232
M. Yamanaka
8.3.2 Uncertainty
8.3.2.1 Eigenvalue Bias
The eigenvalue calculations with the use of MCNP6.1 and SCALE code system
were performed for a total of 1E + 08 histories (1E + 03 active cycles of 1E +
05 each); the statistical error was less than 10 pcm. Through the comparison of
the results of k eff between MCNP6.1 and SCALE6.2/KENO-VI, the difference was
found about 100 pcm in EE1 core and about 200 pcm in E3 core, as shown in
Tables 8.8 and 8.9, respectively. Moreover, eigenvalue bias was dependent on the
neutron spectrum of the core: about 350 pcm and about 600 pcm in EE1 and E3
cores, respectively. Interestingly, the uncertainty induced by nuclear data showed
about 950 pcm in the k eff evaluation by the SCALE code. Also, the uncertainty was
found almost same value regardless of the control rod position, indicating that the
neutronic characteristics are the same even at insertion and withdrawal of control
rods.
To validate the modeling of core configuration and eigenvalue calculations, the
calculated results of excess reactivity and control rod worth compared with the
measured ones in EE1 and E3 cores, as shown in Tables 8.10 and 8.11, respectively. Although eigenvalue bias was smaller than the uncertainty induced by nuclear
Table 8.8 Comparison of k eff values between experiments and calculations (MCNP6.1 and
SCALE6.2) in EE1 core (Ref. [2])
Case Core Inserted
control rod
(position)
Effective multiplication factor k eff
Experiment
MCNP6.1
SCALE6.2
I-1
EE1 –
1.00202 ± 0.00006 1.00534 ± 0.00009 1.00574 ± 0.00009
(947.7 ± 0.3 pcm)*
I-2
EE1 C1 (critical
position)
1.00000
1.00348 ± 0.00009 1.00395 ± 0.00010
(948.3 ± 0.3 pcm)
I-3
EE1 C3 (critical
position)
1.00000
1.00374 ± 0.00009 1.00383 ± 0.00010
(949.0 ± 0.3 pcm)
I-4
EE1 C3 (critical
position)
C1 (full
inserted)
0.99199 ± 0.00001 0.99651 ± 0.00009 0.99533 ± 0.00010
(956.5 ± 0.3 pcm)
I-5
EE1 C3 (critical
position)
C2 (full
inserted)
0.99861 ± 0.00002 1.00359 ± 0.00009 1.00242 ± 0.00010
(949.7 ± 0.3 pcm)
I-6
EE1 C1 (critical
position)
C3 (full
inserted)
0.99501 ± 0.00008 1.00002 ± 0.00009 0.99899 ± 0.00010
(953.7 ± 0.3 pcm)
*Uncertainty by SCALEW6.2/TSUNAMI-3D
M. Yamanaka
8.3.2 Uncertainty
8.3.2.1 Eigenvalue Bias
The eigenvalue calculations with the use of MCNP6.1 and SCALE code system
were performed for a total of 1E + 08 histories (1E + 03 active cycles of 1E +
05 each); the statistical error was less than 10 pcm. Through the comparison of
the results of k eff between MCNP6.1 and SCALE6.2/KENO-VI, the difference was
found about 100 pcm in EE1 core and about 200 pcm in E3 core, as shown in
Tables 8.8 and 8.9, respectively. Moreover, eigenvalue bias was dependent on the
neutron spectrum of the core: about 350 pcm and about 600 pcm in EE1 and E3
cores, respectively. Interestingly, the uncertainty induced by nuclear data showed
about 950 pcm in the k eff evaluation by the SCALE code. Also, the uncertainty was
found almost same value regardless of the control rod position, indicating that the
neutronic characteristics are the same even at insertion and withdrawal of control
rods.
To validate the modeling of core configuration and eigenvalue calculations, the
calculated results of excess reactivity and control rod worth compared with the
measured ones in EE1 and E3 cores, as shown in Tables 8.10 and 8.11, respectively. Although eigenvalue bias was smaller than the uncertainty induced by nuclear
Table 8.8 Comparison of k eff values between experiments and calculations (MCNP6.1 and
SCALE6.2) in EE1 core (Ref. [2])
Case Core Inserted
control rod
(position)
Effective multiplication factor k eff
Experiment
MCNP6.1
SCALE6.2
I-1
EE1 –
1.00202 ± 0.00006 1.00534 ± 0.00009 1.00574 ± 0.00009
(947.7 ± 0.3 pcm)*
I-2
EE1 C1 (critical
position)
1.00000
1.00348 ± 0.00009 1.00395 ± 0.00010
(948.3 ± 0.3 pcm)
I-3
EE1 C3 (critical
position)
1.00000
1.00374 ± 0.00009 1.00383 ± 0.00010
(949.0 ± 0.3 pcm)
I-4
EE1 C3 (critical
position)
C1 (full
inserted)
0.99199 ± 0.00001 0.99651 ± 0.00009 0.99533 ± 0.00010
(956.5 ± 0.3 pcm)
I-5
EE1 C3 (critical
position)
C2 (full
inserted)
0.99861 ± 0.00002 1.00359 ± 0.00009 1.00242 ± 0.00010
(949.7 ± 0.3 pcm)
I-6
EE1 C1 (critical
position)
C3 (full
inserted)
0.99501 ± 0.00008 1.00002 ± 0.00009 0.99899 ± 0.00010
(953.7 ± 0.3 pcm)
*Uncertainty by SCALEW6.2/TSUNAMI-3D