Estimation of radionuclide transport in groundwater at potential accelerator sites N. Prolingheuer, B. Schlögl, M. Herbst, B. Heuel-Fabianek, R. Moormann, R. Nabbi
Institut Agrosphäre
im Institut für Chemie und Dynamik der Geosphäre (ICG)
Content Introduction and Motivation Case study Properties of the aquifer Model Calculation basis Modeling I – Different radionuclides Modeling II – Generalization of the estimated activity concentrations Résumé
Introduction and Motivation • Contamination of groundwater as a result of direct radiation is a problem which arises from operating powerful proton-accelerators • License for building and operating such a facility: Verification that the public, the workes and the environment arelprotected from the danger of radioactivity
Objective: Generalizing the method to predict the resultant activity-concentrations at the boundary of the supervised area for every potential location
Case study
Modeling the „worst case“ => highest concentration
Plan view of the model area
Properties of the aquifer Orientated on the hydrological conditions for the region of Jülich Homogeneous soil: • Aquifer thickness: 16 m in z-direction • Bulk density of 2.0 g cm-3 • Hydraulic gradient i: 0.0025 • Hydraulic conductivity Ks: 404.12 m d-1 • Resulting Darcy-velocity vD 5.49 m d-1 (assuming a value of 0.184 for the saturated water content) • Dispersion length
L:
3.64 m
Model • Dimensions: x,y,z: 100 m/700 m/16 m • The model is discretized by a grid of 1.12 mill. cells partitioned in 51 xnodes (mesh size: 2.0 m), 351 y-nodes (2.0 m) and 65 z-nodes (0.75 m) • Dirichlet boundary conditions for the front and the back are imposed to represent the hydraulic gradient. • No-flow boundaries were assigned to the left site, the right site, the bottom and the top. • Length of the simulation period depends on the point of time when steady state conditions are met.
Calculation basis TRACE • Calculates the saturated and unsaturated water flow • Solves numerically the Richards equation on the base of Galerkins’ finite-element-method • Provides the input data files (3-dimensional velocity field and the water content) for the PARTRACE code.
PARTRACE • Particle-tracking code • Includes the random-walk method which calculates the transport of solutes in a given velocity field ( TRACE) • Includes sorption (linear adsorbing, Freundlich and Langmuir isotherm etc.) and decay (zero- and first order decay) • Output: Breakthrough curves for each position in the flow domain and the distribution of the particles.
Modeling I
Kd
Half-life 32P
45Ca
3H
36Cl
14.26 d 5 cm3/g
163 d 5 cm3/g
12.323 a 0 cm3/g
300000 a 0 cm3/g
55Co
35S
60Co
14C
17.54 h 30 cm3/g
87.5 d 14 cm3/g
5.272 a 30 cm3/g
5730 a 7 cm3/g
24Na
57Co
54Mn
32Si
14.96 h 76 cm3/g
271.79 d 30 cm3/g
312.2 d 50 cm3/g
172 a 35 cm3/g
Aim Draw conclusions concerning the migration of radionuclides in groundwater Determination of the accuracy of the generalization
Input rates Nuclide
Half-life ll
lllllllll llkklll (a) 14 41 45 36 55 57 60 3
24 32 35 32 50
mmmmmm 1
)
K d Aquifer Total produced (d aaallllllllllllllllll Saturation Activity -3 3 -1 aa (cm g ) (Bq m ) -
Number of produced Nuclides -3
(m )
C
5730
3,314E-07
7
3,279E-06
8,548E+05
Ca
103000
1,844E-08
5
1,538E-07
7,206E+05
Ca
0,447
4,252E-03
5
1,005E-08
2,042E-01
Cl
300000
6,330E-09
0
1,300E-05
1,774E+08
Co
2,002E-03
9,484E-01
30
9,468E-13
8,625E-08
Co
0,745
2,550E-03
30
3,549E-12
1,202E-04
Co
5,272
3,602E-04
30
2,718E-12
6,521E-04
12,32
1,541E-04
0
3,431E-05
1,923E+04
Mn
0,855
2,220E-03
50
2,405E-12
9,358E-05
Na
1,708E-03
1,112E+00
76
7,081E-08
5,502E-03
P
3,91E-02
4,861E-02
5
5,970E-08
1,061E-01
S
0,240
7,922E-03
14
1,227E-07
1,338E+00
Si
172
1,104E-05
315
1,408E-10
1,102E+00
V
1,400E+17
1,356E-20
327
1,424E-13
9,071E+11
H
54
Decay Rate
Input rates
Geometry of the linac tunnel
Results
4.1 ‘Real’ radionuclides
Committed effective dose
A=
Activity-concentration (Bq/l)
B=
Rate of annual drinking water (L/a)
DCF = Dose conversion factor (Sv/Bq)
Committed effective doses for members of the public resulting from the calculated activity-concentrations for different radionuclides at the boundary of the supervised area (y= 550 m) with the assumption of an annual drinking-water consumption of 240 L a-1.
• Calculations were done on the basis of a simplified model with homogeneous properties and a steady contamination source. • This homogeneity influences also the development of the particleplume in the aquifer.
Vertical distribution (for x= 50 m) of the activity-concentration Cactiv for 3H for a homogeneous model after a steady contamination of 60 days
Modeling II – Generalization • Generalization of the predicted activity-concentrations at the boundary of the supervised area • Method: Connection between the partition coefficient Kd, the half-life T1/2 (as the determining parameters for the migration) and the estimated concentration ratio C/C0 • Usage of ‘synthetic’ radionuclides (86) to include as much radionuclides as possible • Used limits: Kd: 0-1000 cm3 g-1 T1/2: 0.1-1E+07 d)
Spherical regression for generalization
Resulting spherical transfer function:
z(x,y) = resulting concentration-ratio C/C0, x=
partition coefficient Kd (cm3 g-1)
y=
the half-life T1/2 (d)
Interpolation for generalization
Generalization of the estimated ratio C/C0 via interpolation of the modeled data points using: • linear interpolation, • Kriging and • the modified Shepard’s method.
Resulting contour maps for different interpolation methods
Result: • Reduced matrix (basis: data-set of 62,500 interpolated nodes (250 intervals in x- and y-direction)) where the ratio C/C0 at the boundary of the supervised area can be estimated. • Validity: - Kd from 0 to 1000 cm3 g-1 - T1/2 from 10 days to 28,000 years
Résumé • ‘Worst case’ modeling (conservative estimation). • The generalization was done by establishing a connection between the resultant ratio C/C0, the partition coefficient Kd and the half-life T1/2. • Usage of spherical regression and modified Shepard’s interpolation for the generalization. • In comparison with the results for modeled radionuclides the Shepard interpolation is more accurate than the spherical transfer function. • For this simplified model it is now possible to estimate the resultant activity-concentration for nearly each radionuclide at the boundary of the supervised area.
• The combination of a small partition coefficient and a high half-life causes the highest resultant activity-concentrations. • Thus, 3H, 36Cl and 14C are the most significant radionuclides concerning the compliance with the legal limits for radiation. • For higher partition coefficients (Kd > 20 cm3 g-1) in connection with a small half-life (in the range of days or a few years) the probability is high that all nuclides are really decayed before reaching the fence of the supervised area. • By generalizing the migration of radionuclides in groundwater a simplification was achieved proving the compliance of the resultant activity concentrations with the legal limits for radiation at the boundary of the supervised area. • Simple verification if a shielding is effective or not (using different input rates for different shielding)
