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Development of a model for the approximation of the neutron and photon flux in a BWR spent fuel assembly
Annals of Nuclear Energy 57 (2013) 256–262
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Development of a model for the approximation of the neutron and photon flux in a BWR spent fuel assembly Riccardo Rossa 1, Paolo Peerani ⇑ European Commission, Joint Research Centre, ITU, Ispra (VA), Italy
a r t i c l e
i n f o
Article history: Received 10 August 2012 Received in revised form 16 January 2013 Accepted 17 January 2013 Available online 15 March 2013 Keywords: Nuclear safeguards Neutron detectors Gamma detectors
a b s t r a c t This paper proposes a simplified model built with Matlab to compute an approximation of the neutron and photon flux in a BWR spent fuel assembly in a pond. Starting from a reduced number of Monte Carlo simulations, a set of transmission probabilities has been calculated. These values allow the estimation of the particle flux inside a fuel assembly placed in a generic storage rack. This calculation is possible provided the transmission probability has been calculated for the desired value of burnup and cooling time of the assemblies in the rack. The validity of the model has been tested first with a uniform pattern of the storage rack and finally with a generic configuration. Reference values from the equivalent Monte Carlo simulations show very good agreement and the relative error between the two measures is always within few percents. The main advantage of this simplified model is the great reduction of computational time required to perform the estimation and the fact that the basic idea behind the model can be applied to any fuel geometry and type of storage pond. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Over 80% of the material placed under safeguards today is in the form of spent fuel assemblies and one of the main way to verify it is by Non-Destructive Assays (NDAs). The main goal for the safeguards inspections is to verify that no material has been diverted to other purposes by detecting the eventual gross and partial defect from the fuel assembly. Gross defect is the replacement of an entire fuel assembly with a dummy made of other material (e.g. natural uranium or stainless steel), while partial defect concerns the removal of fuel pins inside a fuel assembly. Current NDA techniques rely on total neutron and gamma interaction detectors to perform the measurements. The most common instruments for the safeguards verifications are the Digital Cherenkov Viewing Device (DCVD), the Spent Fuel Attribute Tester (SFAT) and the Fork detector (FDET). The DCVD is based on the emission of the Cherenkov radiation by spent fuel assemblies. This radiation arises when a particle travels with a speed higher than the speed of light in the medium (e.g. water in the spent fuel pool). Spent fuel assemblies are strong sources of beta particles, gamma rays and neutrons, and all these particles can produce Cerenkov light (directly or indirectly). The SFAT couples a gamma detector (such as CdZnTe) with customized collimator/shielding and a multichannel analyzer (MCA). ⇑ Corresponding author. Tel.: +39 0332 785625; fax: +39 0332 785072. 1
E-mail address: [email protected] (P. Peerani). Currently at SCK-CEN in Mol (Belgium).
0306-4549/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.anucene.2013.01.021
This instrument verifies the spent fuel by detecting the presence of the Cs-137 peak that is by far the main gamma emission in an irradiated fuel assembly. The Fork detector couples two sets of ion chambers and fission chambers for measuring opposite sides of the fuel assembly simultaneously. Each arm contains an ionization chamber to measure the total gamma-ray output and two fission chambers to compute the neutron flux (Reilly et al., 1991). Current techniques can reach a satisfactory level of accuracy only if the burnup and cooling time are known; this requires that these data are provided by the operator. This is why several research centers and international agencies are putting significant effort to develop more precise measurement methods that allow deriving conclusions without relying on information provided by the operator. The European Commission with the JRC–ITU located in Ispra is studying the application of a novel technology (the PDET detector developed by the Lawrence Livermore National Laboratories) to BWR fuel assemblies immersed in a spent fuel pond. This detector is composed of a series of neutron and gamma detectors to be inserted within the fuel assembly that is being verified. The Partial Defect Tester (also known as PDET) employs a set of neutron and photon detectors to have a spatial distribution of the two fluxes within a fuel assembly. This experimental device has been designed, modeled and tested by LLNL with PWR assemblies (Sitaraman and Ham, 2009; Ham et al., 2009), considering that this type of assemblies allows the insertion of multiple detectors in the guide tubes already
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Fig. 1. MCNP model of the BWR fuel assembly. The numbers and letters refer to the measurement positions (being WH the Water Hole).
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present in the geometry. The guide tubes are used for the insertion of the control rods during normal operations and, once the assembly is stored in the spent fuel pool, they provide room for the insertion of small detectors. Since each fuel pin emits neutrons and photons according to its history (namely burnup and cooling time) the diversion of some pins will alter the magnitude of the neutron and photon flux in the fuel assembly cross section. It is the distortion of the expected flux shape that allows the inspector to detect a gross or partial defect. The results reported by LLNL in (Sitaraman and Ham, 2009; Ham et al., 2009) suggest the capability for the PDET to detect a gross defect without the support of the operator’s data. This aspect, coupled with the fact that the assembly under investigation does not have to be moved from the storage position, is a clear advantage from the current NDA techniques. Moreover Ham and coworkers have demonstrated the capability of PDET to detect a partial defect at a level of removal of a certain number of pins. It is difficult to state exactly which the minimum detectable number of removed pins is. It has been shown that even the removal of eight pins (corresponding to 3% in a 17 17 fuel assembly) can be detected if the pins are clustered together. Probably a higher number of pins can be removed and remain undetected with a more clever diversion strategy (dispersed symmetric removal). Anyway it will be impossible to maintain the flux profile unchanged when the diversion will exceed 20–25% of
Fig. 2. Model of the storage rack. The central fuel assembly under investigation is depicted in white and has the 16 measurement positions colored in orange. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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the total number of pins. This is well below the current target of partial defect detection stated by IAEA (removal of 50% of fuel). The insertion of multiple detectors inside a PWR assembly does not have major technical problem, but the situation changes when the same concept is applied to a BWR assembly. A generic BWR assembly contains less fuel pins compared to a PWR assembly (e.g. 8 8 lattice instead of 17 17), but these have a larger diameter and pitch, resulting in similar external dimension (a square of about 16 cm versus the 22 of a PWR). However, inside the BWR assembly there are no guide tubes due to the different geometry of control rods (generally having a cruciform shape with blades inserted between neighboring fuel elements. In some cases there might be water holes used to have better neutron moderation during normal operations. In the BWR assembly considered in this study there is only one central water hole. During the feasibility study for the application of the PDET to BWR assemblies an issue that has been investigated was the influence of the neighbor assemblies to the measured assembly. Considering that most of the spent fuel is currently stored under water in the spent fuel pond, the Monte Carlo model considered a 3 3 storage rack. 2. Monte Carlo model 2.1. Geometry of the fuel assembly and storage rack The reference model for this study will be the 8 8 ASEA BWR fuel (Fig. 1). This type of assembly has one central water hole, used in normal condition to have better neutron moderation. This hole appears like the most suitable location where inserting small neutron and gamma detectors. Anyway the availability of a single measurement point would rule out the possibility to detect a diversion using radiation profiles without relying on operator’s declaration. This is because there can be several combinations of burnup and cooling time that will give the same ratio between the neutron and photon flux. Therefore the identification of the irradiation history of the fuel assembly cannot be done unequivocally. Considering the suggestions from LLNL (Ham, 2012), due to the larger distance between the fuel pins, additional 16 measurement positions have been identified inside the assembly. These measurement locations are shown in Fig. 1 and are depicted in red.2 The storage rack for the study has been based on detailed information of the Swedish interim storage facility CLAB (Eliasson et al., 2012). This installation has 10 ponds containing storage baskets with spent fuel assemblies. There are three common types of baskets which are filled by both BWR and PWR assemblies. All the types of assemblies stored in CLAB can be inserted in all three types of baskets. The geometry considered in this study contains nine BWR assemblies and it is a reduction of a 25-positions basket. In this configuration there is a small water gap between the fuel and the basket and the walls of the storage basket are made of borated steel (at least 1.6% of Boron). The spent fuel pools are filled with water that is not borated and this will influence the neutron signal of the detectors. Fig. 2 shows the lattice of the storage rack. 2.2. Spent fuel composition and source terms The spent fuel compositions have been calculated with ORIGENARP (Bowman et al., 1998) under the conditions: – Initial Enrichment (IE): 3%.
