Primary Loop Components with SCALE6.0
Mario Matijević, Dubravko Pevec, Krešimir Trontl
University of Zagreb, Faculty of Electrical Engineering and Computing, Department of Applied Physics
Unska 3
10000 Zagreb, Croatia
mario.matijevic@fer.hr, dubravko.pevec@fer.hr, kresimir.trontl@fer.hr
ABSTRACT
A 3D simulation model of typical pressurized water reactor (PWR) primary loop components for effective dose rates calculation based on hybrid deterministic-stochastic methodology was created. Shielding calculations have been performed using MAVRIC shielding sequence of SCALE6.0 code package. A detailed model of a combinatorial geometry, materials and characteristics of a generic two loop PWR facility are based on best available input data. The sources of ionizing radiation in PWR primary loop components included neutrons and photons originating from critical core and photons from activated coolant in two primary loops. Detailed calculations of reactor pressure vessel and upper reactor head have been performed. The efficiency of particle transport for obtaining global Monte Carlo dose rates was further examined and quantified with flexible adjoint source positioning in phase-space. Shielding calculations were also performed for reduced PWR facility model which included reactor core and adjacent concrete structures with steam generator and pump. It was demonstrated that definition of air as a global adjoint source gave lower uncertainty of photon dose rates. Activation of primary loop coolant, which becomes additional gamma source in working reactor, was considered. The gamma dose rates were presented for brief and detailed MAVRIC calculations. Control and numerical parameters of the MAVRIC shielding sequence with hybrid methodology have been optimized for effective Monte Carlo deep penetration shielding calculation.
1 INTRODUCTION
A hybrid deterministic-stochastic methodology is frequently used when facing Monte Carlo (MC) simulations for deep penetration shielding problems. The ultimate goal of such automatic variance reduction (VR) techniques is to achieve acceptable precision for the MC results in reasonable time. Automatic preparation of such VR parameters in phase-space domain is done via deterministic transport theory methods (SN) by generating space-energy mesh-based adjoint function distribution. This is used when optimization of localized results is needed, such as point or region detectors. For MC simulation resulting in uniform statistical uncertainty over large portions of phase-space, overlaid with mesh grid tally, additional SN
forward calculation is needed for adjoint source scaling. The FW-CADIS (Forward-Weighted Consistent Adjoint Driven Importance Sampling) method [1] in MAVRIC (Monaco with Automated Variance Reduction using Importance Calculations) shielding sequence of SCALE6.0 code package [2] is used with aforementioned hybrid methodology. The objective in this paper is to determine the dose rates throughout typical PWR primary loop components.
This represents a challenging real-life shielding problem for which analog MC approach is
not possible so automatic linking between Denovo SN and Monaco MC methods [2] is presented.
SCALE6.0 general geometry package (SGGP) was used for modeling of the typical PWR facility based on the H.B.Robinson-2 Pressure Vessel Benchmark (HBR-2) [3] critical core (2300 MWth). Calculational results (reaction rates for six reactions) were compared with benchmark results obtained by TORT SN transport code in previous paper [4], where satisfactory results were obtained. This allowed the assessment of the accuracy with which the calculations predicted the neutron flux attenuation through the reactor internals [5]. With previous HBR-2 benchmark calculations, we now extended its geometry to the full-size typical PWR facility including primary loop components and concrete surroundings. Typical industrial and text-book data were used for dimensions and materials required: reactor internals, upper and lower reactor pressure vessel (RPV) head, biological shield, steam generators, primary pumps and pipes, concrete structures such as floors and walls.
Calculation of fast neutron interactions with coolant and RPV are presented first, where we investigated (n,p) reaction on oxygen and iron. This detailed simulation model is focused on reactor internals with flexible adjoint source positioning in phase-space. Neutron and gamma dose rates from critical core were also quantified. Shielding calculations for reduced PWR facility model were performed next. Simulation model included reactor core and adjacent concrete structures with steam generator and pump. Global adjoint source was defined as a whole phase-space for neutrons but for photons that source had additional focus on air to achieve better particle transmission. Activation of primary loop coolant, which becomes additional gamma source in working reactor, was considered last. Global adjoint source was again defined over model but with focus on air. The gamma dose rates were presented for brief and detailed MAVRIC simulation models. Advantage of using MAVRIC/FW-CADIS methodology over manual VR techniques was quantified for this last case.
