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Operator declaration verification technique for spent fuel at reprocessing facilities
Nuclear Instruments and Methods in Physics Research B 168 (2000) 98±108
www.elsevier.nl/locate/nimb
Operator declaration veri®cation technique for spent fuel at reprocessing facilities William S. Charlton a,*, Bryan L. Fearey a, Charles W. Nakhleh a, Theodore A. Parish b, Robert T. Perry a, Jane Poths a, John R. Quagliano a, William D. Stanbro a, William B. Wilson a a
NIS-7 Stafeguards Systems Group, Los Alamos National Laboratory, Mail Stom E 541, Los Alamos, NM 87545, USA b Texas A&M University, College Station, TX 77843, USA Received 9 March 1999; received in revised form 8 October 1999
Abstract A veri®cation technique for use at reprocessing facilities, which integrates existing technologies to strengthen safeguards through the use of environmental monitoring, has been developed at Los Alamos National Laboratory. This technique involves the measurement of isotopic ratios of stable noble ®ssion gases from on-stack emissions during reprocessing of spent fuel using high-precision mass spectrometry. These results are then compared to a database of calculated isotopic ratios using a data analysis method to determine speci®c fuel parameters (e.g., burnup, fuel type, reactor type, etc.). These inferred parameters can be used to verify operator declarations. The integrated system (mass spectrometry, reactor modeling, and data analysis) has been validated using on-stack measurements during reprocessing of fuel from a US production reactor. These measurements led to an inferred burnup that matched the declared burnup to within 3.9%, suggesting that the current system is sucient for most safeguards applications. Partial system validation using gas samples from literature measurements of power reactor fuel has been reported elsewhere. This has shown that the technique developed here may have some diculty distinguishing pressurized water reactor (PWR) from boiling water reactor (BWR) fuel; however, it consistently can distinguish light water reactor (either PWR or BWR) fuels from other reactor fuel types. Future validations will include advanced power reactor fuels (such as breeder reactor fuels) and research reactor fuels as samples become available. Ó 2000 Elsevier Science B.V. All rights reserved. Keywords: Spent fuel; Reprocessing; Mass spectrometry; Safeguards
1. Introduction
*
Corresponding author. Tel.: +505-665-8576; fax: +505667-7626. E-mail address: [email protected] (W.S. Charlton).
The discovery in 1991 of a large, clandestine weapons program in Iraq led to a call for improvements in international safeguards on nuclear facilities and materials. The International Atomic Energy Agency (IAEA) responded with an eort
0168-583X/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 0 6 3 3 - 3
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called ``Programme 93+2'' to develop new and more ecient safeguards techniques [1]. The product of this eort is known as the ``Model Protocol'' and is described in the IAEA document INFCIRC/540 [2]. INFCIRC/540 provides the basis for States to reach agreements with the IAEA on additional safeguards measures. Among the possible additions to safeguards contemplated in INFCIRC/540 is the use of environmental sampling. Large-scale reprocessing plants pose a particular challenge to IAEA safeguards [3]. One environmental monitoring (EM) technique that may prove widely applicable to the safeguarding of reprocessing facilities is the monitoring of atmospheric noble gas concentrations present in the facilityÕs stack gases [4]. Fissiogenic noble gases are not chemically bound in the spent nuclear fuel. Thus, they are readily released during reprocessing. These gases contain isotopes that allow for the extraction of information concerning reactor type, fuel type, burnup, and operational history. The two most prominent ®ssiogenic noble gases are Xe and Kr. Therefore, these two elements present the most useful signal for these EM techniques. The relative concentrations of the ®ssiogenically produced stable Xe and Kr isotopes depend on the neutron energy spectrum in the reactor, the ®ssioning isotopes, the power level, and the total number of ®ssions. Therefore, the Xe and Kr released from the fuel provide a unique signature of the fuel characteristics. Some previous attempts have been made to make use of these gaseous emissions; however, these studies proved inconclusive [5,6]. Los Alamos National Laboratory (LANL) has been studying advances in EM techniques for use in IAEA safeguards for several years [4,7]. This paper describes the development and application of a technique for estimating several characteristics of spent fuel (e.g., burnup and reactor type) being reprocessed [8]. This technique uses highprecision measurements of stable noble gas isotopic ratios in samples taken from a reprocessing plant exhaust stack. Using sophisticated data analysis techniques, these ratios are coupled with a database of calculated isotopic ratios to infer spent fuel parameters for fuel being reprocessed.