2 For interpretation of color in Fig. 1, the reader is referred to the web version of this article.
– Burnup (BU): 14–28–42 GWd/t. – Cooling Time (CT): 1–30 years. Each irradiation cycle lasted 350 days and two successive irradiation cycles have been separated by 30 days of cooling time. Adjusting the power level to 40 MW/t, each irradiation cycle resulted in a burnup of 14 GWd/t. Considering that the cooling time had a very small influence on the detectors’ response, only two values for that parameter have been considered. In order to easily identify the characteristics of the fuel assemblies used for the simulations, they have been identified by four numbers: the first two represent the burnup in GWd/t while the other two are the years of cooling time after discharge. The list of isotopes in the spent fuel used in the Monte Carlo simulations (Pelowitz, 2011) has been reduced to 37 (both fission products and minor actinides) which represents the principal absorbers (Cerne et al., 1987). The list is further reduced to 25 for the simulations involving photons, since the photon libraries account only for elements and not for the single isotopes. Neutrons are generated within all pins containing spent fuel in all the fuel assemblies. The source intensity is proportional to the total neutron emission of the assembly; value that is taken from the Origen simulations. All pins within a fuel assembly are considered having the same source intensity. The spectrum used for the neutron source is a Watt spectrum with parameters of Cm-244, which is accounting for over 90% of the total neutron source in the spent fuel. As in the case of neutron generation, photons are generated taking into account the total gamma emission of the fuel pin. All pins within a fuel assembly are considered having the same source intensity. The photon source has been modeled as a line at 662 keV, the main emission of Cs-137, which is accounting for over 80% of the total photon source in the spent fuel after some years of cooling time. 3. Model of the transmission probabilities 3.1. Basic concept of the model The goal of the model is to provide an initial estimate of the neutron and photon flux in the measurement positions without running additional MCNP simulations. This model accounts for assemblies with different burnup and cooling time, allowing the building of a generic storage pattern. The signal in the water hole measurement position in the central fuel assembly will have a contribution from all eight neighboring assemblies and from the central assembly itself:
R / ðS1 þ S3 þ S7 þ S9 Þ PCO þ ðS2 þ S4 þ S6 þ S8 Þ PEO þ S5 POO where R is the response of the detector placed in the water hole (e.g. number of neutrons/photons), S1, S3, S7, and S9 are the source terms of the corner assemblies, S2, S4, S6, and S8 are the source terms of the lateral assemblies, S5 is the source term of the central assembly, PCO is the transmission probability from a corner assembly to the central one, PEO is the transmission probability from a lateral assembly to the central one, and POO is the transmission probability within the central assembly. The transmission probability is defined as the probability that a particle emitted in an assembly (corner, lateral, or central) will reach the measurement position in the central fuel assembly where the PDET is inserted. This formula has been generalized for the calculations of the other 16 measurement positions:
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X RK / SI PIK I
where RK is the response of the K-th detector (K = 1, 2, . . ., 16), SI is the source terms of one assemblies (I = 1, 2, . . ., 9), PIK is the transmission probability from the assembly I to the measurement position K. 3.2. Calculation of the transmission probabilities The transmission probabilities have been calculated running few modified Monte Carlo simulations of the storage rack. These simulations contained a complete rack of identical fuel assemblies (i.e. same isotopic composition) but the particles are emitted by only one fuel assembly. Nevertheless the other eight assemblies are still in the MCNP model, to account for the absorption and the scattering of particles against other fuel assemblies and therefore to provide a more accurate simulation of the real situation. Considering the symmetry of the system only three simulations were needed, placing as source term the central assembly (O–O), one lateral assembly (E–O), and one corner assembly (C–O). With this procedure it is possible to compute the amount of particles that are coming to the detector area using the flux tally F4 in the MCNP code. The transmission probabilities (POO, PEO or PCO respectively) are obtained by multiplying the flux tally by the volume of the detector itself. Tables 1–3 (first row) show the transmission probabilities for the water hole computed according to the procedure described above. The other rows contain the probabilities for other positions described later in the article. The statistical uncertainty of the simulations is always below 1%. By looking at the values in the tables it is evident that the neutrons are traveling in the storage rack much more than the photons. This is due to the high attenuation of the high-Z materials present in the storage pool (e.g. uranium in the fuel assemblies). The use of borated water will lower the transmission probability for neutrons, while letting roughly unchanged the photon absorption. The very low probability values for the set of C–O simulations support the decision to consider only the 3 3 lattice instead of the full 5 5 geometry of the real storage basket. 4. Validation of the model The transmission probabilities calculated in the previous chapter have been introduced in the Matlab code (MATLAB, 2012) for
the building of the simplified model. This script has been written in order to speed up calculations and minimize the input required by the user. With this code, the user has only to insert the four-digit identifier for the fuel assemblies according to the convention explained on Section 2.2 of this article. Then the program takes as input the transmission probabilities corresponding to the pattern of the storage rack and calculates the neutron and photon signal in the central fuel assembly. The formula used to obtain the results is the general relationship reported in Section 3.1. The first set of tests concerned a uniform storage rack, composed of nine fuel assemblies with the same isotopic composition and source term. Table 4 shows the results from a full MCNP modelling and the simplified model using Matlab to combine the three transmission probabilities and the fuel history information, and reporting also the relative error between the two calculations. Only the value of the fluxes in the water hole is considered at the moment and reported in Table 4. The model will be extended to the other measurement positions in the next section. From these initial results, the model seems to approximate very well the Monte Carlo simulations, with an agreement of around 5% for the neutron population and 3% for the photon flux. The larger discrepancies for neutrons are due to the more complex physical modeling of transport depending on many variables. The relative error between the two calculations can be attributed to the statistical uncertainty of the MCNP model and to the approximation of symmetry of the central water hole. This is not entirely correct because the channel is slightly moved from the center of the fuel assembly as it is shown in Fig. 1. Looking at the numerical values it is evident that using only the signal of the water hole it will not be possible to have an indication of the irradiation history of the fuel assembly. This is because the values are so similar that will be within the measurement error of the real instrumentation. Therefore the same model has been applied to additional positions, in order to have multiple values of both fluxes to try and have a unique signature dependent on the burnup and cooling time of the assembly. 5. Extension to the other measurement positions As shown in Fig. 1, the dimensions and geometry of the BWR assembly seem to allow the insertion of detectors between the single fuel pins. A total of 16 positions have been considered in this stage of the analysis, using the same concept for the calculation of the
Table 1 Transmission probabilities. Source assembly: central position (O–O). Pos.
OO1401N
OO1401P
OO1430N
OO1430P
OO2810N
OO2810P
OO4201N
OO4201P
OO4230N
OO4230P
WH 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16
0.1351 0.0892 0.1077 0.1073 0.0895 0.1077 0.1302 0.1291 0.1069 0.1079 0.1307 0.1296 0.1072 0.0896 0.1077 0.1082 0.0890
0.0130 0.0099 0.0115 0.0114 0.0099 0.0115 0.0133 0.0130 0.0114 0.0114 0.0133 0.0132 0.0115 0.0098 0.0115 0.0114 0.0099
0.1326 0.0876 0.1056 0.1054 0.0881 0.1060 0.1280 0.1269 0.1052 0.1059 0.1286 0.1276 0.1053 0.0877 0.1059 0.1063 0.0875
0.0130 0.0099 0.0115 0.0114 0.0099 0.0115 0.0133 0.0130 0.0114 0.0114 0.0133 0.0132 0.0115 0.0098 0.0115 0.0114 0.0099
0.1189 0.0788 0.0951 0.0946 0.0784 0.0952 0.1150 0.1139 0.0939 0.0949 0.1155 0.1146 0.0941 0.0786 0.0950 0.0953 0.0785
0.0130 0.0099 0.0115 0.0114 0.0099 0.0115 0.0133 0.0130 0.0114 0.0114 0.0133 0.0133 0.0115 0.0099 0.0115 0.0115 0.0099
0.1052 0.0692 0.0837 0.0831 0.0689 0.0843 0.1018 0.1007 0.0829 0.0838 0.1031 0.1017 0.0831 0.0685 0.0835 0.0840 0.0687
0.0131 0.0099 0.0115 0.0114 0.0099 0.0115 0.0133 0.0130 0.0115 0.0115 0.0133 0.0133 0.0115 0.0099 0.0115 0.0115 0.0099
0.1000 0.0656 0.0794 0.0787 0.0652 0.0797 0.0970 0.0957 0.0788 0.0793 0.0981 0.0962 0.0789 0.0651 0.0790 0.0796 0.0650
0.0131 0.0099 0.0115 0.0114 0.0099 0.0115 0.0133 0.0130 0.0115 0.0115 0.0133 0.0133 0.0115 0.0099 0.0115 0.0115 0.0099
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Table 2 Transmission probabilities. Source assembly: lateral position (E–O). Pos.
