- Open Access
Numerical modeling of radionuclide migration through a borehole disposal site
© Yeboah et al.; licensee Springer. 2014
Received: 11 December 2013
Accepted: 13 March 2014
Published: 21 March 2014
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 two-dimensional 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.
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 × 107 m/y). The broad valley of the Onyasia River flanks the site on its eastern margin with swampy conditions generally found north-east of the site. Surface run-off in this area is very low, however, after heavy storms there is flow of water over the horizon below the top-soil (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).
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 two-dimensional conceptual model as shown in Figure 2.
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.
A two-dimensional numerical model was developed using Comsol Multiphysics (ver.3.4) similar to the proposed model in Figure 2. The lithology of the system was characterized by a porosity of 0.35, a transverse dispersivity of 0.005 m, a longitudinal dispersivity of 0.5 m and a hydraulic conductivity ranging from 10-15 to 10-5 m/s.
Where D ii , D jj are the principal components of the dispersion tensor based on the Darcy’s velocity, D ij and D ji are the cross terms of the dispersion tensor, the subscript “L” denotes longitudinal dispersivity, “T” the transverse dispersivity. v is the magnitude of the Darcy’s velocity vector, D m represents the effective molecular diffusion in a saturated porous media and i, j are the spatial coordinates.
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
Where R is the recharge rate (m/s).
Solute transport: 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
Results and discussions
Ghana’s inventory of disused sources (Essel et al. 2011)
Disused low dose sources
Total initial activity (Bq)
5.66 × 1012
1.75 × 106
Non-Destructive Testing (NDT)
4.09 × 10°/4.90 × 10-1
3.70 × 1011/1.85 × 1012
3.00 × 101/ 1.80 × 103
3.50 × 101
1.25 × 104
2.26 × 106
6.66 × 102
1.67 × 103
6.21 × 109
2.22 × 1010
7.03 × 109
3.70 × 107
2.60 × 107
Disused high dose sources
2.78 × 108
1.85 × 108
2.22 × 108
4.25 × 1010
2.22 × 104
1.11 × 102
n3.70 × 102
4.77 × 103
7.40 × 10-1
1.18 × 103
9.25 × 10-6/ml
1.85 × 102
3.7 × 10°
2.22 × 103
The models describe the steady-state 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 time-dependent and finds a solution to the solute transport equation.
homogeneous hydraulic conductivity in porous subsurface medium and
heterogeneous hydraulic conductivity in a fractured medium.
Physical parameters used in the homogenous model for flow and transport
Initial activity concentration
Effective diffusion coefficient
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 60Co
Evolution of 137Cs
Evolution of 241Am
The migration of three radionuclides namely, 60Co, 137Cs and 241Am have been simulated using a two-dimensional finite element numerical model code (Comsol Multiphysics).
Neglecting heterogeneity, simulated results showed that, all three radionuclides (60Co, 137Cs, 241Am) 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 water-table and this caused the flow velocity to sweep the radionuclides with medium (137Cs) to long (241Am) half-life toward the surface endangering human population, the environment and biota.
For 60Co, 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 half-life.
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.
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.
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