Severe accident gamma dose distribution through NPP Krško

Severe accident gamma dose distribution through NPP Krško
containment and auxiliary building calculated using
SCALE6/MAVRIC sequence
Mario Matijević, Davor Grgić, Dubravko Pevec
University of Zagreb, Faculty of Electrical Engineering and Computing
Unska 3
10000 Zagreb, Croatia
[email protected], [email protected], [email protected]
ABSTRACT
The ORNL SCALE6.2b4 code package was used for the Monte Carlo model
preparation of the NPP Krško corresponding to reactor, primary loop components,
containment and adjoining buildings. A fairly detailed model of the reactor with concrete
compartments housing primary pumps and steam generators was developed using as-built
dimensions. Auxiliary buildings (AB) were modeled as empty in this work, taking into
account the bulk dimensions of concrete walls and floors. An analysis of gamma dose
distribution in the case of hypothetical SBO accident was performed using hybrid
deterministic-stochastic FW-CADIS methodology of the MAVRIC shielding sequence.
Preparation of the gamma source was done using isotopic concentrations calculated with
RADTRAD code and 18-groups ORIGEN energy structure. The source is homogenous and
distributed over all air regions in the containment. The influence of melted material in reactor
cavity is not taken into account. Under such conditions the aim was to calculate gamma dose
rates through different floors, sections and buildings, posing significant shielding problem.
Special attention was given to gamma doses in the containment and in AB rooms close to the
containment. For that purpose, the integrated discrete ordinates code Denovo, based on the
adjoint transport theory, was used for calculation of variance reduction parameters (weight
windows and biased source) over the XYZ meshes covering the problem domain. Denovo
utilizes Koch-Baker-Alcouffe parallel transport sweep algorithm and Krylov iteration on
multigroup equations giving space-energy dependent fluxes and variance reduction
parameters. These variance reduction parameters, that work in tandem, are automatically
transferred to the functional module Monaco for the final, optimized Monte Carlo transport.
Different adjoint source locations were investigated, giving optimized dose rates over
localized or distributed phase-space regions.
1
INTRODUCTION
A hybrid deterministic-stochastic shielding methodology of SCALE6.2b4 code package
[1] was used for calculations of accidental gamma-dose field map through NPP Krško
containment building and auxiliary buildings (AB). This hybrid approach is nowadays
preferred for complex models with deep penetration shielding problems, since shortcomings
of classical Monte Carlo (MC) variance reduction techniques (VR) are well known. The
methodology is based on deterministic transport theory and the concept of adjoint neutron
flux (i.e. importance function) which is the solution of the adjoint Boltzmann equation applied
to neutron transport [2]. The typical deterministic solver is based on discrete ordinate methods
411.1
411.2
(SN) which approximate space-energy adjoint flux for preparation of VR parameters which
will effectively bias MC simulation towards one specific region. This is known as the
Consistent Adjoint Importance Sampling (CADIS) [3] formalism and it is used for
optimization of localized results, such as point detectors. Generalization of this methodology
for optimizing global MC distribution is a more complicated process which involves
additional SN forward calculation needed for redistribution (biasing) of the adjoint source in
phase-space. This FW-CADIS [4] methodology has been successfully applied to real life
shielding problems resulting in MC simulations with uniform relative errors over large
problem domains [5].
In this paper we have used the FW-CADIS methodology implemented in the MAVRIC
sequence of the SCALE6.2b4 code package to obtain gamma dose distribution map
throughout Krško PWR facility with containment and auxiliary buildings. The objective of
this paper was accomplished by a two-step approach: the accidental source preparation with
the RADTRAD [6] code linked to a hybrid shielding calculation with the SCALE6.2b4 using
different adjoint source capabilities. This task represents a challenging shielding problem
which can be effectively solved only via novel hybrid methodology with automatic
preparation of the mesh-based VR parameters [7]. The resulting shielding calculations are
thus focused on the MAVRIC capabilities to produce global, well-converged gamma flux
originating from accidental scenario where air-regions inside containment liner become filled
with gaseous effluents. The SCALE6.2b4 general geometry package (SGGP) of the KENOVI code [1] was used for MC model preparation of the Krško nuclear island, with detailed
description of the containment interior while the auxiliary, intermediate and turbine building
contain only concrete floors and walls. That may change in the future revision of the model.
Typical industrial and text-book data were used for the necessary dimensions and material
compositions.
This paper is organized as follows. Section 2 gives the description of the SCALE6.2b4
code package with focus on the MAVRIC shielding capabilities. Section 3 shows MAVRIC
model preparation of the Krško nuclear island housing reactor, primary loop elements,
containment, and the rest of the external buildings. Section 4 gives MAVRIC gamma dose
rates over different regions (floors) of Krško model using different adjoint source positions.