EO1401N
EO1401P
EO1430N
EO1430P
EO2810N
EO2810P
EO4201N
EO4201P
EO4230N
EO4230P
WH 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16
0.0320 0.0377 0.0448 0.0447 0.0377 0.0278 0.0327 0.0334 0.0279 0.0197 0.0230 0.0232 0.0198 0.0132 0.0153 0.0153 0.0132
0.0003 0.0014 0.0017 0.0017 0.0014 0.0004 0.0004 0.0004 0.0004 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001
0.0308 0.0367 0.0436 0.0435 0.0366 0.0270 0.0316 0.0322 0.0268 0.0190 0.0221 0.0222 0.0189 0.0126 0.0146 0.0145 0.0127
0.0003 0.0014 0.0017 0.0017 0.0014 0.0004 0.0004 0.0004 0.0004 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001
0.0247 0.0312 0.0372 0.0371 0.0313 0.0217 0.0257 0.0262 0.0218 0.0147 0.0171 0.0173 0.0149 0.0094 0.0108 0.0109 0.0096
0.0003 0.0014 0.0017 0.0017 0.0014 0.0004 0.0004 0.0004 0.0004 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001
0.0185 0.0248 0.0299 0.0299 0.0249 0.0163 0.0195 0.0199 0.0164 0.0103 0.0122 0.0124 0.0104 0.0062 0.0073 0.0072 0.0064
0.0003 0.0014 0.0017 0.0017 0.0014 0.0004 0.0004 0.0004 0.0004 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001
0.0164 0.0230 0.0273 0.0275 0.0230 0.0146 0.0173 0.0179 0.0147 0.0090 0.0106 0.0107 0.0090 0.0053 0.0062 0.0061 0.0054
0.0003 0.0014 0.0017 0.0017 0.0014 0.0004 0.0004 0.0004 0.0004 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001
Table 3 Transmission probabilities. Source assembly: corner position (C–O). Pos.
CO1401N
CO1401P
CO1430N
CO1430P
CO2810N
CO2810P
CO4201N
CO4201P
CO4230N
CO4230P
WH 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16
0.0115 0.0206 0.0164 0.0123 0.0084 0.0164 0.0140 0.0111 0.0077 0.0122 0.0109 0.0088 0.0064 0.0084 0.0077 0.0064 0.0048
<0.0001 0.0005 0.0002 0.0001 <0.0001 0.0002 0.0001 <0.0001 <0.0001 0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
0.0110 0.0200 0.0158 0.0119 0.0081 0.0158 0.0134 0.0107 0.0073 0.0116 0.0103 0.0084 0.0061 0.0081 0.0073 0.0061 0.0045
<0.0001 0.0005 0.0002 0.0001 <0.0001 0.0002 0.0001 <0.0001 <0.0001 0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
0.0084 0.0167 0.0127 0.0092 0.0061 0.0127 0.0103 0.0080 0.0055 0.0091 0.0078 0.0061 0.0044 0.0061 0.0054 0.0044 0.0032
<0.0001 0.0005 0.0002 0.0001 <0.0001 0.0002 0.0001 <0.0001 <0.0001 0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
0.0055 0.0126 0.0091 0.0062 0.0039 0.0092 0.0072 0.0052 0.0034 0.0062 0.0052 0.0039 0.0026 0.0040 0.0034 0.0027 0.0018
<0.0001 0.0005 0.0002 0.0001 <0.0001 0.0002 0.0001 <0.0001 <0.0001 0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
0.0046 0.0114 0.0081 0.0054 0.0033 0.0081 0.0062 0.0045 0.0028 0.0053 0.0043 0.0032 0.0022 0.0034 0.0028 0.0022 0.0015
<0.0001 0.0005 0.0002 0.0001 <0.0001 0.0002 0.0001 <0.0001 <0.0001 0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
Table 4 Comparison of the Matlab model with the MCNP simulations. Values are in n/s or in p/ s. Matlab
MCNP
Rel. Err.
1401 Neutron Photon
269.90 125.39
259.10 121.96
0.042 0.028
1430 Neutron Photon
261.94 125.39
250.83 121.96
0.044 0.028
2810 Neutron Photon
219.46 125.62
209.11 122.16
0.050 0.028
4201 Neutron Photon
175.58 125.85
167.25 122.41
0.050 0.028
4230 Neutron Photon
160.68 125.85
152.92 122.42
0.051 0.028
transmission probabilities and comparing the Matlab model with the MCNP simulations. Tables 5–7 show the comparison of the two calculations. Considering the promising results of the model (all values except one are within the 5% error with the respective MCNP simulation), the concept has been applied to a generic storage rack.
Maintaining the same geometry of the fuel rack, assemblies with different burnup and cooling time have been introduced in both calculations to form the loading configuration reported in Fig. 3. The central fuel assembly (depicted in orange) is the one under investigation. The results from this generic test case are reported in Table 7 in the ‘TEST – N’ and ‘TEST – P’ columns. The relative source strength of each assembly is computed from the total neutron or photon emission available in the Origen calculations. Confirming the results from the uniform rack, also in the generic loading pattern the Matlab model has a very good agreement with the Monte Carlo simulation, with a relative error that is always within the 7%. As in the previous cases the photon simulations show even better agreement than the neutron simulations, but in both cases it is possible to state that the great improvement in the computational time outbalances the relative error with the MCNP simulation. The advantage of having several detectors inside the same fuel assembly is evident in the test case. The loading of the storage rack in this case is not uniform and leads to a different contribution of each assembly to the flux values. Table 8 reports the neutron and photon flux for the different fuel assemblies modeled in the study. By adding multiple measurement positions it is possible to have this indication and to cross-check the operator’s declaration.
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R. Rossa, P. Peerani / Annals of Nuclear Energy 57 (2013) 256–262 Table 5 Comparison of the Matlab model with the MCNP simulations. Values are in n/s or in p/s. Pos.
WH 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16
1401N
1401P
1430N
1430P
Matlab
MCNP
Rel. Err.
Matlab
MCNP
Rel. Err.
Matlab
MCNP
Rel. Err.
Matlab
MCNP
Rel. Err.
269.90 203.83 234.14 233.81 204.03 234.14 250.94 249.97 233.43 216.78 251.38 250.39 216.16 204.12 216.59 217.01 203.59
259.10 204.31 224.19 224.61 204.04 224.88 249.42 254.05 224.86 226.10 250.93 251.16 223.43 202.96 225.21 227.05 203.74
0.0417 0.0023 0.0444 0.0409 0.0001 0.0412 0.0061 0.0160 0.0381 0.0412 0.0018 0.0030 0.0326 0.0057 0.0383 0.0442 0.0007
125.39 116.75 123.84 123.14 116.62 124.03 127.21 124.70 123.53 120.30 127.17 126.79 120.68 116.36 120.57 120.49 116.62
121.96 116.22 121.32 121.65 116.24 122.42 125.95 125.88 120.83 122.32 127.17 126.48 121.81 117.02 121.75 122.40 116.80
0.0281 0.0045 0.0208 0.0122 0.0032 0.0131 0.0099 0.0094 0.0223 0.0165 0.0000 0.0024 0.0093 0.0056 0.0097 0.0156 0.0015
261.94 198.12 227.24 227.20 198.54 227.69 243.60 242.68 226.86 210.36 244.14 243.28 209.98 198.22 210.52 210.69 198.08
250.83 199.52 217.05 218.28 199.08 218.83 241.85 246.33 218.63 218.70 243.32 244.28 217.03 198.71 218.76 220.03 198.13
0.0443 0.0070 0.0470 0.0409 0.0027 0.0405 0.0072 0.0148 0.0376 0.0382 0.0034 0.0041 0.0325 0.0024 0.0377 0.0424 0.0003
125.39 116.75 123.84 123.14 116.62 124.03 127.20 124.70 123.52 120.31 127.17 126.79 120.68 116.36 120.57 120.49 116.62
121.96 116.22 121.32 121.65 116.25 122.42 125.95 125.88 120.83 122.32 127.17 126.48 121.81 117.02 121.75 122.40 116.80
0.0281 0.0045 0.0208 0.0123 0.0032 0.0131 0.0100 0.0094 0.0223 0.0164 0.0000 0.0024 0.0093 0.0056 0.0097 0.0156 0.0015
Table 6 Comparison of the Matlab model with the MCNP simulations. Values are in n/s or in p/s. Pos.