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The information gained from this analysis could be used in an international safeguards regime to help verify declarations made by facility operators. This technique has been partially tested using literature measurements from power reactor fuels, and these validations are presented elsewhere [8,9]. The LANL technique is capable of performing two dierent forms of analysis: the forward and backward analyses. The forward analysis involves the determination and con®rmation of spent fuel burnup from a sample of gas released from reprocessed spent fuel when all information pertaining to the fuel is present (i.e., the reactor type, fuel type, fuel enrichment, operational history, etc.). The backward analysis involves the determination of spent fuel parameters from a gas sample collected during reprocessing of spent fuel when only minimal information is available about the reprocessed fuel. The backward analysis is signi®cantly more complicated and is the main thrust of the work presented in this report. 2. Proposed veri®cation procedure The proposed system couples a unique highprecision mass spectrometer with an extremely accurate ®ssiogenic gas database through the use of two data analysis techniques. The ®ssiogenic gas database contains Xe and Kr ®ssiogenic isotopic ratios as a function of burnup for an extensive set of fuel and reactor types. These ratios were calculated using a series of state-of-the-art reactor analysis codes, and the calculational accuracy has been benchmarked whenever possible [8]. The complete system integration can be seen in Fig. 1. The ®rst step in the use of this technique is to acquire a gas sample on-stack from the reprocessing facility during the dissolution of spent fuel. This gas sample can then be processed using the LANL mass spectrometry system to determine the Xe and Kr isotopic gas ratios due to ®ssion. The current LANL system has been fully developed for determining Xe isotopic ratios; however, the system is still being developed for use in measuring Kr isotopic ratios at comparable levels. These measured ratios (Xe, Kr, or both) are then
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3. Measurement system
Fig. 1. Veri®cation technique overview.
compared to the calculated database using sophisticated data analysis techniques. This results in a set of inferred spent fuel parameters that can include information such as burnup, reactor type, fuel type, and/or operational history. The technique developed here may be used to accurately analyze stable noble gases and characterize spent fuel from reprocessing facilities. Signi®cant advantages in the quantity and quality of inferred information accrue from using as many measured isotopic ratios as possible. The use of an extensive database and multiple data analysis methods results in a highly versatile technique. Also, since the gas samples can be taken on-stack (i.e., away from most of the reprocessing activities), the proposed method is non-invasive and thus free from the added costs and complexity that more intrusive sampling would entail. The technique described here is intended for use by inspectors to help verify operator declarations. This technique would not eliminate the need for standard IAEA inspections and would still require analysis of the facilities exhaust system to con®rm that the ®ssion gas has not been simply diverted away from the stack. The blending of fuels to hide the reprocessing of one low-burnup fuel would be dicult (but not impossible) for a facility to accomplish. This blending would likely result in an inferred burnup from the proposed technique that corresponded to some average of the fuels blended; however, this would most likely not correspond exactly to either of the fuels reprocessed and might alert the inspector of an inconsistency.