Section 5 gives discussion and conclusions while the referenced literature is given at the end
of the paper. Part of the activity is performed to support NEK Equipment survivability project
where thermalhydraulic and radiological parameters should be determined in so called design
extended conditions.
2
THE SCALE6.2B4 CODE PACKAGE
The SCALE6.2b4 code package is the latest beta version of the ORNL's modular code
developed for the U.S.NRC for the evaluation of nuclear facilities in wide areas of use. The
code has ability to perform a whole spectrum of different calculations: criticality, shielding,
radiation source term, spent fuel with depletion/decay option, reaction physics, and
sensitivity/uncertainty analyses using analytical sequences. The MAVRIC shielding sequence
is based on the CADIS methodology, which is used for effective biasing MC transport via
deterministic VR parameters: importance map (i.e. weight windows) and biased source
distribution. The Denovo SN code [8] is used as a deterministic solver utilizing Koch-BakerAlcouffe transport sweep algorithm with Krylov multigroup iteration on orthogonal meshes.
These VR parameters are then transferred to the Monaco code for the final, optimized MC
calculation. In case of multiple point detectors and/or mesh tally over large phase-space, an
extension of the CADIS called FW-CADIS is used to obtain optimized results on different
Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 14 ̶ 17, 2015
411.3
locations in the same calculation. Additional forward Denovo calculation is needed to
inversely weight multiple adjoint sources (point and region detectors, mesh tally cells) which
will result in similar MC uncertainties. In both MAVRIC methodologies the inverse
relationship between particle statistical weight and adjoint function is assured, so detector
location will have high importance and low particle weight. For shielding calculations
v7_27n19g library was used for memory demanding Denovo solver and v7_200n47g library
for Monaco particle transport. Primary data for both libraries originate from the ENDF/BVII.0 nuclear data file [9].
3
MAVRIC MODEL OF THE KRŠKO NUCLEAR ISLAND
The SCALE6.2b4/MAVRIC code was used for the MC model preparation of the NPP
Krško corresponding to reactor, primary loop components, containment, and adjoining
buildings. Auxiliary buildings were modeled as empty in this work, taking into account the
bulk dimensions of concrete walls and floors. The RADTRAD code was used for gamma
source preparation for the case of hypothetical Station BlackOut (SBO) accident while the
analyses of gamma dose map distribution was performed using hybrid deterministicstochastic FW-CADIS methodology of the MAVRIC shielding sequence.
3.1
Geometry Preparation
A well established MC model of the Krško PWR facility was done in previous shielding
analyses [10]. A fairly detailed model of the reactor with concrete compartments housing
primary pumps and steam generators was developed using as-built dimensions. The final
geometry generalization was now performed to include auxiliary, intermediate and turbine
buildings, forming a complete nuclear island. Plant documents [11][12] were used for
containment and other civil structures dimensions and typical industrial and text-book data
were used for definition of material mixtures (Figure 1 and Figure 2).
Figure 1: MAVRIC model of the Krško nuclear island (external air hidden)
Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 14 ̶ 17, 2015
411.4
Figure 2: Layout of the MAVRIC model with different buildings
3.2
RADTRAD Accidental Source Preparation
Preparation of the accidental gamma source was done using isotopic concentrations
calculated with RADTRAD code and 18-groups ORIGEN energy structure [13]. The source
is homogenous and distributed over all air regions in the containment. The influence of
melted material in reactor cavity is not taken into account at the moment. Under such
conditions the aim was to calculate gamma dose rates through different floors, sections and
buildings, posing significant shielding problem. Special attention was given to gamma doses
in the containment and in AB rooms close to the containment to determine environmental
conditions for operation of accident mitigation equipment.