The paper is organized as follows. Section 2 gives the description of the SCALE6.0 code package with MAVRIC shielding sequence. Section 3 shows SGGP simulation model of PWR facility and summarizes RPV calculations. Section 4 gives dose rates for reduced PWR simulation model while Section 5 presents calculation of primary coolant activation. Section 6 gives conclusions while the referenced literature is given at the end of the paper.
2 SCALE6.0 CODE PACKAGE
The SCALE6.0 code system was developed for the U.S.NRC to enable standardized analyses and evaluation of nuclear facilities. The criticality sequence (CSAS6) uses a 3D multigroup MC transport code KENO-VI to provide problem-dependent, cross-section processing followed by calculation of the neutron multiplication factor keff. KENO-VI has the ability to save fission distribution (in space and energy) of a critical system into a file over user-specified 3D mesh grid and energy structure of the cross section library. This methodology was implemented into SCALE6.0 code package to enable modeling criticality accident alarm systems (CAAS). The MC shielding analysis capabilities in SCALE6.0 are based on Consistent Adjoint Driven Importance Sampling (CADIS) methodology [6] which is used to create an importance map (space-energy weight windows) and biased source distribution. Integrated SN code Denovo is used for automatic generation of space-energy VR parameters over Cartesian mesh for the functional module Monaco. The Monaco is a multigroup fixed-source 3D MC transport code, which is used by MAVRIC shielding sequence of the SCALE6.0 code package. Automated or manual VR can have source description in the form of CAAS fission source or with user defined source distribution.
When computing several tallies at once or a mesh tally over a large volume of space, an
extension of the CADIS method called FW-CADIS [7][8] can be used to obtain uniform relative uncertainties - multiple adjoint sources (or mesh cells) are weighted inversely by the expected tally forward value from Denovo. For criticality safety analyses the v7-238 library was used, while for the shielding calculations v7-27n19g library was used. Primary data for both libraries originate from the ENDF/B-VII.0 nuclear data library [9].
3 REACTOR PRESSURE VESSEL CALCULATIONS
Calculational methods for determining the neutron fluence are necessary to estimate the fracture toughness of the pressure vessel materials, which is main factor when considering lifetime extension for nuclear power plants. The first step was CSAS6/KENO-VI criticality calculations of the full-sized HBR-2 reactor using 4050 batches with first 50 batches skipped in order for the fission source distribution to converge and with 5000 neutrons per batch. The obtained effective multiplication factor of the reactor for v7-238 library was keff = 1.00012±0.00013. The cycle-average critical boron concentration dissolved in water was 392 ppm. Total CPU time on QuadCore Q6600 with 8 GB of RAM was 81.21 minutes. The CAAS source containing space-energy fission distributions for non-skipping generations over user-defined 3D Cartesian mesh was generated with criticality run. Together with total neutron source strength of 1.771020 n/s (2300 MWth), this mesh is then used as the source term in MAVRIC. The simulation model of the full-sized HBR-2 reactor with primary loop components is shown in Figure 1. The MAVRIC sequence was used for the calculation of high energy threshold reaction 16O(n,p)16N* on coolant (secondary gamma emission via nitrogen activation) and 54Fe(n,p)54Mn on RPV (standard dosimetry reaction). The continuous (n,p) cross sections were collapsed in v7-27n19g format using Ajax/Paleale routines inside SCALE6.0 and then used as a spectrum of MAVRIC adjoint source. For the latter gamma dose rates calculation we used built-in response function ID=9504.
Figure 1: MAVRIC model of reactor and primary loop components 3.1 Results of (n,p) reactions on coolant
MAVRIC/FW-CADIS simulation model of HBR-2 reactor had SN and MC mesh with 55x55x100 (3·105 cells) and Denovo S6/P2 parameters (Quadrature/Legendre) with multigroup flux tolerance ε=10-6. Monaco had 5·107 histories and total CPU time was 3.11 days. Figure 2 shows global adjoint source with focus on coolant and Monaco (n,p) reaction rates (/atom/s) with relative uncertainty (RE) in y=0 plane. The water and withdrawn control rods present difficult region for neutrons to reach upper head so adjoint source is gradually
increased in axial direction. Excellent MC results were obtained with relative error (RE) less than 10% on average. The self-shadowing effect is present since center of the core is without neutron transport, i.e. it has marginal contribution to coolant irradiation. This is consequence of FW-CADIS methodology where results are optimized only for coolant (water-focused adjoint source).