One of the most important portions of this veri®cation method is the measurement system. Determining spent fuel parameters from noble gas emissions requires highly precise and accurate measurements of the isotopic ratios of the ®ssion gases. The LANL technique makes use of a unique, high-precision mass spectrometer (described below) that allows for high-accuracy isotopic ratio determination even for samples with a low signalto-noise ratio. Compared to the background-air, the concentration of the ®ssion gases on-stack at a reprocessing facility is low. This necessitates the use of a high-precision instrument that will allow for the extraction of the ®ssiogenic component with a high degree of accuracy. The most valuable isotopic ratios for use in this technique are 131 Xe/134 Xe, 132 Xe/134 Xe, 83 Kr/86 Kr and 84 Kr/86 Kr. 134 Xe and 86 Kr have been chosen as the normalizing isotopes due to their larger ®ssion yield and limited dependence on operational parameters. Additional isotopic ratios, that have much smaller ®ssiogenic components (e.g., 130 Xe/134 Xe and 82 Kr/86 Kr), can still prove useful in these analyses. Also, since the 135 Xe neutron absorption cross section is so large (2.6 ´ 106 barns), the 136 Xe/134 Xe isotopic ratio contains information regarding the operational history of the fuel and may be used to determine factors such as power level and percent downtime. The use of the 136 Xe/134 Xe isotopic ratio has been explored to a limited extent, allowing only for qualitative comments regarding operational history. In the future, more eort will be expended on this subject to extend its use into determining quantitative information such as percent downtime and/or power level. The current measurement system is capable of accurately determining Xe isotopic ratios. Xe was the initial focus in this study because of its generally larger ®ssion yields and smaller backgroundair concentration. Kr isotopes appear with a much higher concentration in natural air and have slightly smaller ®ssion yields; thus, the measurement instrumentÕs precision must be excellent to acquire valuable information on ®ssiogenic Kr gases. The addition to the LANL instrument of
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detectors to determine Kr isotopic ratios is in process. 3.1. Sampling This technique makes use of gas samples taken on-stack at reprocessing facilities, ordinarily via isostatic sampling. The measurement system typically requires liter-sized gas samples that can be acquired using standard evacuated bottles. Generally, the dilution of the radioisotopes in the stack gases results in samples that present no radiological hazard and can be handled and transported without any special procedures. It may be possible to make use of the existing air-handling system at a given reprocessing facility to increase the ease with which these samples can be taken. Exact sampling protocol will likely be determined on a case-by-case basis. The LANL technique allows for the direct removal of background-air from the ®ssiogenic-gas-containing sample (see Section 5.1 below); however, it is also recommended that background-air samples be acquired to aid in con®rmation of the removal of the natural-air contaminant. 3.2. Mass spectroscopy There are two principal challenges associated with Xe mass spectrometry for this project. First, the xenon isotopic composition in stack gas samples must be analyzed with high accuracy to extract the ®ssiogenic Xe signature in the presence of the more abundant atmospheric Xe, which fortunately has a dierent isotopic composition. The second challenge is to develop robust sample analysis methods that will enable rapid, routine analysis of numerous stack gas samples. These two goals are met through a new plasma-source, multicollector mass spectrometer developed at LANL. This spectrometer provides Xe isotopic analysis on liter-sized air samples with a reproducibility of 0.05% in the isotopic ratios (at ambient air concentrations of 0.087 ppm). An analysis takes less than 30 min and does not require concentration of Xe in the sample. Rapidity of analysis, simplicity of procedure, and modest required sample size are some of this systemÕs major advantages compared
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to other state-of-the-art, dynamic, gas mass spectrometers, although the accuracy of this system may be less. This mass spectrometer utilizes the Mattauch± Herzog geometry [10], with the Xe multi-collector located at a 24 cm radius in the extended focal plane of the magnet. High ionization eciency is achieved by a 2.45 GHz microwave plasma ion source operated at low pressure (2.6 ´ 10ÿ5 atm of Ar) [11]. Ions are accelerated through 8 kV from the ion source, pass through a quadrupole triplet lens system for beam shaping and into the instrument. Detection is through simultaneous collection of masses 129±136 with Faraday cups. To ®t the tight spacing and tolerances (a 0.9 mm centerto-center spacing per mass unit and a slit width of 0.046 mm), the collectors are assembled as a stack of metalized ceramic plates with a nine-slit mask mounted in front. This collector assembly is located at the focal plane within the gap of the analyzed magnet, which provides excellent secondary electron supression. Simultaneous detection of the Xe isotopes yields two primary advantages: (1) increased accuracy by compensating for ¯uctuations in ion beam intensity due to instability in the plasma source and (2) excellent duty cycle and thus sample utilization. The associated gas-handling system (Fig. 2) and protocol to run the samples are simple by design. An air-like sample ¯ows through a getter and into the ion source at a rate controlled by the leak valve and monitored on the pressure transducer. The
Fig. 2. Mass spectrometry and gas handling system.