WH 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16
2810N
2810P
4201N
4201P
Matlab
MCNP
Rel. Err.
Matlab
MCNP
Rel. Err.
Matlab
MCNP
Rel. Err.
Matlab
MCNP
Rel. Err.
219.46 168.02 191.79 191.22 167.65 191.78 203.95 202.96 190.72 176.98 204.39 203.60 176.20 167.86 176.98 177.36 167.75
209.11 167.90 182.98 183.01 168.55 184.05 201.41 204.78 183.03 184.63 202.88 203.63 181.70 167.50 183.49 183.24 167.30
0.0495 0.0007 0.0482 0.0449 0.0053 0.0420 0.0126 0.0089 0.0420 0.0414 0.0074 0.0002 0.0303 0.0021 0.0355 0.0321 0.0027
125.62 116.99 124.07 123.37 116.85 124.25 127.47 124.94 123.76 120.49 127.44 127.02 120.91 116.55 120.82 120.71 116.86
122.16 116.42 121.53 121.86 116.54 122.62 126.17 126.17 121.11 122.50 127.39 126.74 122.03 117.20 121.92 122.57 117.01
0.0283 0.0048 0.0209 0.0124 0.0027 0.0133 0.0103 0.0097 0.0218 0.0164 0.0004 0.0022 0.0092 0.0056 0.0090 0.0151 0.0013
175.58 134.42 153.14 152.84 134.13 153.88 163.53 162.51 152.48 141.89 164.64 163.40 141.44 133.79 141.84 142.04 133.97
167.25 135.11 146.55 147.48 135.40 148.66 161.90 165.00 146.51 148.19 163.54 163.07 146.06 132.81 146.61 147.41 133.88
0.0498 0.0051 0.0450 0.0363 0.0094 0.0351 0.0101 0.0151 0.0407 0.0425 0.0067 0.0020 0.0316 0.0074 0.0325 0.0365 0.0007
125.85 117.21 124.33 123.64 117.05 124.49 127.69 125.12 124.04 120.70 127.68 127.26 121.16 116.76 121.08 120.96 117.08
122.41 116.63 121.82 122.11 116.79 122.81 126.47 126.39 121.31 122.69 127.64 126.93 122.29 117.48 122.15 122.76 117.21
0.0281 0.0050 0.0206 0.0126 0.0023 0.0137 0.0096 0.0100 0.0225 0.0162 0.0003 0.0026 0.0093 0.0061 0.0087 0.0147 0.0011
Table 7 Comparison of the Matlab model with the MCNP simulations. Values are in n/s or in p/s. Pos.
WH 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16
4230N
4230P
TEST – N
TEST – P
Matlab
MCNP
Rel. Err.
Matlab
MCNP
Rel. Err.
Matlab
MCNP
Rel. Err.
Matlab
MCNP
Rel. Err.
160.68 123.92 140.42 140.13 123.62 140.95 149.92 148.83 139.87 129.97 150.91 149.26 129.90 123.56 130.03 130.17 123.42
152.92 124.09 133.75 135.28 124.35 137.00 148.63 150.78 134.36 136.04 149.69 149.36 133.85 121.71 134.18 134.93 122.92
0.0508 0.0013 0.0498 0.0359 0.0059 0.0288 0.0087 0.0129 0.0410 0.0446 0.0081 0.0006 0.0295 0.0152 0.0309 0.0352 0.0041
125.85 117.20 124.33 123.64 117.05 124.48 127.69 125.12 124.03 120.70 127.68 127.26 121.15 116.76 121.07 120.95 117.07
122.42 116.62 121.81 122.11 116.78 122.81 126.47 126.38 121.30 122.68 127.65 126.93 122.29 117.48 122.14 122.76 117.21
0.0281 0.0050 0.0207 0.0126 0.0023 0.0137 0.0096 0.0100 0.0225 0.0162 0.0003 0.0026 0.0093 0.0061 0.0087 0.0147 0.0011
49.29 32.75 39.36 40.78 37.68 37.75 44.96 46.38 42.47 40.11 47.25 48.21 44.38 39.64 44.35 45.48 43.05
48.95 34.13 39.70 41.55 38.28 39.25 45.79 48.08 43.71 42.31 48.23 49.27 45.68 42.36 46.31 47.37 45.03
0.0070 0.0403 0.0087 0.0187 0.0157 0.0384 0.0182 0.0353 0.0284 0.0518 0.0205 0.0215 0.0285 0.0643 0.0422 0.0398 0.0439
9.72 9.99 10.05 9.88 9.35 10.27 10.05 9.68 10.68 10.83 10.62 10.79 11.53 12.78 12.15 12.34 13.59
10.23 10.25 9.96 9.89 9.68 10.17 10.24 10.38 10.65 10.73 10.65 10.75 11.44 13.45 12.06 12.00 14.25
0.0498 0.0260 0.0090 0.0011 0.0348 0.0094 0.0183 0.0674 0.0025 0.0099 0.0029 0.0039 0.0080 0.0497 0.0075 0.0283 0.0463
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Fig. 3. Composition of the loading pattern for the generic test.
Table 8 Neutron and photon flux for the different fuel assemblies modeled in the study. Fuel assembly
N flux (n/s/tHM)
P flux (pn/s/tHM)
1401 1430 2801 2830 4201 4230
6.741E + 06 2.851E + 06 2.071E + 08 6.111E + 07 7.843E + 08 2.432E + 08
1.290E + 16 8.289E + 14 2.258E + 16 1.692E + 15 3.160E + 16 2.470E + 15
6. Conclusions This paper presented a simplified model for the estimation of the neutron and photon flux inside a BWR fuel assembly. The use of the model can be rather general, but in this case it has been used to speed up the feasibility study of an innovative NDA technique for the safeguards of spent nuclear fuel. The first part of the study has been the modeling of the storage rack in which a total of nine spent fuel assemblies can be inserted. By running a reduced set of Monte Carlo simulations it has been possible to calculate the transmission factors for each measurement position inside the fuel assembly under investigation. The testing of the model considered first a uniform pattern for the storage rack, obtaining very good agreement between the model and the MCNP simulation.
The last part of the validation consisted in the simulation of a generic loading pattern of assemblies with different burnup and cooling time (hence neutron and photon emissions). Also in this general case the Matlab model performed very well, scoring a relative error between the model and the MCNP simulation of less than 7%. Thanks to the Matlab script, the user needs only to insert the desired burnup and cooling time of the nine assemblies to have the results. The MCNP simulations on the other hand require few hours to give the values of the neutron and photon fluxes with a statistical uncertainty of less than 1%. Given this significant reduction of computational time the Matlab model can be used in the first stages of a feasibility study to get a rather good approximation in a very short time frame. References Bowman, S., et al., 1998. ORIGEN-ARP: Isotope Generation and Depletion Code, CCC732, ORNL/NUREG/CSD-2/V1/R6, September 1998. Cerne, S., Hermann, O., Westfall, R., 1987. Reactivity and Isotopic Composition of spent PWR fuel as a function of Initial Enrichment, Burnup, and Cooling Time, ORNL/CSD/TM-244, Oak Ridge National Laboratory, October 1987. Eliasson, A., et al., 2012. Private, communications, April–May 2012. Ham, Y.S., 2012. Private, Communications, June 2012. Ham, Y.S., Sitaraman, S., Shin, H., Eom, S., Kim, H., 2009. Experimental Validation of the Methodology for Partial Defect Verification of the Pressurized Water Reactor Spent Fuel Assemblies – INMM 2009, Tucson, AZ, July 2009 – LLNLCONF-413954. MATLAB, 2012. The Language Of Technical Computing.: www.mathworks.com. Pelowitz, D., 2011. MCNPX User’s Manual Version 2.7.0, Los Alamos National Laboratory, April 2011 . Reilly et al., 1991. Passive Nondestructive Assay of Nuclear Materials, LA-UR-90732, March 1991. Sitaraman, S., Ham, Y.S., 2009. Symmetric Pin Diversion Detection using a Partial Defect Detector (PDET) – Lawrence Livermore National Laboratory – LLNLCONF-413603.
