, Legon, Ghana
Abstract
The migration of radionuclides from a borehole repository located about 20 km from the Akwapim fault line which lies in an area of high seismicity was analyzed for some selected radionuclides. In the event of a seismic activity, fractures and faults could be rejuvenated or initiated resulting in container failure leading to the release of radionuclides. A numerical model was solved using a twodimensional finite element code (Comsol Multiphysics) by taking into account the effect of heterogeneities. Results showed that, the fractured medium created preferential pathways indicating that, fault zones generated potential paths for released radionuclides from a radioactive waste repository. The results obtained showed that variations in hydraulic conductivity as a result of the heterogeneity considered within the domain significantly affected the direction of flow.
Introduction
The site for the Borehole Disposal Facility is within the Accra Plains and is situated on the boundary between the Dahomeyan System and the Togo Series (Figure
Geological map of the region immediately around the proposed site.
Geological map of the region immediately around the proposed site.
The whole of the site is covered by loose unconsolidated and weathered material that may reflect the presence of troughs formed by down faulted blocks which indicates the existence of seismic activity in the geologic past and it probably results from movements along the Akwapim fault line (Junner & Bates 1995).
The only major river near the Borehole Disposal Facility (BDF) site is River Onyasia, located about 1.3 km from the proposed facility and drains southwards through Achimota village to Accra. The Onyasia River has a depth of 0.6 m, a width of 6.8 m and a measured velocity of 0.8 m/s (2.5 × 10^{7} m/y). The broad valley of the Onyasia River flanks the site on its eastern margin with swampy conditions generally found northeast of the site. Surface runoff in this area is very low, however, after heavy storms there is flow of water over the horizon below the topsoil (Darko et al. 1995).
Seismic surveys conducted in the area mapped out two weak lines suspected to have been caused as a result of faults or fractures. However, these have not been used in numerical modelling to follow and predict the migration of radionuclides at the site in case a seismic accident occurs (Essel et al. 2011).
Methodology
Model definition
The hydrogeologic setting for groundwater flow at steady state shall be described by the conceptual model shown in Figure
Conceptual model.
Conceptual model.
Scenario development
In order to predict radionuclide release, the engineering barriers are assumed to fail in the event of a seismic activity. The system is thus, simplified into a twodimensional conceptual model as shown in Figure
The radionuclides are initially confined in the canister until a seismic activity occurs, leading to a crack of the barrier system such that the radionuclide inventory is released into the groundwater which is the major transport medium. It is assumed in the calculations performed that radionuclides start being released from the canister 30 years after closure of the repository.
Numerical illustrations
A twodimensional numerical model was developed using Comsol Multiphysics (ver.3.4) similar to the proposed model in Figure
The timedependent solute transport equation as described by equation (1):
Here, the dispersion tensor
Where
Governing equations
Fluid flow: assumptions
▪ On the scale simulated, the fracture system behaves as an equivalent porous medium
▪ The groundwater flow is assumed to be homogenous and subject to recharge
▪ Additionally, groundwater flows under steady state conditions. This means that, the velocity of flow is considered not to change with time since groundwater flow is naturally a slow process.
Fluid flow: domain equations and boundary conditions
Steady groundwater flow is expressed with a conservation equation formulated with Darcy’s law and expressed as:
Where
Where,
Where
Figure
Boundary Conditions for Groundwater Flow.
Boundary conditions for groundwater flow.
A zero flux Neumann condition represents the symmetry boundary at
Hydraulic head is specified at
The annual average precipitation rate is recorded as 800 mm/y equivalent to 2.537 × 10^{8} m/s. The water table receives about 10% of this value. From a topographic height of
Solute transport: assumptions
Transport of radionuclides is based on the following assumptions:
▪ Radioactive decay is the only reaction considered in the model. It is assumed to occur throughout the model in the liquid phase;
▪ For the purposes of this work, no gaseous release is considered;
▪ Transport of radionuclides is assumed to occur in the saturated zone;
Solute transport: domain equations and boundary conditions
For the transport equation, the initial and boundary conditions for solute transport are shown in Figure
Solute Transport
Solute transport.
Where
The Neumann condition defining the zero flow boundaries is:
Finally, the initial condition indicating that the subsurface on the site is free of contaminants at the beginning of the simulation is:
Results and discussions
Numerical simulations were considered for Cobalt60 (short halflife), Cesium137 (medium halflife) and Americium241 (long halflife) migrating from the repository through the subsurface environment for a 2dimensional crosssection along the streamlines of groundwater flow. These considerations were made because of the high amount of activity contained in the waste packages and the variability of their halflife as shown in Table
Disused low dose sources
Radionuclide
Total initial activity (Bq)
Application
Form
Unit pieces
Cs137
5.66 × 10^{12}
Level gauges
Sealed
30
Co60
1.75 × 10^{6}
NonDestructive Testing (NDT)
Sealed
2
Cs137/Co60
4.09 × 10°/4.90 × 10^{1}