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getter removes all reactive gases, so that the sample enters the ion source as Ar with traces of other noble gases (100 and 10 ppm of Kr and Xe, respectively). The Ar naturally present in air provides the pressure needed to sustain the plasma. Once an ion beam is established with the sample, the peak shape and sensitivity are optimized with the quadrupole triplet lens system and steering electrodes. Data are then collected for the six stable, heavy Xe isotopes (129 Xe, 130 Xe, 131 Xe, 132 Xe, 134 Xe and 136 Xe) and associated baselines over a period of time to monitor mass-bias eects and acquire adequate statistical data. Unknown sample analysis is alternated with Xe analysis on ambient air samples to provide data for the mass-bias correction and relative collector eciencies. The ®ssiogenic component is then calculated based on the dierence between the sample and the measured air value (see Section 5.1). A further advantage of this system is minimal cross-talk between samples (or ``memory eect''). No signi®cant memory eect was detected when switching between atmospheric samples and ®ssiogenic samples that had up to a 50% overabundance of 136 Xe/132 Xe compared to the atmospheric value. Keeping the Xe in a matrix (air or Ar) appears to help reduce sorption of Xe on the walls of the vacuum system. 4. Reactor modeling The calculated database of Xe and Kr isotopic ratios as a function of spent fuel characteristics has been created using a series of state-of-the-art reactor analysis codes (including HELIOS [12], DANT/CINDER [13] and MCNP/ORIGEN [14]). These codes allow for the calculation of Xe and Kr isotopic ratios as a function of burnup for essentially all types of reactors [including pressurized water reactors (PWRs), boiling water reactors (BWRs), Canadian deuterium±uranium reactors (CANDUs), graphite moderated reactors (e.g., HTGRs and RBMKs), and liquid metal fast breeder reactors (LMFBRs)]. These codes have recently been benchmarked for this work using previous measurements from the literature to determine the codesÕ accuracy in calculating ®ssion
noble gas concentrations in spent nuclear fuel for as many reactor types as were available. The existing code systems can generate ®ssion noble gas isotopic ratios for any existing reactor and fuel type to within 2% for a wide range of burnups. The database of isotopic ratios was created as a function of burnup, reactor type, and fuel type. Below is a brief description of the models used in performing these calculations, some of the benchmark results, and comparisons of noble gas isotopic ratios for several reactor systems. 4.1. Calculational model Through the use of numerical experiments and reactor benchmarks, it was determined that accurate assembly-level calculations can be performed using a modi®ed pin cell (see below) [15]. The use of a pin cell calculation, as opposed to an assembly calculation, signi®cantly decreases the required computing time and allows for an increase in the number of datapoints available in the database. The pin cell that was used was modi®ed so that the fuel-to-moderator ratio was identical to that existing in the assembly. The pin cell model consisted of nine ¯at-¯ux fuel regions for the burnup calculations. The power reactor calculations were performed with burnup step sizes of 100 MWd/ MTU for burnups between 0 and 1000 MWd/ MTU and 1000 MWd/MTU for burnups between 1000 and 50 000 MWd/MTU. Larger burnup step sizes yielded the same degree of accuracy in the calculation, but 1000 MWd/MTU was chosen to allow for more accurate interpolations in the database of isotopic ratios. The production reactor fuel calculations were performed with burnup step sizes of 10 MWd/MTU for burnups between 0 and 400 MWd/MTU and 100 MWd/MTU for burnups between 400 and 5000 MWd/MTU. Radial leakage from the full core calculation and reactivity control characteristics (control rod level and chemical shim concentrations) were shown to have a negligible eect (<0.08%) on the resultant ®ssion product noble gas isotopic ratios. Changes in power level signi®cantly aected only the 136 Xe/ 134 Xe isotopic ratio, while all other values remained essentially unchanged.
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Table 1 Reactor systems from the literature used in reactor physics benchmarking Reactor name
Reactor type
Burnup range (MWd/MTU)
Borsselle [16] Calvert Clis [17±19] Garigliano [6] Genkai [20] Gundremmingen [21] Halden [22±24] Mihama [20] Obrigheim [25] Pickering [26] Shippingport [27] Trino Vercellese [28,29] Turkey Point [30]
PWR PWR BWR PWR BWR HBWR PWR PWR CANDU PWR PWR PWR
31 000±32 000 18 680±46 460 9800±14 480 29 440±38 700 14 390±25 900 15 040±28 600 6900±21 200 15 600±36 260 9200 2414±22 000 3399±27 758 30 510±31 560
4.2. Calculation benchmarks To verify the accuracy of the calculated database, the reactor physics code systems were benchmarked to various measurements from the literature. Table 1 contains a list of all reactor systems used in the benchmarking process, as well as the reactor types, burnup ranges for the spent fuel, and the information reported in the literature. As can be seen, a fairly extensive set of reactors was used to perform the benchmarking calculations. The only reactor system of importance missing from this group is graphite-moderated reactors (e.g., HTGR and RBMK reactors). These systems will be benchmarked to the database as measurements of their fuel become available. In general, it was found that the calculated isotopic ratios for Xe and Kr compared to the literature measurements within 2%. Detailed descriptions of the results from these benchmarks can be found elsewhere [15]. These literature measurements have been used only to benchmark the accuracy of the calculated database; however, in the future they may also be used to aid in validating the proposed monitoring system (i.e., data analysis and reactor simulation).