Contents lists available at SciVerse ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Development of a model for the approximation of the neutron and photon flux in a BWR spent fuel assembly Riccardo Rossa 1, Paolo Peerani ⇑ European Commission, Joint Research Centre, ITU, Ispra (VA), Italy
a r t i c l e
i n f o
Article history: Received 10 August 2012 Received in revised form 16 January 2013 Accepted 17 January 2013 Available online 15 March 2013 Keywords: Nuclear safeguards Neutron detectors Gamma detectors
a b s t r a c t This paper proposes a simplified model built with Matlab to compute an approximation of the neutron and photon flux in a BWR spent fuel assembly in a pond. Starting from a reduced number of Monte Carlo simulations, a set of transmission probabilities has been calculated. These values allow the estimation of the particle flux inside a fuel assembly placed in a generic storage rack. This calculation is possible provided the transmission probability has been calculated for the desired value of burnup and cooling time of the assemblies in the rack. The validity of the model has been tested first with a uniform pattern of the storage rack and finally with a generic configuration. Reference values from the equivalent Monte Carlo simulations show very good agreement and the relative error between the two measures is always within few percents. The main advantage of this simplified model is the great reduction of computational time required to perform the estimation and the fact that the basic idea behind the model can be applied to any fuel geometry and type of storage pond. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Over 80% of the material placed under safeguards today is in the form of spent fuel assemblies and one of the main way to verify it is by Non-Destructive Assays (NDAs). The main goal for the safeguards inspections is to verify that no material has been diverted to other purposes by detecting the eventual gross and partial defect from the fuel assembly. Gross defect is the replacement of an entire fuel assembly with a dummy made of other material (e.g. natural uranium or stainless steel), while partial defect concerns the removal of fuel pins inside a fuel assembly. Current NDA techniques rely on total neutron and gamma interaction detectors to perform the measurements. The most common instruments for the safeguards verifications are the Digital Cherenkov Viewing Device (DCVD), the Spent Fuel Attribute Tester (SFAT) and the Fork detector (FDET). The DCVD is based on the emission of the Cherenkov radiation by spent fuel assemblies. This radiation arises when a particle travels with a speed higher than the speed of light in the medium (e.g. water in the spent fuel pool). Spent fuel assemblies are strong sources of beta particles, gamma rays and neutrons, and all these particles can produce Cerenkov light (directly or indirectly). The SFAT couples a gamma detector (such as CdZnTe) with customized collimator/shielding and a multichannel analyzer (MCA). ⇑ Corresponding author. Tel.: +39 0332 785625; fax: +39 0332 785072. 1
E-mail address: [email protected] (P. Peerani). Currently at SCK-CEN in Mol (Belgium).
0306-4549/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.anucene.2013.01.021
This instrument verifies the spent fuel by detecting the presence of the Cs-137 peak that is by far the main gamma emission in an irradiated fuel assembly. The Fork detector couples two sets of ion chambers and fission chambers for measuring opposite sides of the fuel assembly simultaneously. Each arm contains an ionization chamber to measure the total gamma-ray output and two fission chambers to compute the neutron flux (Reilly et al., 1991). Current techniques can reach a satisfactory level of accuracy only if the burnup and cooling time are known; this requires that these data are provided by the operator. This is why several research centers and international agencies are putting significant effort to develop more precise measurement methods that allow deriving conclusions without relying on information provided by the operator. The European Commission with the JRC–ITU located in Ispra is studying the application of a novel technology (the PDET detector developed by the Lawrence Livermore National Laboratories) to BWR fuel assemblies immersed in a spent fuel pond. This detector is composed of a series of neutron and gamma detectors to be inserted within the fuel assembly that is being verified. The Partial Defect Tester (also known as PDET) employs a set of neutron and photon detectors to have a spatial distribution of the two fluxes within a fuel assembly. This experimental device has been designed, modeled and tested by LLNL with PWR assemblies (Sitaraman and Ham, 2009; Ham et al., 2009), considering that this type of assemblies allows the insertion of multiple detectors in the guide tubes already
R. Rossa, P. Peerani / Annals of Nuclear Energy 57 (2013) 256–262
Fig. 1. MCNP model of the BWR fuel assembly. The numbers and letters refer to the measurement positions (being WH the Water Hole).
257
present in the geometry. The guide tubes are used for the insertion of the control rods during normal operations and, once the assembly is stored in the spent fuel pool, they provide room for the insertion of small detectors. Since each fuel pin emits neutrons and photons according to its history (namely burnup and cooling time) the diversion of some pins will alter the magnitude of the neutron and photon flux in the fuel assembly cross section. It is the distortion of the expected flux shape that allows the inspector to detect a gross or partial defect. The results reported by LLNL in (Sitaraman and Ham, 2009; Ham et al., 2009) suggest the capability for the PDET to detect a gross defect without the support of the operator’s data. This aspect, coupled with the fact that the assembly under investigation does not have to be moved from the storage position, is a clear advantage from the current NDA techniques. Moreover Ham and coworkers have demonstrated the capability of PDET to detect a partial defect at a level of removal of a certain number of pins. It is difficult to state exactly which the minimum detectable number of removed pins is. It has been shown that even the removal of eight pins (corresponding to 3% in a 17 17 fuel assembly) can be detected if the pins are clustered together. Probably a higher number of pins can be removed and remain undetected with a more clever diversion strategy (dispersed symmetric removal). Anyway it will be impossible to maintain the flux profile unchanged when the diversion will exceed 20–25% of
Fig. 2. Model of the storage rack. The central fuel assembly under investigation is depicted in white and has the 16 measurement positions colored in orange. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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the total number of pins. This is well below the current target of partial defect detection stated by IAEA (removal of 50% of fuel). The insertion of multiple detectors inside a PWR assembly does not have major technical problem, but the situation changes when the same concept is applied to a BWR assembly. A generic BWR assembly contains less fuel pins compared to a PWR assembly (e.g. 8 8 lattice instead of 17 17), but these have a larger diameter and pitch, resulting in similar external dimension (a square of about 16 cm versus the 22 of a PWR). However, inside the BWR assembly there are no guide tubes due to the different geometry of control rods (generally having a cruciform shape with blades inserted between neighboring fuel elements. In some cases there might be water holes used to have better neutron moderation during normal operations. In the BWR assembly considered in this study there is only one central water hole. During the feasibility study for the application of the PDET to BWR assemblies an issue that has been investigated was the influence of the neighbor assemblies to the measured assembly. Considering that most of the spent fuel is currently stored under water in the spent fuel pond, the Monte Carlo model considered a 3 3 storage rack. 2. Monte Carlo model 2.1. Geometry of the fuel assembly and storage rack The reference model for this study will be the 8 8 ASEA BWR fuel (Fig. 1). This type of assembly has one central water hole, used in normal condition to have better neutron moderation. This hole appears like the most suitable location where inserting small neutron and gamma detectors. Anyway the availability of a single measurement point would rule out the possibility to detect a diversion using radiation profiles without relying on operator’s declaration. This is because there can be several combinations of burnup and cooling time that will give the same ratio between the neutron and photon flux. Therefore the identification of the irradiation history of the fuel assembly cannot be done unequivocally. Considering the suggestions from LLNL (Ham, 2012), due to the larger distance between the fuel pins, additional 16 measurement positions have been identified inside the assembly. These measurement locations are shown in Fig. 1 and are depicted in red.2 The storage rack for the study has been based on detailed information of the Swedish interim storage facility CLAB (Eliasson et al., 2012). This installation has 10 ponds containing storage baskets with spent fuel assemblies. There are three common types of baskets which are filled by both BWR and PWR assemblies. All the types of assemblies stored in CLAB can be inserted in all three types of baskets. The geometry considered in this study contains nine BWR assemblies and it is a reduction of a 25-positions basket. In this configuration there is a small water gap between the fuel and the basket and the walls of the storage basket are made of borated steel (at least 1.6% of Boron). The spent fuel pools are filled with water that is not borated and this will influence the neutron signal of the detectors. Fig. 2 shows the lattice of the storage rack. 2.2. Spent fuel composition and source terms The spent fuel compositions have been calculated with ORIGENARP (Bowman et al., 1998) under the conditions: – Initial Enrichment (IE): 3%.