Sealed
2
Cs137/Am241
3.70 × 10^{11}/1.85 × 10^{12}

Sealed
3
Cs137/Am 241:Be
3.00 × 10^{1}/ 1.80 × 10^{3}
Nuclear gauges
Sealed
1
Am241
3.50 × 10^{1}
Smoke detectors
Sealed
105
Sr90
1.25 × 10^{4}
Thickness gauges
Sealed
33
Ir192
2.26 × 10^{6}
NDT
Sealed
1
Cd109
6.66 × 10^{2}
Research
Sealed
6
Am241
1.67 × 10^{3}
Nuclear gauge
Sealed
1
I131
6.21 × 10^{9}

Unsealed
2
Cf252
2.22 × 10^{10}

Sealed
2
Ra226
7.03 × 10^{9}

Sealed
19 needles
H3
3.70 × 10^{7}
Nuclear gauge
Unsealed (liquid)
2750 L
C14
2.60 × 10^{7}

Unsealed (gas)
7empty cylinders
Disused high dose sources
Co60
2.78 × 10^{8}
Gamma cellresearch
Sealed
1
Co60
1.85 × 10^{8}
Teletherapy
Sealed
1
Co60
2.22 × 10^{8}
Food irradiator
Sealed
1
I129*
4.25 × 10^{10}

sealed
1
Fe59
2.22 × 10^{4}

sealed
2
Co57
1.11 × 10^{2}

sealed
3
Zn65
n3.70 × 10^{2}

sealed
1
Sr89
4.77 × 10^{3}

sealed
1
Tl204
7.40 × 10^{1}

sealed
2
P32
1.18 × 10^{3}
Research
Unsealed
4
S35
9.25 × 10^{6}/ml

Unsealed
5
Ca45
1.85 × 10^{2}

Unsealed
3
Na22
3.7 × 10°

Unsealed
4
In113 m
2.22 × 10^{3}

Unsealed
12
Computer simulations
The models describe the steadystate fluid flow and follows up with a transient solute transport simulation. Two partial differential equations (PDE) were solved for and these were assigned in separate mathematics interfaces in Comsol Multiphysics (version 3.4). The first partial differential equation (PDE) is stationary and it finds a solution to the Darcy velocity while the second partial differential equation (PDE) is timedependent and finds a solution to the solute transport equation.
To test the effect of heterogeneity on solute behavior, a twodimensional numerical transport model was created to investigate solute transport under two hydrogeologic conditions:
(1) homogeneous hydraulic conductivity in porous subsurface medium and
(2) heterogeneous hydraulic conductivity in a fractured medium.
Table
Parameter
Value
Description
Units
R
2.537e8
Vertical recharge
m/s
N
0.15
Effective porosity