Heavy metal isotopics reported
Noble gas isotopics reported
as a function of burnup for several reactor systems. The results chosen are representative of their particular class of reactor (e.g., PWR or BWR). Figs. 3 and 4 illustrate the dierences expected for various reactors. As can be seen in Fig. 3, the 131 Xe/134 Xe ratio is fairly invariant for dierent reactor systems. This is due to the small changes in the 131 Xe ®ssion yield with changes in energy and ®ssioning isotope and the large eect of the 131 Xe absorption cross section. Conversely, as seen in Fig. 4, the 132 Xe/134 Xe isotopic ratio varies up to 25% with changes in reactor type. Similar behavior is found for the Kr isotopes. These results show that the 131 Xe/134 Xe ratio provides a direct indication of whether a repro-
4.3. Reactor type comparisons Using selected results from the database, comparisons were made for calculated isotopic ratios
Fig. 3. 131 Xe/134 Xe isotopic ratio versus burnup for various reactor systems.
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5.1. Background-air correction
Fig. 4. 132 Xe/134 Xe isotopic ratio versus burnup for various reactor systems.
cessed fuel is of low burnup or high burnup regardless of the reactor type that produced the fuel. The other isotopic ratios yield information suggesting the actual spent fuel characteristics (such as reactor type and fuel enrichment). These results also illustrate the need for an extremely accurate measurement system and calculated database to allow for con®dent determination of spent fuel characteristics (e.g., for PWR versus BWR analysis). This demonstrates that non-rigorous reactor physics calculations and standard commercial mass spectrometers are insucient to achieve discrimination (as well as being limited in their ability to remove background-air contributions). 5. Data analysis LANL has developed the means to perform both forward and reverse analysis on the resultant measurements using a coupled Bayesian and Principal Component Analysis/Principal Component Regression (PCA/PCR) analysis tool. With these two techniques combined, the integrated system is signi®cantly more robust (able to analyze more diverse data sets). These techniques are crucial to the determination of reactor type, fuel type, and burnup. The data analysis tool automatically yields combined uncertainties using all available information. Descriptions of the two analysis techniques and the background-air correction are given below.
Because any realistically acquired samples will contain both a ®ssiogenic component and a natural-air component, the sampleÕs measured isotopic ratios will consist of a combination of the ®ssiogenic and atmospheric-air noble gases. Because some noble gas isotopes (for instance, 129 Xe and 80 Kr) are not produced in signi®cant quantities via ®ssion, these measured non-®ssiogenic isotopes can be used to remove the background-air contaminant. This requires using known natural abundances of the Xe and Kr isotopes in air (either assumed or measured). If the abundances of all measured noble gas isotopes in atmospheric-air (relative to the abundance of the non-®ssiogenic isotope) are known, then the ®ssiogenic component of that isotope can be determined using x x x Nf;u Nm;u Nm;air ÿ ; 129 129 129 Nm;u Nm;air Nm;air
1
x is the ®ssiogenic component of where Nf;u the concentration of isotope x in the unknown 129 is the concentration of the nonsample, Nm;air ®ssiogenic isotope (in this case 129 Xe) in atmox is the measured concentration of spheric-air, Nm;u 129 ®ssiogenic isotope x in the unknown sample, Nm;u is the measured concentration of the non-®ssiox is the genic isotope in the unknown sample, Nm;air concentration of ®ssiogenic isotope x in atmospheric-air. Considering the element Xe with normalizing isotope 134 Xe and non-®ssiogenic isotope 129 Xe, the isotopic ratio of interest is given by x 129 x 129 x Nm;u =Nm;u ÿ Nm;air =Nm;air Nf;u : 2 134 Nf;u 134 =N 129 ÿ N 134 =N 129 Nm;u m;u m;air m;air
Thus, given a measurement of the isotope of interest and the normalizing isotope relative to 129 Xe in the unknown sample and in atmospheric-air, the background-air contaminant can be removed directly. A similar technique can be used for the Kr gases using 78 Kr and/or 80 Kr as the gas lacking a signi®cant ®ssiogenic component.