2 For interpretation of color in Fig. 1, the reader is referred to the web version of this article.
– Burnup (BU): 14–28–42 GWd/t. – Cooling Time (CT): 1–30 years. Each irradiation cycle lasted 350 days and two successive irradiation cycles have been separated by 30 days of cooling time. Adjusting the power level to 40 MW/t, each irradiation cycle resulted in a burnup of 14 GWd/t. Considering that the cooling time had a very small influence on the detectors’ response, only two values for that parameter have been considered. In order to easily identify the characteristics of the fuel assemblies used for the simulations, they have been identified by four numbers: the first two represent the burnup in GWd/t while the other two are the years of cooling time after discharge. The list of isotopes in the spent fuel used in the Monte Carlo simulations (Pelowitz, 2011) has been reduced to 37 (both fission products and minor actinides) which represents the principal absorbers (Cerne et al., 1987). The list is further reduced to 25 for the simulations involving photons, since the photon libraries account only for elements and not for the single isotopes. Neutrons are generated within all pins containing spent fuel in all the fuel assemblies. The source intensity is proportional to the total neutron emission of the assembly; value that is taken from the Origen simulations. All pins within a fuel assembly are considered having the same source intensity. The spectrum used for the neutron source is a Watt spectrum with parameters of Cm-244, which is accounting for over 90% of the total neutron source in the spent fuel. As in the case of neutron generation, photons are generated taking into account the total gamma emission of the fuel pin. All pins within a fuel assembly are considered having the same source intensity. The photon source has been modeled as a line at 662 keV, the main emission of Cs-137, which is accounting for over 80% of the total photon source in the spent fuel after some years of cooling time. 3. Model of the transmission probabilities 3.1. Basic concept of the model The goal of the model is to provide an initial estimate of the neutron and photon flux in the measurement positions without running additional MCNP simulations. This model accounts for assemblies with different burnup and cooling time, allowing the building of a generic storage pattern. The signal in the water hole measurement position in the central fuel assembly will have a contribution from all eight neighboring assemblies and from the central assembly itself:
R / ðS1 þ S3 þ S7 þ S9 Þ PCO þ ðS2 þ S4 þ S6 þ S8 Þ PEO þ S5 POO where R is the response of the detector placed in the water hole (e.g. number of neutrons/photons), S1, S3, S7, and S9 are the source terms of the corner assemblies, S2, S4, S6, and S8 are the source terms of the lateral assemblies, S5 is the source term of the central assembly, PCO is the transmission probability from a corner assembly to the central one, PEO is the transmission probability from a lateral assembly to the central one, and POO is the transmission probability within the central assembly. The transmission probability is defined as the probability that a particle emitted in an assembly (corner, lateral, or central) will reach the measurement position in the central fuel assembly where the PDET is inserted. This formula has been generalized for the calculations of the other 16 measurement positions:
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X RK / SI PIK I
where RK is the response of the K-th detector (K = 1, 2, . . ., 16), SI is the source terms of one assemblies (I = 1, 2, . . ., 9), PIK is the transmission probability from the assembly I to the measurement position K. 3.2. Calculation of the transmission probabilities The transmission probabilities have been calculated running few modified Monte Carlo simulations of the storage rack. These simulations contained a complete rack of identical fuel assemblies (i.e. same isotopic composition) but the particles are emitted by only one fuel assembly. Nevertheless the other eight assemblies are still in the MCNP model, to account for the absorption and the scattering of particles against other fuel assemblies and therefore to provide a more accurate simulation of the real situation. Considering the symmetry of the system only three simulations were needed, placing as source term the central assembly (O–O), one lateral assembly (E–O), and one corner assembly (C–O). With this procedure it is possible to compute the amount of particles that are coming to the detector area using the flux tally F4 in the MCNP code. The transmission probabilities (POO, PEO or PCO respectively) are obtained by multiplying the flux tally by the volume of the detector itself. Tables 1–3 (first row) show the transmission probabilities for the water hole computed according to the procedure described above. The other rows contain the probabilities for other positions described later in the article. The statistical uncertainty of the simulations is always below 1%. By looking at the values in the tables it is evident that the neutrons are traveling in the storage rack much more than the photons. This is due to the high attenuation of the high-Z materials present in the storage pool (e.g. uranium in the fuel assemblies). The use of borated water will lower the transmission probability for neutrons, while letting roughly unchanged the photon absorption. The very low probability values for the set of C–O simulations support the decision to consider only the 3 3 lattice instead of the full 5 5 geometry of the real storage basket. 4. Validation of the model The transmission probabilities calculated in the previous chapter have been introduced in the Matlab code (MATLAB, 2012) for
the building of the simplified model. This script has been written in order to speed up calculations and minimize the input required by the user. With this code, the user has only to insert the four-digit identifier for the fuel assemblies according to the convention explained on Section 2.2 of this article. Then the program takes as input the transmission probabilities corresponding to the pattern of the storage rack and calculates the neutron and photon signal in the central fuel assembly. The formula used to obtain the results is the general relationship reported in Section 3.1. The first set of tests concerned a uniform storage rack, composed of nine fuel assemblies with the same isotopic composition and source term. Table 4 shows the results from a full MCNP modelling and the simplified model using Matlab to combine the three transmission probabilities and the fuel history information, and reporting also the relative error between the two calculations. Only the value of the fluxes in the water hole is considered at the moment and reported in Table 4. The model will be extended to the other measurement positions in the next section. From these initial results, the model seems to approximate very well the Monte Carlo simulations, with an agreement of around 5% for the neutron population and 3% for the photon flux. The larger discrepancies for neutrons are due to the more complex physical modeling of transport depending on many variables. The relative error between the two calculations can be attributed to the statistical uncertainty of the MCNP model and to the approximation of symmetry of the central water hole. This is not entirely correct because the channel is slightly moved from the center of the fuel assembly as it is shown in Fig. 1. Looking at the numerical values it is evident that using only the signal of the water hole it will not be possible to have an indication of the irradiation history of the fuel assembly. This is because the values are so similar that will be within the measurement error of the real instrumentation. Therefore the same model has been applied to additional positions, in order to have multiple values of both fluxes to try and have a unique signature dependent on the burnup and cooling time of the assembly. 5. Extension to the other measurement positions As shown in Fig. 1, the dimensions and geometry of the BWR assembly seem to allow the insertion of detectors between the single fuel pins. A total of 16 positions have been considered in this stage of the analysis, using the same concept for the calculation of the
Table 1 Transmission probabilities. Source assembly: central position (O–O). Pos.
OO1401N
OO1401P
OO1430N
OO1430P
OO2810N
OO2810P
OO4201N
OO4201P
OO4230N
OO4230P
WH 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16
0.1351 0.0892 0.1077 0.1073 0.0895 0.1077 0.1302 0.1291 0.1069 0.1079 0.1307 0.1296 0.1072 0.0896 0.1077 0.1082 0.0890
0.0130 0.0099 0.0115 0.0114 0.0099 0.0115 0.0133 0.0130 0.0114 0.0114 0.0133 0.0132 0.0115 0.0098 0.0115 0.0114 0.0099
0.1326 0.0876 0.1056 0.1054 0.0881 0.1060 0.1280 0.1269 0.1052 0.1059 0.1286 0.1276 0.1053 0.0877 0.1059 0.1063 0.0875
0.0130 0.0099 0.0115 0.0114 0.0099 0.0115 0.0133 0.0130 0.0114 0.0114 0.0133 0.0132 0.0115 0.0098 0.0115 0.0114 0.0099
0.1189 0.0788 0.0951 0.0946 0.0784 0.0952 0.1150 0.1139 0.0939 0.0949 0.1155 0.1146 0.0941 0.0786 0.0950 0.0953 0.0785
0.0130 0.0099 0.0115 0.0114 0.0099 0.0115 0.0133 0.0130 0.0114 0.0114 0.0133 0.0133 0.0115 0.0099 0.0115 0.0115 0.0099
0.1052 0.0692 0.0837 0.0831 0.0689 0.0843 0.1018 0.1007 0.0829 0.0838 0.1031 0.1017 0.0831 0.0685 0.0835 0.0840 0.0687
0.0131 0.0099 0.0115 0.0114 0.0099 0.0115 0.0133 0.0130 0.0115 0.0115 0.0133 0.0133 0.0115 0.0099 0.0115 0.0115 0.0099
0.1000 0.0656 0.0794 0.0787 0.0652 0.0797 0.0970 0.0957 0.0788 0.0793 0.0981 0.0962 0.0789 0.0651 0.0790 0.0796 0.0650
0.0131 0.0099 0.0115 0.0114 0.0099 0.0115 0.0133 0.0130 0.0115 0.0115 0.0133 0.0133 0.0115 0.0099 0.0115 0.0115 0.0099
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Table 2 Transmission probabilities. Source assembly: lateral position (E–O). Pos.
