VGB POWERTECH 5 (2021) - International Journal for Generation and Storage of Electricity and Heat

VGB PowerTech 5 l 2021
Radioactivity calculation for retired nuclear power plant
from five surveillance capsules from the
plant.
2. Materials and methods
2.1 General activity calculation
The neutron-induced activation phenomenon
is well known. The activity of the product
nuclide when it is produced at a constant
rate R (atoms/s) due to neutron irradiation
is written as [8]
(1)
Where A is activity (Bq), and λ is the decay
constant (s -1 ) of the product nuclide. In Eq.
(1), the constant production rate R can be
written as
Relative Thermal Power
1.2
1,0
0.8
0.6
0.4
0.2
(2)
where N 0 is the number of target nuclides
irradiated by the neutron flux Φ(E) (neutrons/cm
2 -s), and σ(E) (cm 2 ) is the microscopic
cross-section for the activation reaction.
To calculate the activity manually, the
integral term in Eq. (2) must be approximated
in summation form as Σ σ Φ.
If the target nuclide is irradiated by neutron
irradiation for time i (s) and undergoes
decay for time j (s), the activity becomes
(3)
where A 0 is the initial activity (Bq) indicating
the production of activity according to
Eq. (1) during time t (s). Therefore, it is
possible to calculate the activity including
both irradiation period and decay period.
Traditionally, this simple equation is used
to estimate radioactivity distribution.
2.2 Activity calculation considering
operation history and flux level
The method considering operation history
and flux level is related to production rate
R represented by Eq. (2). If the neutron
flux Φ(E) in Eq. (2) is changed, production
rate R also change. Assuming that the neutron
flux is constant during a certain period,
we can obtain R in period i as
(4)
where n represents the last number of the
group-wise neutron spectrum; 47 neutron
energy group is applied in this study. Φ i j is
the j th group neutron spectrum during the
period i. The discretization through Eq. (4)
allows manual calculation of activity. In
Eq. (4), the neutron spectrum Φ i j can be
calculated as
(5)
Where P i is the relative thermal power level
of the i th period and – is the j group neutron
spectrum corresponding to the full power
level. In this study, cycle-specific Φ full j values
were calculated for each cycle using
0.0
0 50 100 150 200 250 300 350 400 450 500
the RAPTOR-M3G neutron transport code
[9] with the BUGLE-96 cross-section library
[10].
By applying relative thermal power level P i ,
we can consider two activation phenomena.
First, the contribution ratios for low
power operation periods can be considered
comparing with full power operation.
Thus, different saturated activity curves for
each period can be considered even if the
neutron flux level is constant in a fuel cycle.
Second, it is also possible to reflect the decay
for the periods of zero power. In this
study, P i was considered monthly; the relative
thermal power distribution over the
plant lifetime is shown in (F i g u r e 1 ).
If the final activity considering operation
history and flux level is represented by A i
for the i th month, Eq. (3) is rewritten as
(6)
Therefore, we can calculate the precise activity
of reaction of interest by applying P i
presented in Eq. (5).
The characteristics of targets or products
such as the reaction of interest, target
atomic information, and product half-life
are also required as input. The main characteristics
of the three reactions of interest
are shown in (Ta b l e 1 ). The group-wise
microscopic cross-sections used in this
study are presented in (Ta b l e 2 ).
Based on above, we can calculate the activity
considering the plant-specific operation
history.
2.3 Neutron transport calculation
To calculate Φ full j in Eq. (5), which is
group-wise neutron spectrum corresponding
to the full power level, the RAPTOR-
Months from Start-up
Fig. 1. Monthly normalized reactor thermal power level for the plant.
Tab. 1. Radiological characteristics for the
reactions of interest.
– Reaction of Interest
– 90 % Neutron Energy
Response*
– Target Atom Fraction
– Target Atomic Mass
– Product Half-Life
– Reference
– Reaction of Interest
– 90 % Neutron Energy
Response*
– Target Atom Fraction
– Target Atomic Mass
– Product Half-Life
– Reference
– Reaction of Interest
– 90 % Neutron Energy
Response*
– Target Atom Fraction
– Target Atomic Mass
– Product Half-Life
– Reference
Copper
Iron
Nickel
: 63 Cu (n,a) 60 Co
: 4.53–11.0 MeV
: 0.6917
: 63.546 g/mol
: 1925.5 day
: [11]
: 54 Fe (n,p) 54 Mn
: 2.27–7.54 MeV
: 0.0585
: 55.845 g/mol
: 312.1 day
: [12]
: 58 Ni (n,p) 58 Co
: 1.98–7.51 MeV
: 0.6808
: 58.933 g/mol
: 70.8 day
: [13]
* Energies between which 90 % of activity is
produced (235U fission spectrum). Ref. [14]
M3G code was used. RAPTOR-M3G is a
three dimensional parallel discrete ordinates
radiation transport code developed
by Westinghouse, verified by the
US NRC (Nuclear Regulatory Committee)
in Reference [15]. The methodology employed
by RAPTOR-M3G is essentially
the same as the methodology employed
by the TORT code [16]. RAPTOR-M3G
was designed from its inception as a
parallel-processing code and adheres to
modern best practices of software development.
The BUGLE‐96 cross-section library was
used for the neutron transport calculations.
The BUGLE-96 library provides a
67 group coupled neutron-gamma ray
63