3.3
Calculational Parameters
RADTRAD3.03 code was used to calculate the activity of the source term released in
the containment during "nothing works" NPP Krško SBO sequence. Model has just one
compartment (containment) and environment. Containment sprays are not available and
natural deposition is not taken into account to maximize the activity available in the
containment atmosphere. Design containment air leakage is assumed till Passive Containment
Filtered Vent (PCFV) actuation (about 11.87 hours after SBO initiation). The time of opening
and subsequent volumetric flow from the containment atmosphere are based on SBO MAAP
4.0.7 calculation. The explicit MAAP calculation covers first 300000 s and RADTRAD
calculation was performed up to 30 days using conservative assumptions. Any material
removed from the containment atmosphere decreases doses in containment and shine doses
from the containment and surrounding buildings. Nuclide inventory is calculated for NPP
Krško Cycle 26 using ORIGEN 2.2 [13] and realistic depletion based on fuel assembly power
and burnup data. Plant power is increased for 2% compared to nominal plant power. Release
fractions, a timing for release of radioactive materials from the reactor core, and assumed
Iodine chemical fractions are based on PWR severe accident recommendations from NUREG1465. RADTRAD code was modified to make available time dependent isotopic activities
released to containment atmosphere for further use. Using that isotopic activities and small
auxiliary program based on 18-groups ORIGEN library gamma spectrum, energy dependent
Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 14 ̶ 17, 2015
411.5
photon source was obtained for use within SCALE6.2b4/MAVRIC sequence. The source
corresponding to activity after 2 hours from accident initiation gives largest dose rate in AB
and it was used for the MC calculation.
The MAVRIC sequence was used with the FW-CADIS methodology on the workstation
with 32 GB RAM and Core i-7 CPU. The adjoint source was investigated with different
positioning influencing significantly the final Monaco simulation. The spectrum of the adjoint
source was always ANSI standard (1977) gamma flux-to-dose-rate factors in rem/h. In the
first case the adjoint source was defined as all air regions external to containment and internal
to rest of the buildings, giving the phase-space where the optimized gamma dose rates are to
be determined. This is so called global shielding problem where Monaco results with uniform
uncertainties must be found everywhere with focus on air [14]. In the second case we used
several point detectors as point adjoint sources around the containment, optimizing the results
only in the vicinity of the detectors. This approach is more computationally costly, since
pseudo-flux ray tracing must be performed for every detector on every collision site, but
better MC statistics is pin-pointed on desired locations in the phase-space [15]. Global mesh
tally was defined in both cases, to better capture gamma dose convergence over the global
unit. It must be stressed that accuracy of the Denovo SN fluxes is not paramount, since only
their overall space shape will accelerate final Monaco calculation. Because of that and
memory optimization we used Denovo with these options: S8/P1 parameters, multigroup flux
tolerance of 10-6, Step Characteristic spatial differencing with zero flux fix-up [16]. In order
to get a more accurate solutions from the mesh-based SN calculations, Denovo was used with
macromaterial option which represents the material in each voxel as a volume-weighted
mixture of real materials. With tolerance of 0.01 and about 30 elementary materials, the
macromaterial table contained 4716 effective transport materials used for Denovo SN solver.
For each calculation we used Denovo with v7_27n19g library while Monaco was used with
v7_200n47g library to better capture effects of low-energy photon transport pertinent to MC
biasing scheme.
4
MAVRIC GAMMA DOSE MAPS
Two approaches have been used to test hybrid shielding methodology in case of SBO
accident: volumetric adjoint source over external air and point adjoint sources for selected
point detector locations in the containment and auxiliary buildings. The importance map1
represent the region(s) for which VR parameters will be generated using FW-CADIS to bias
Monaco and produce optimized results on those locations. Source sampling is also done from
biased source distribution function, determined from the adjoint SN solution, to work in
tandem with the importance map. Denovo representation of the SBO source is shown in
Figure 3. This section gives results of accidental gamma dose rates for different spatial
optimization.
1
This concept is very similar to Weight Windows (WW) from MCNP code, but in MAVRIC each cell of
importance map represents average particle weight by arithmetic mean. MCNP uses lower weights in meshbased WWINP file.
Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 14 ̶ 17, 2015
411.6
Figure 3: Denovo SN representation of the RADTRAD accidental source
4.1
Results of Global FW-CADIS
The SN mesh had 200x200x200 cells while the MC mesh had 160x160x160 cells over
the reduced global unit in xyz space. The Monaco code had 2000 batches with 2·105 photons
per batch giving total 140·106 histories. The short importance map option was turned on to
spatially limit our calculation only to AB rooms in the vicinity of the containment. We
focused on external air to produce better photon extraction through empty concrete structures
on different floors and model sections. Figure 4 is showing adjoint source distribution on the
elevation z=342 cm (primary pipes plane). Thus every material which is not air is excluded
from the adjoint source and depicted in white in Figure 4. Most difficult regions for photon
transport are the ones with the highest adjoint source strength to ensure the same number of
particles as in regions close to the real accidental source. Forward Denovo took 1.5 h, adjoint
Denovo 1.6 h, while Monaco took 52.1 h of CPU time on Core i7-3090K 3.2 GHz processor.