EO1401N
EO1401P
EO1430N
EO1430P
EO2810N
EO2810P
EO4201N
EO4201P
EO4230N
EO4230P
WH 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16
0.0320 0.0377 0.0448 0.0447 0.0377 0.0278 0.0327 0.0334 0.0279 0.0197 0.0230 0.0232 0.0198 0.0132 0.0153 0.0153 0.0132
0.0003 0.0014 0.0017 0.0017 0.0014 0.0004 0.0004 0.0004 0.0004 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001
0.0308 0.0367 0.0436 0.0435 0.0366 0.0270 0.0316 0.0322 0.0268 0.0190 0.0221 0.0222 0.0189 0.0126 0.0146 0.0145 0.0127
0.0003 0.0014 0.0017 0.0017 0.0014 0.0004 0.0004 0.0004 0.0004 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001
0.0247 0.0312 0.0372 0.0371 0.0313 0.0217 0.0257 0.0262 0.0218 0.0147 0.0171 0.0173 0.0149 0.0094 0.0108 0.0109 0.0096
0.0003 0.0014 0.0017 0.0017 0.0014 0.0004 0.0004 0.0004 0.0004 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001
0.0185 0.0248 0.0299 0.0299 0.0249 0.0163 0.0195 0.0199 0.0164 0.0103 0.0122 0.0124 0.0104 0.0062 0.0073 0.0072 0.0064
0.0003 0.0014 0.0017 0.0017 0.0014 0.0004 0.0004 0.0004 0.0004 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001
0.0164 0.0230 0.0273 0.0275 0.0230 0.0146 0.0173 0.0179 0.0147 0.0090 0.0106 0.0107 0.0090 0.0053 0.0062 0.0061 0.0054
0.0003 0.0014 0.0017 0.0017 0.0014 0.0004 0.0004 0.0004 0.0004 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001
Table 3 Transmission probabilities. Source assembly: corner position (C–O). Pos.
CO1401N
CO1401P
CO1430N
CO1430P
CO2810N
CO2810P
CO4201N
CO4201P
CO4230N
CO4230P
WH 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16
0.0115 0.0206 0.0164 0.0123 0.0084 0.0164 0.0140 0.0111 0.0077 0.0122 0.0109 0.0088 0.0064 0.0084 0.0077 0.0064 0.0048
<0.0001 0.0005 0.0002 0.0001 <0.0001 0.0002 0.0001 <0.0001 <0.0001 0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
0.0110 0.0200 0.0158 0.0119 0.0081 0.0158 0.0134 0.0107 0.0073 0.0116 0.0103 0.0084 0.0061 0.0081 0.0073 0.0061 0.0045
<0.0001 0.0005 0.0002 0.0001 <0.0001 0.0002 0.0001 <0.0001 <0.0001 0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
0.0084 0.0167 0.0127 0.0092 0.0061 0.0127 0.0103 0.0080 0.0055 0.0091 0.0078 0.0061 0.0044 0.0061 0.0054 0.0044 0.0032
<0.0001 0.0005 0.0002 0.0001 <0.0001 0.0002 0.0001 <0.0001 <0.0001 0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
0.0055 0.0126 0.0091 0.0062 0.0039 0.0092 0.0072 0.0052 0.0034 0.0062 0.0052 0.0039 0.0026 0.0040 0.0034 0.0027 0.0018
<0.0001 0.0005 0.0002 0.0001 <0.0001 0.0002 0.0001 <0.0001 <0.0001 0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
0.0046 0.0114 0.0081 0.0054 0.0033 0.0081 0.0062 0.0045 0.0028 0.0053 0.0043 0.0032 0.0022 0.0034 0.0028 0.0022 0.0015
<0.0001 0.0005 0.0002 0.0001 <0.0001 0.0002 0.0001 <0.0001 <0.0001 0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
Table 4 Comparison of the Matlab model with the MCNP simulations. Values are in n/s or in p/ s. Matlab
MCNP
Rel. Err.
1401 Neutron Photon
269.90 125.39
259.10 121.96
0.042 0.028
1430 Neutron Photon
261.94 125.39
250.83 121.96
0.044 0.028
2810 Neutron Photon
219.46 125.62
209.11 122.16
0.050 0.028
4201 Neutron Photon
175.58 125.85
167.25 122.41
0.050 0.028
4230 Neutron Photon
160.68 125.85
152.92 122.42
0.051 0.028
transmission probabilities and comparing the Matlab model with the MCNP simulations. Tables 5–7 show the comparison of the two calculations. Considering the promising results of the model (all values except one are within the 5% error with the respective MCNP simulation), the concept has been applied to a generic storage rack.
Maintaining the same geometry of the fuel rack, assemblies with different burnup and cooling time have been introduced in both calculations to form the loading configuration reported in Fig. 3. The central fuel assembly (depicted in orange) is the one under investigation. The results from this generic test case are reported in Table 7 in the ‘TEST – N’ and ‘TEST – P’ columns. The relative source strength of each assembly is computed from the total neutron or photon emission available in the Origen calculations. Confirming the results from the uniform rack, also in the generic loading pattern the Matlab model has a very good agreement with the Monte Carlo simulation, with a relative error that is always within the 7%. As in the previous cases the photon simulations show even better agreement than the neutron simulations, but in both cases it is possible to state that the great improvement in the computational time outbalances the relative error with the MCNP simulation. The advantage of having several detectors inside the same fuel assembly is evident in the test case. The loading of the storage rack in this case is not uniform and leads to a different contribution of each assembly to the flux values. Table 8 reports the neutron and photon flux for the different fuel assemblies modeled in the study. By adding multiple measurement positions it is possible to have this indication and to cross-check the operator’s declaration.
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R. Rossa, P. Peerani / Annals of Nuclear Energy 57 (2013) 256–262 Table 5 Comparison of the Matlab model with the MCNP simulations. Values are in n/s or in p/s. Pos.
WH 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16
1401N
1401P
1430N
1430P
Matlab
MCNP
Rel. Err.
Matlab
MCNP
Rel. Err.
Matlab
MCNP
Rel. Err.
Matlab
MCNP
Rel. Err.
269.90 203.83 234.14 233.81 204.03 234.14 250.94 249.97 233.43 216.78 251.38 250.39 216.16 204.12 216.59 217.01 203.59
259.10 204.31 224.19 224.61 204.04 224.88 249.42 254.05 224.86 226.10 250.93 251.16 223.43 202.96 225.21 227.05 203.74
0.0417 0.0023 0.0444 0.0409 0.0001 0.0412 0.0061 0.0160 0.0381 0.0412 0.0018 0.0030 0.0326 0.0057 0.0383 0.0442 0.0007
125.39 116.75 123.84 123.14 116.62 124.03 127.21 124.70 123.53 120.30 127.17 126.79 120.68 116.36 120.57 120.49 116.62
121.96 116.22 121.32 121.65 116.24 122.42 125.95 125.88 120.83 122.32 127.17 126.48 121.81 117.02 121.75 122.40 116.80
0.0281 0.0045 0.0208 0.0122 0.0032 0.0131 0.0099 0.0094 0.0223 0.0165 0.0000 0.0024 0.0093 0.0056 0.0097 0.0156 0.0015
261.94 198.12 227.24 227.20 198.54 227.69 243.60 242.68 226.86 210.36 244.14 243.28 209.98 198.22 210.52 210.69 198.08
250.83 199.52 217.05 218.28 199.08 218.83 241.85 246.33 218.63 218.70 243.32 244.28 217.03 198.71 218.76 220.03 198.13
0.0443 0.0070 0.0470 0.0409 0.0027 0.0405 0.0072 0.0148 0.0376 0.0382 0.0034 0.0041 0.0325 0.0024 0.0377 0.0424 0.0003
125.39 116.75 123.84 123.14 116.62 124.03 127.20 124.70 123.52 120.31 127.17 126.79 120.68 116.36 120.57 120.49 116.62
121.96 116.22 121.32 121.65 116.25 122.42 125.95 125.88 120.83 122.32 127.17 126.48 121.81 117.02 121.75 122.40 116.80
0.0281 0.0045 0.0208 0.0123 0.0032 0.0131 0.0100 0.0094 0.0223 0.0164 0.0000 0.0024 0.0093 0.0056 0.0097 0.0156 0.0015
Table 6 Comparison of the Matlab model with the MCNP simulations. Values are in n/s or in p/s. Pos.
