Numerical modeling of radionuclide migration through a borehole disposal site
 Serwaa Yeboah^{1, 2}Email author,
 Thomas T Akiti^{1} and
 John J Fletcher^{1}
https://doi.org/10.1186/219318013155
© Yeboah et al.; licensee Springer. 2014
Received: 11 December 2013
Accepted: 13 March 2014
Published: 21 March 2014
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.
Keywords
Introduction
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
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 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.
Numerical illustrations
A twodimensional 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.
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
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  

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.
 (1)
homogeneous hydraulic conductivity in porous subsurface medium and
 (2)
heterogeneous hydraulic conductivity in a fractured medium.
Physical parameters used in the homogenous model for flow and transport
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)  
${\mathit{t}}_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{1ex}{$2$}\right.}$  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
Evolution of ^{137}Cs
Evolution of ^{241}Am
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.
Declarations
Authors’ Affiliations
References
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 Junner NR, Bates DA: Reports on the geology and hydrology of the coastal area east of the Akwapim Range, Gold Coast Geological Survey Memoir, No.7. 1995.Google Scholar
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Copyright
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.