Figure 4: Adjoint source distribution on elevation z=342 cm
The gamma dose map through operating floor deck (i.e. control room elevation) of the
Krško model is shown in Figure 5. The associated MC relative errors on one sigma level are
shown in Figure 6. One can notice better MC statistics inside large air regions closest to the
containment, while thick concrete walls and floors are preventing photon penetration to
farther rooms. If one is interested in optimized results only for say control room, then
different MC biasing is in order but at the expense of other regions.
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411.7
Figure 5: Gamma dose rates (rem/h) at elevation 1 m above z=115.55 m
Figure 6: Relative error of gamma dose rates at elevation 1 m above z=115.55 m
Results of the axial gamma dose rates through reactor axial midplane (y=0) are shown
in Figure 7 while associated relative errors are shown in Figure 8. Satisfactory results indicate
that most of the air-regions outside of the containment receive photons. With more Monaco
histories the overall MC statistics should be better but even this does not assure reasonable
results in a distant, heavy shielded regions. Point detectors, region detectors and volumetric
adjoint sources are a better choice of computational strategy in such cases. Point detector
tallies are however CPU costly since ray tracing through MC geometry must be utilized for
every site of particle interaction to compute pseudo flux contribution. This strategy was
explored in the next paragraph so that comparison to simplified Krško model with pointkernel code MicroShield [17] can be done using specific point detector locations.
Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 14 ̶ 17, 2015
411.8
Figure 7: Gamma dose rates (rem/h) at axial midplane y=0 cm
Figure 8: Relative error of gamma dose rates at axial midplane y=0 cm
For consistency and additional check, the same calculation was repeated with
SCALE6.1 code (production version), but with minor changes, since that program version has
limited RAM allocation and absence of discrete gamma line spectrum description. The SN
mesh was 180x180x180, MC mesh was 150x150x150, gamma spectrum was defined as
multigroup narrow binned histogram and macromaterial tolerance was set to 0.018 giving
1821 transport materials. Similar CPU timing was needed for all functional modules to run.
One can notice a good agreement of gamma dose rates in y=0 plane for SCALE6.1 and
SCALE6.2b4. This comparison is shown in Figure 9.
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411.9
Figure 9: Comparison of gamma dose rates in y=0 plane
4.2
Results of FW-CADIS with Point Detectors
Point detectors represent a form of VR technique for computing particle flux at a
specific point. Estimation of the probability of the particle striking point detector is done at
every source emission site and at interaction site via ray tracing algorithm. In FW-CADIS
each point detector is an adjoint source with defined location and energy spectra
(corresponding to gamma dose) so that optimized results should be found at detector site and
reasonable results in the detector vicinity. Figure 10 is showing results of gamma dose rates in
plane of detectors (1 m above elevation 115.55 m) while Figure 11 is showing associated
relative errors. It can be seen that accurate dose rates and associated rather small relative
errors are predicted mostly near inserted point detector locations.
Figure 10: Gamma dose rates (rem/h) for point detectors VR at elevation 116.55 m
Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 14 ̶ 17, 2015
411.10
Figure 11: Relative error of gamma dose rates for point detectors VR at elevation 116.55 m
Taking into account the long calculation time for realistic model and in order to be able
to compare results with point doses calculated with simple point kernel model implemented in
the MicroShield code, simple containment model is prepared for additional SCALE6.2b4
calculation. Model strictly follows MicroShield model used for the calculation of doses in
auxiliary building and in main control room after design bases accidents. Simple cylinder has
radius 16.04 m and height 55 m and represents containment volume. It is filled with air and
has 3.8 cm thick steel liner. Annulus is additional air space with thickness 1.52 m, followed
by 0.76 m thick concrete and outside air space where detectors are located at 10, 100 and 200
cm from concrete surface. Simple containment MC model uses the same convergence criteria
and tolerances, and number of particles as realistic plant model (2000 batches, 200000
particles per batch, point detector VR model uses 2000 batches with 25000 particles per
batch).