Figure 2: Adjoint source and Monaco results for 16O(n,p)16N* reaction (/atom/s) with RE 3.2 Results of (n,p) reactions on RPV
This portion of calculations shows reaction rates of 54Fe(n,p)54Mn on upper reactor head which is defined as a volumetric adjoint source. Figure 3 shows adjoint source and Monaco (n,p) reaction rates with RE in y=0 plane.
Figure 3: Adjoint source and Monaco results for 54Fe(n,p)54Mn reaction (/atom/s) with RE MAVRIC/FW-CADIS simulation model of RPV had SN and MC mesh with 55x55x100 (3·105 cells) and Denovo S6/P2 parameters with tolerance ε=10-6. Monaco had 2·107 histories and total CPU time was 2.16 days. Adjoint source is inversely scaled with expected (n,p) reaction rates (from forward Denovo) but it has insufficient strength to attract enough number of neutrons to produce statistically valid MC results (regardless of histories). The massive attenuation of neutron flux between reactor core and upper head is too strong for this adjoint source, so alternative definitions were proposed. The best of them was global adjoint source without focus on material – this is in general unrealistic demand for MAVRIC, to optimize the results for all materials and all space. Still, this approach was investigated with SN and MC mesh with 60x60x100 (3.6·105 cells), total of 5·107 histories and CPU time was 3.43 days.
Figure 4 shows global adjoint source and Monaco (n,p) reaction rates with RE in y=0 plane.
The upper head statistics could be improved with larger number of histories since the space above head is also adjoint source which attracts neutrons from reactor core.
Figure 4: Adjoint source and Monaco results for 54Fe(n,p)54Mn reaction (/atom/s) with RE 3.3 Results of gamma dose rates
This calculation considers the ability of MAVRIC/FW-CADIS for transportation of all 46 coupled neutron/photon groups in v7-27n19g library. This is serious increase in computer memory requirements in contrast to high-energy threshold reactions, where only highest energy groups are engaged. The global adjoint source was defined without focus on material and with energy spectrum of photon dose rates (built-in function ID=9504). SN and MC mesh were 60x60x100 (3.6·105 cells), Monaco had 5·107 histories and CPU time was 3.93 days.
Figure 5: Global adjoint source and Monaco dose rates (rem/h) for photons with RE Photon dose rates with RE are shown in Figure 5. Excellent MC results were obtained with RE less than 10% on average over all mesh cells. In contrast to neutrons, where strong axial attenuation (coolant+control rods) prevents neutron transport to the upper head, photon calculation predicts upper head ring as a most troublesome region (carbon steel).
4 REDUCED PWR FACILITY MODEL CALCULATIONS
These calculations investigate the possibility of neutron and gamma transport from critical core through reduced model geometry: reactor core with biological shield and adjacent concrete structures with steam generator and pump. This phase-space defines adjoint source,
i.e. the place where optimized dose rates of neutrons and photons are determined. The boundary conditions were vacuum type. Denovo was used with S4/P1 and ε=10-6 parameters.
CAAS source caused memory errors so space-flat critical core with Watt thermal fission spectrum distribution of 235U (a=1.028 MeV, b=2.249/MeV) was used [2]. Figure 6 shows reduced PWR model geometry with mesh importance map.
Figure 6: Reduced PWR geometry (mesh importance map) 4.1 Neutron case (without focus on air)
MAVRIC/FW-CADIS had SN and MC mesh 65x50x100 (3.25·105 cells). Monaco was used with 5·107 histories and CPU time was ~ 2 days. Global adjoint source had neutron dose spectrum (built-in function ID=9029). Figure 7 shows MC dose rates with RE for neutrons in y=0 plane. Excellent results were obtained regarding the size and attenuation power of the model in question. White areas inside pressure vessel and below reactor floor (z=0 cm) are consequences of transport optimization by FW-CADIS methodology, i.e. global adjoint source without focus on material. Neutrons are thus preferably transported by importance map through materials of lower density (air), not through concrete. One has to note dose rate attenuation over 13 orders of magnitude from core to the model periphery.