alpha_L
0.5
Longitudinal dispersivity
m^{2}/s
alpha_T
0.005
Transverse dispersivity
m^{2}/s
K1
3.17e5
Hydraulic conductivity
m/s
C_in
2.22e8 (Co60)
Initial activity concentration
Bq/m^{3}
5.66e12 (Cs137)
3.5e7 (Am241)
D_m
2.78e6 (Co60)
Effective diffusion coefficient
m^{2}/s
2.54e9 (Cs137)
3.17e9 (Am241)
5.27 (Co60)
Radioactive halflife
Years
30 (Cs137)
432 (Am241)
Model simulation results
Throughout the models, the amount of contaminant is shown by the colour bar. The activity concentration degree is indicated by the various colours, with red indicating an intense concentration.
Evolution of ^{60}Co
Radionuclide movement (streamline plot) and concentration estimates (surface plots) of ^{60}Co simulated at various times are illustrated in Figures
A plot showing the migration of ^{60}Co
A plot showing the migration of^{60}Co. a: From time of release to 250 years. b: From time of release to 500 years. c: From time of release to 1000 years
A plot of ^{60}Co showing the effect of increased conductivity after 100 years.
A plot of ^{ 60 } Co showing the effect of increased conductivity after 100 years.
Figure
A graph showing the evolution of ^{60}Co activity concentration as a function of time
A graph showing the evolution of ^{ 60 } Co activity concentration as a function of time.
Evolution of ^{137}Cs
^{137}Cesium has a halflife of 30 years and an initial activity concentration of 5.66 × 10^{12} Bq/m^{3}. Evolution of ^{137}Cs contaminant source are shown in Figure
A plot showing the migration of ^{137}Cs
A plot showing the migration of^{137}Cs. a: From time of release to 250 years. b: From time of release to 500 years.
Figure
A plot of ^{137}Cs showing the effect of increased conductivity
A plot of^{137}Cs showing the effect of increased conductivity. a: After 40 years. b: After 60 years.
Figure
A graph showing the evolution of ^{137}Cs activity concentration as a function of time.
A graph showing the evolution of ^{ 137 } Cs activity concentration as a function of time.
Evolution of ^{241}Am
The simulation was implemented for ^{241}Am contaminant source with an initial activity concentration of 3.5 × 10^{7} Bq/m^{3}, a halflife of 432 years and a flow velocity of 3.534 × 10^{8} m/s. Figure
A plot showing the migration of ^{241}Am
A plot showing the migration of^{241}Am. a: From time of release to 250 years. b: From time of release to 1000 years.
Figure
A plot of ^{241}Am showing the effect of increased conductivity
A plot of^{241}Am showing the effect of increased conductivity. a: After 40 years. b: After 60 years.
Figure
A graph showing the evolution of ^{241}Am activity concentration as a function of time.
A graph showing the evolution of ^{ 241 } Am activity concentration as a function of time.
Conclusions
The migration of three radionuclides namely, ^{60}Co, ^{137}Cs and ^{241}Am have been simulated using a twodimensional finite element numerical model code (Comsol Multiphysics).
Neglecting heterogeneity, simulated results showed that, all three radionuclides (^{60}Co, ^{137}Cs, ^{241}Am) within the low conductivity medium sunk steeply downward into the groundwater flow system by diffusing into the flowing groundwater. This caused the flow velocity to move readily with the radionuclide source causing contamination of groundwater resources.
In the presence of fractures, preferential pathways were created which gave rise to a rapid increase of the watertable and this caused the flow velocity to sweep the radionuclides with medium (^{137}Cs) to long (^{241}Am) halflife toward the surface endangering human population, the environment and biota.
For ^{60}Co, the plume was not noticeably seen at the surface even in the presence of high hydraulic conductivity but was rather diluted into deeper groundwater flow systems as it decayed away. This was attributed to the short radioactive halflife.
The results obtained showed contamination to be more sensitive to variations in hydraulic conductivity as a result of the heterogeneity considered within the domain. However, impact on groundwater was still inevitable.
Recommendation
It is recommended that, proper structural geological mapping including the use of stereograms should be made to be able to determine the fractures before radioactive waste is disposed of in an area.
Competing interests
The authors declare that they have no competing interests.
Authors’ contribution
SY, TTA, JJF carried out numerical modelling of radionuclide migration through a borehole disposal site, participated in the sequence alignment and drafted the manuscript. All authors read and approved the final manuscript.