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where Rm is the set of all measured ratios or
5.2. Bayesian analysis The Bayesian analysis technique is based on BayesÕ theorem, which relates the probability that the hypothesis is true, given the data, to the probability that we would observe the measured data if the hypothesis were true. In simplest terms, BayesÕ theorem can be seen as [31] prob hypothesisjdata; I / prob datajhypothesis; I prob hypothesisjI;
3
where the standard probability theory notation has been used. In this analysis, BayesÕ theorem is utilized by comparing each of the models (Mj ) in the calculated database and determining which model is most likely to correctly represent the reprocessed fuel. This is achieved by ®rst converting each measured isotopic ratio Rm i to a burnup value for each model through interpolation in the calculated database. A combined average burnup (Bj ) is then created for each model (Mj ) based on all the ratios. The calculated ratios Rci based on the average burnup (Bj ) for each model (Mj ) can then be determined. Using these calculated ratios and the maximum entropy formulation, the probability that a given model at the modelÕs average burnup would result in the observance of the measured ratio is generated using the following equation: p Rm i jMj ; Bj ; I
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1 ri Mj ; Bj ÿ 2 ! c ÿ Rm i ÿ Ri Mj ; Bj ; exp 2r2i Mj ; Bi 4
where ri (Mj ,Bj ) is the standard deviation of the calculated isotopic ratio. These are calculated for each model in the database. Each model can then be compared to some nominal model using a version of BayesÕ theorem [32] p Mj ; Bj jRm ; I p Mj ; Bj jI Y p Rm i jMj ; Bj ; I ; BjR m ; I p M; BjI p M; p Rm i jM; B; I
m m Rm Rm 1 ; R2 ; R3 ; . . .:
6
Based on the values calculated using Eq. (5), the most appropriate model and burnup value for the observed data can be inferred. It should be noted that these decisions are computationally intensive and that as the calculated database becomes more comprehensive (i.e., more models are added), the computational time for this analysis increases. It may be appropriate in the future to alter the existing format of the database to allow for faster computations on more portable machines. 5.3. Principal component analysis/principal component regression (PCA/PCR) Principal component analysis (PCA) attempts to ®nd the eigenvalues and eigenvectors of the covariance matrix of all the mass spectrometric isotopic ratios in the calibration set by employing a singular value decomposition (SVD). SVD performs the following: Xmn Umm Smn Vnn0 ;
7
where X is the experimental data matrix of m mass spectra of n channels, S is a diagonal matrix of positive square roots of eigenvalues, and V 0 contains the eigenvectors of X 0 X . Note that X 0 X is the covariance matrix and the prime (0 ) denotes a matrix transpose. The results of the PCA model allow the analyst to classify or identify which of the modeled reactors is most likely related to an arbitrary unknown mass spectral signature at future times. Once this categorization is made, the burnup rate for the identi®ed reactor can be determined from a regression equation using principal component regression (PCR). This involves the following: 0 0 Xmn Vnk0 Tkm Tmk ; Vkn Xmm
8
Qkp Dkk Tkm Ymp ;
9
Amp Pmn Vnk0 Qkp ;
10
i
5
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where k is chosen by the analyst from the PCA model, Tkm are matrixes of scores, and Ymp are the known reference burnup rates associated with the m mass spectra. The index p only runs to one because we are only trying to predict one dependent variable: the burnup rate. In general, p is greater than one if a plurality of dependent variables needs to be predicted. Dkk is a diagonal matrix of reciprocal eigenvalues, Qkp are the chemical loadings (i.e., how the burnup rates look in the reduced k-dimensional coordinate system), Pmn are the unknown validation spectra to be predicted, and Amp is the predicted quantity (e.g., burnup). The scores, which are related to the eigenvalues, contain information on how spectral samples relate to each other for a given kth dimension. Eq. (8) essentially projects the mass spectra into the modi®ed coordinate system, Eq. (9) transforms the associated reference burnup rates into the same new coordinate system, and Eq. (10) is the regression equation permitting prediction of burnup rates. There are some practical advantages to using principal components as opposed to other statistical tools. These include increased applicability with low signal-to-noise ratios, allowing replicates in the model, producing eigenvectors that may have physically meaningful patterns to an expert, and reducing the number of independent variables needed for graphical diagnostics. To some degree PCA/PCR complements the Bayesian analysis technique mentioned above. This use of complementary techniques adds to the robustness of the proposed system. 