Table 1: Calculated point dose rates
Position
RC center
10 cm in AB
100 cm in AB
(el. 127.8 m)
(el. 116.55 m)
(el. 116.55 m)
Dose rate
(mGy/hr)
Relative
error
Dose rate
(mGy/hr)
Relative
error
(mGy/hr)
Relative
error
MicroShield
7.27·106
-
123.9
-
116.9
-
SCALE6.2b4
simple
10.5·106
0.0006
164.6
0.052
145.2
0.013
SCALE6.2b4
realistic
8.69·106
0.017
49.6
0.15
47.4
0.14
SCALE6.2b4
realistic PD
9.37·106
0.002
45.8
0.0131
41.7
0.0126
Code
Dose rate
Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 14 ̶ 17, 2015
411.11
The gamma dose rates calculated with point kernel and different MC models are given
in Table 1. The MicroShield model and the simple SCALE6.2b4 containment are as close as
possible to each other with calculation assumptions. They have the same geometry, material
compositions and photon source spectrum and intensity. SCALE6.2b4 uses 47 groups gamma
library for transport calculation. MicroShield results are obtained using concrete buildup
factors for modelling auxiliary buildings and air buildup factors for modelling containment
interior. We have not expected that point kernel code will predict lower dose rates (between
20 and 30%) than MC code (Table 1). Realistic SCALE6.2b4 models have lower dose rates
compared to empty containment model, as expected. The reduction is rather small for doses
within containment and significant for doses in AB rooms close to the containment. MC
models with volume VR predict similar dose rates as MC models with point detector VR, but
relative uncertainty is typically for one order of magnitude larger and calculation load 2-3
times lower.
The gamma dose at point 10 cm from shield building within AB for period of 1 year
after SBO is calculated using MicroShield and it is 3.86 Gy. Radioactive decay and air
leakage are taken into account after final actuation of PCFV system. Time dependent dose
rate (RADTRAD and MicroShield) just outside containment at elevation 116.55 m is shown
in Figure 12. Based on verification calculation using MC models at point of maximum dose
rate (2 hours) the values are conservative taking into account realistic civil structures. Based
on comparison for simple containment model the dose is underestimated for up to 30%
compared to MC results.
N EK SB O PC FV
120
Gamma dose rate outside RB (mGy/hr)
110
100
90
80
70
60
50
40
30
20
10
10
0
10
1
10
2
10
3
Time (hr)
Figure 12: Gamma dose rate outside RB after SBO accident, MicroShield el. 116.55 m
Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 14 ̶ 17, 2015
411.12
5
DISCUSSION AND CONCLUSIONS
FW-CADIS shielding capabilities of the SCALE6.2b4/MAVRIC sequence were
demonstrated for a large model of the Krško nuclear island. The aforementioned stochasticdeterministic methodology was successfully applied to find gamma dose map in case of SBO
accident. Such deep penetration shielding problems are entirely dependent on advanced VR
techniques that will accelerate MC flux convergence in specific regions of user's interest. For
MAVRIC this means generation of accurate importance map based on forward and adjoint SN
transport solution. Since memory consumption grows quickly for high SN/PN parameters with
multi-million mesh cells, we have restricted Denovo solutions to S8/P1 which proved
reasonable and without negative fluxes. The new macromaterial option in Denovo solver must
be mentioned, since it proved to be a very elegant way to refine SN solution without calling for
extra memory.
This paper presents hybrid shielding analysis of Krško nuclear island using
SCALE6.2b4 code package. A complex MC model was prepared to analyze photon flux
attenuation through different floors, sections and concrete buildings in case of hypothetical
SBO accident. The accidental source was calculated with RADTRAD code and 18 group
ORIGEN energy structure having uniform distribution over all air regions in the containment.
Quantification of gamma dose rates demonstrated powerful attenuation of concrete
surroundings by many orders of magnitude, posing a challenging shielding problem. The FWCADIS methodology proved to be very versatile with different adjoint source definition. We
have explored possibility to produce reasonable results everywhere in external air (global
solution) oppositely to point detector localized solution where specific points were pinpointed. These differences are noticeable in the mesh tally distributions giving gamma dose
maps on different intersections.
The subject of the paper is closely related to MC shielding calculation in realistic plant
geometry, but is part of a more general problem related to calculation of dose rates after
severe accidents to be used for mitigation equipment qualification. Taking into account the
amount of calculation needed as well as the time required it is not realistic to expect full MC
calculation of all aspects of the problem. The post-accident dose up to one year after SBO
accident is still calculated using MicroShield point kernel code, but dose rates are verified
with more detailed MC model at the point of expected maximum dose rate (2h after SBO). It
was found that point kernel model is not giving conservative dose rates as compared to MC
results for the same geometry, but taking into account gross simplifications done in geometry
of concrete structures obtained results are still conservative compared to realistic MC model.
Based on this finding it is important to check results of point kernel calculations in cases
when geometry is not just "simple pipe" against properly formulated reference MC models.
ACKNOWLEDGMENTS
This work was supported by Croatian Science Foundation under the grant number 3522.
The work is performed to support NPP Krško Equipment survivability project
evaluations and access to plant’s data is highly appreciated.
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Proceedings of the International Conference Nuclear Energy for New Europe, Portorož, Slovenia, September 14 ̶ 17, 2015