WH 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16
2810N
2810P
4201N
4201P
Matlab
MCNP
Rel. Err.
Matlab
MCNP
Rel. Err.
Matlab
MCNP
Rel. Err.
Matlab
MCNP
Rel. Err.
219.46 168.02 191.79 191.22 167.65 191.78 203.95 202.96 190.72 176.98 204.39 203.60 176.20 167.86 176.98 177.36 167.75
209.11 167.90 182.98 183.01 168.55 184.05 201.41 204.78 183.03 184.63 202.88 203.63 181.70 167.50 183.49 183.24 167.30
0.0495 0.0007 0.0482 0.0449 0.0053 0.0420 0.0126 0.0089 0.0420 0.0414 0.0074 0.0002 0.0303 0.0021 0.0355 0.0321 0.0027
125.62 116.99 124.07 123.37 116.85 124.25 127.47 124.94 123.76 120.49 127.44 127.02 120.91 116.55 120.82 120.71 116.86
122.16 116.42 121.53 121.86 116.54 122.62 126.17 126.17 121.11 122.50 127.39 126.74 122.03 117.20 121.92 122.57 117.01
0.0283 0.0048 0.0209 0.0124 0.0027 0.0133 0.0103 0.0097 0.0218 0.0164 0.0004 0.0022 0.0092 0.0056 0.0090 0.0151 0.0013
175.58 134.42 153.14 152.84 134.13 153.88 163.53 162.51 152.48 141.89 164.64 163.40 141.44 133.79 141.84 142.04 133.97
167.25 135.11 146.55 147.48 135.40 148.66 161.90 165.00 146.51 148.19 163.54 163.07 146.06 132.81 146.61 147.41 133.88
0.0498 0.0051 0.0450 0.0363 0.0094 0.0351 0.0101 0.0151 0.0407 0.0425 0.0067 0.0020 0.0316 0.0074 0.0325 0.0365 0.0007
125.85 117.21 124.33 123.64 117.05 124.49 127.69 125.12 124.04 120.70 127.68 127.26 121.16 116.76 121.08 120.96 117.08
122.41 116.63 121.82 122.11 116.79 122.81 126.47 126.39 121.31 122.69 127.64 126.93 122.29 117.48 122.15 122.76 117.21
0.0281 0.0050 0.0206 0.0126 0.0023 0.0137 0.0096 0.0100 0.0225 0.0162 0.0003 0.0026 0.0093 0.0061 0.0087 0.0147 0.0011
Table 7 Comparison of the Matlab model with the MCNP simulations. Values are in n/s or in p/s. Pos.
WH 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16
4230N
4230P
TEST – N
TEST – P
Matlab
MCNP
Rel. Err.
Matlab
MCNP
Rel. Err.
Matlab
MCNP
Rel. Err.
Matlab
MCNP
Rel. Err.
160.68 123.92 140.42 140.13 123.62 140.95 149.92 148.83 139.87 129.97 150.91 149.26 129.90 123.56 130.03 130.17 123.42
152.92 124.09 133.75 135.28 124.35 137.00 148.63 150.78 134.36 136.04 149.69 149.36 133.85 121.71 134.18 134.93 122.92
0.0508 0.0013 0.0498 0.0359 0.0059 0.0288 0.0087 0.0129 0.0410 0.0446 0.0081 0.0006 0.0295 0.0152 0.0309 0.0352 0.0041
125.85 117.20 124.33 123.64 117.05 124.48 127.69 125.12 124.03 120.70 127.68 127.26 121.15 116.76 121.07 120.95 117.07
122.42 116.62 121.81 122.11 116.78 122.81 126.47 126.38 121.30 122.68 127.65 126.93 122.29 117.48 122.14 122.76 117.21
0.0281 0.0050 0.0207 0.0126 0.0023 0.0137 0.0096 0.0100 0.0225 0.0162 0.0003 0.0026 0.0093 0.0061 0.0087 0.0147 0.0011
49.29 32.75 39.36 40.78 37.68 37.75 44.96 46.38 42.47 40.11 47.25 48.21 44.38 39.64 44.35 45.48 43.05
48.95 34.13 39.70 41.55 38.28 39.25 45.79 48.08 43.71 42.31 48.23 49.27 45.68 42.36 46.31 47.37 45.03
0.0070 0.0403 0.0087 0.0187 0.0157 0.0384 0.0182 0.0353 0.0284 0.0518 0.0205 0.0215 0.0285 0.0643 0.0422 0.0398 0.0439
9.72 9.99 10.05 9.88 9.35 10.27 10.05 9.68 10.68 10.83 10.62 10.79 11.53 12.78 12.15 12.34 13.59
10.23 10.25 9.96 9.89 9.68 10.17 10.24 10.38 10.65 10.73 10.65 10.75 11.44 13.45 12.06 12.00 14.25
0.0498 0.0260 0.0090 0.0011 0.0348 0.0094 0.0183 0.0674 0.0025 0.0099 0.0029 0.0039 0.0080 0.0497 0.0075 0.0283 0.0463
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Fig. 3. Composition of the loading pattern for the generic test.
Table 8 Neutron and photon flux for the different fuel assemblies modeled in the study. Fuel assembly
N flux (n/s/tHM)
P flux (pn/s/tHM)
1401 1430 2801 2830 4201 4230
6.741E + 06 2.851E + 06 2.071E + 08 6.111E + 07 7.843E + 08 2.432E + 08
1.290E + 16 8.289E + 14 2.258E + 16 1.692E + 15 3.160E + 16 2.470E + 15
6. Conclusions This paper presented a simplified model for the estimation of the neutron and photon flux inside a BWR fuel assembly. The use of the model can be rather general, but in this case it has been used to speed up the feasibility study of an innovative NDA technique for the safeguards of spent nuclear fuel. The first part of the study has been the modeling of the storage rack in which a total of nine spent fuel assemblies can be inserted. By running a reduced set of Monte Carlo simulations it has been possible to calculate the transmission factors for each measurement position inside the fuel assembly under investigation. The testing of the model considered first a uniform pattern for the storage rack, obtaining very good agreement between the model and the MCNP simulation.
The last part of the validation consisted in the simulation of a generic loading pattern of assemblies with different burnup and cooling time (hence neutron and photon emissions). Also in this general case the Matlab model performed very well, scoring a relative error between the model and the MCNP simulation of less than 7%. Thanks to the Matlab script, the user needs only to insert the desired burnup and cooling time of the nine assemblies to have the results. The MCNP simulations on the other hand require few hours to give the values of the neutron and photon fluxes with a statistical uncertainty of less than 1%. Given this significant reduction of computational time the Matlab model can be used in the first stages of a feasibility study to get a rather good approximation in a very short time frame. References Bowman, S., et al., 1998. ORIGEN-ARP: Isotope Generation and Depletion Code, CCC732, ORNL/NUREG/CSD-2/V1/R6, September 1998. Cerne, S., Hermann, O., Westfall, R., 1987. Reactivity and Isotopic Composition of spent PWR fuel as a function of Initial Enrichment, Burnup, and Cooling Time, ORNL/CSD/TM-244, Oak Ridge National Laboratory, October 1987. Eliasson, A., et al., 2012. Private, communications, April–May 2012. Ham, Y.S., 2012. Private, Communications, June 2012. Ham, Y.S., Sitaraman, S., Shin, H., Eom, S., Kim, H., 2009. Experimental Validation of the Methodology for Partial Defect Verification of the Pressurized Water Reactor Spent Fuel Assemblies – INMM 2009, Tucson, AZ, July 2009 – LLNLCONF-413954. MATLAB, 2012. The Language Of Technical Computing.: www.mathworks.com. Pelowitz, D., 2011. MCNPX User’s Manual Version 2.7.0, Los Alamos National Laboratory, April 2011 . Reilly et al., 1991. Passive Nondestructive Assay of Nuclear Materials, LA-UR-90732, March 1991. Sitaraman, S., Ham, Y.S., 2009. Symmetric Pin Diversion Detection using a Partial Defect Detector (PDET) – Lawrence Livermore National Laboratory – LLNLCONF-413603.