Figure 7: Monaco neutron dose rates (rem/h) and RE
4.2 Photon case (with focus on air)
The MAVRIC/FW-CADIS photon dose rates from critical core are presented for coupled neutron-photon transport in Figure 8. MC mesh was 65x55x105 (~ 3.80·105 cells) while SN mesh was more detailed, 80x70x140 (7.84·105 cells). Reactor core had Watt spectrum of 235U with included fission photons (~7 photons/fission). Denovo was used with S4/P1 and ε=10-6 parameters. Monaco had 7.5·107 histories and CPU time was little over 2 days. In contrast to neutron case, adjoint source with gamma dose spectrum (built-in function ID=9504) had focus on air inside model. This approach enabled further transport of photons through thick concrete walls (1 m) because of inner air which attracts them in adjoint methodology. Evidently more detailed SN mesh produces more stable MC results but with increased memory and computer storage requirements [10].
Figure 8: Monaco photon dose rates (rem/h) and RE 5 PRIMARY LOOP COOLANT ACTIVATION
Energies of the emitted photons from the coolant were taken from ANSI/ANS-18.1- 1999 [11], where activities for more than 50 isotopes (grouped in 6 categories) are listed. The bulk of the activity is coming from excited 16N* (7.13 s half life), generated by (n,p) reaction on oxygen, which accounts for 94-97 % of the activity of the coolant (92% emission of 6.12 MeV photons). Using parameters for a generic two-loop PWR coolant (40 μCi/g of 16N*) it is possible to calculate specific photon strength of coolant (1.08·106 photons/s/g). That value was corrected (multiplied by 0.75) because of short half-life of 16N* and with added long- term activity of other nuclides we get 8.46·105 photons/s/g [11]. Using total volume of coolant (1.53·108 cm3), total mass (1.21·108 g) and its density (0.79 g/cm3), we obtained total gamma source of 1.02·1014 photons/s. Together with photon emission spectra of 16N*
prepared for multigroup v7-27n19g library, we obtained complete coolant distributed source.
Figure 9 shows brief MAVRIC/FW-CADIS results for photon dose rates from activated coolant source in y=0 plane. SN and MC mesh was 55x55x110 (3.30·105 cells), Denovo had S4/P1 parameters with ε=10-6 and Monaco had 2.5·107 histories. Adjoint source was whole phase-space with gamma dose spectrum (built-in function ID=9504). Total CPU time was 1.55 days. The same calculation was performed using manual VR (targetWeights=1, windowRatio=5) with CPU time 2.11 days. Similar results (magnitude) of dose rates were obtained but uncertainties were much larger with deficient distribution (Figure 10, x=0 plane).
For manual VR there is no photon transportation through the first layer of concrete
surroundings. Optimized calculation had focus on air inside model and increased mesh densities (8·105 cells for SN and 4·105 cells for MC mesh). Denovo had S4/P1 with ε=10-6 and Monaco had 12.5·107 histories. Total CPU time was 2.5 days and output file was 8.5 GB.
Excellent MC results were obtained with RE less than 10% through the air-regions of the model (Figure 11). Mesh density of Denovo and Monaco plays important role for quality of MC distribution but also poses significant memory and storage burden.
Figure 9: Monaco photon dose rates (rem/h) and RE
Figure 10: RE for manual VR Figure 11: RE for optimized FW-CADIS 6 CONCLUSIONS
A detailed shielding analysis of the typical PWR reactor with critical HBR-2 core was performed. A carefully constructed model was developed to analyze attenuation of neutron and gamma dose rates through structural components and concrete using MAVRIC shielding sequence of SCALE6.0. Source terms included neutrons and photons from critical core and photons from activated coolant. Detailed shielding calculations of RPV demonstrated versatile ability of MAVRIC/FW-CADIS to generate mesh-based VR parameters for uniform MC uncertainties of complex model. Extending simulation model on reduced PWR facility showed similar behavior for calculating dose rates over larger phase-space. Adjoint source definition with focus on selected materials showed benefits in deep penetration shielding problems, especially when alternating layers of concrete and air are present. Ability to define volumetric distributed sources in MAVRIC has enabled inclusion of coolant-activated gamma source through primary loop elements. Quantification of dose rates showed powerful attenuation of concrete surroundings by many orders of magnitude. The amount of coolant gamma dose in the vicinity of primary elements is comparable to gamma doses from the reactor. Continuation of the research would be determination of radiation field inside
complete containment building and investigation of numerical dependency between SN and MC modules inside hybrid MAVRIC/FW-CADIS methodology.
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