6. System validation The proposed technique has been validated using on-stack measurements taken during the reprocessing of spent fuel from a US production reactor. The samples were acquired during the dissolution of weapons-grade spent fuel with a declared burnup of 178 MWd/MTU. The complete system generated an inferred burnup of 171 13 MWd/MTU and correctly matched the measured samples to the reactor type (see Fig. 5). Thus, the inferred burnup was in error by only
Fig. 5. Measured 131 Xe/134 Xe isotopic ratio versus burnup for a US production reactor compared to the HELIOS calculated result (inferred fuel burnup using the LANL technique and the declared fuel burnup are shown).
3.9%, which is most likely within the uncertainty of the declared burnup. This fuel represents a good test of the system because of the small signal-tonoise ratio in low-burnup fuel and the increased diculty in modeling this reactor. On the other hand, from an analysis of Figs. 3 and 4, the production reactor stable noble gas isotopic ratios are clearly dierent from those of any other fuel at low burnup values. Therefore, it is unlikely that the analysis would incorrectly determine the reactor type for this fuel dissolution. This validation demonstrates the accuracy of this technique; however, the ability of this technique to distinguish between dierent power reactor fuels has not been fully tested (especially for PWR versus BWR). Full system tests for power reactor fuels (including on-stack sample collection) will require the cooperation of a commercial reprocessing facility; this is being explored. Current eorts are also being made to acquire samples from other spent fuel operations, research reactor storage facilities, and other sources to aid in the system viability demonstration. This validation shows that the current techniqueÕs accuracy is sucient for many safeguards applications (e.g., distinguishing between low-and high-burnup fuels). However, continued validation for other power and production reactor fuel is necessary to demonstrate the robustness of this technique.
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7. Conclusions Los Alamos National Laboratory has been actively studying techniques for strengthening safeguards at reprocessing facilities through environmental monitoring techniques. The method proposed here involves the integration of a high-precision mass spectrometer, several reactor analysis codes, and sophisticated data analysis techniques. The integrated system allows for the determination of speci®c fuel parameters such as burnup and reactor type. The complete methodology has been benchmarked for on-stack samples acquired during reprocessing of fuel from a US production reactor. These measurements led to an inferred burnup that matched the declared burnup to within 3.9%. Future work is necessary to demonstrate the robustness of this system for production, power, and research reactor fuels. Also, advances are needed in the database, data analysis tools, and user interface to increase its portability and usability by inspectors. Currently, the database is stored as a series of text ®les at LANL and could be placed into a more sophisticated and accessible format. The data analysis tools requires some degree of integration and increased portability if they are to be easily usable by inspectors (currently the codes are only available at LANL). Acknowledgements The authors would like to thank Holly R. Trellue and David I. Poston for their eorts in helping run the Monteburns code system. Also, thanks must be given to Rudi J.J. StammÕler and Aldo Ferri for aiding in the use of HELIOS. Los Alamos National Laboratory is operated by the University of California for the US Department of Energy under contract W-7405-ENG-36.
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Application of Safeguards, INFCIRC/540, International Atomic Energy Agency, Vienna, 1997. T. Shea, S. Deron, F. Franssen, D. Hope, N. Islam, S. Johnson, E. Kuhn, G. Laszlo, D. Neal, T. Renis, Safeguarding reprocessing plants: principles, past experiences, current practices, and future trends, J.N.M.M. 21 (4) (1993) 17. C.W. Nakhleh, R.T. Perry, J. Poths, W.D. Stanbro, W.B. Wilson, B.L. Fearey, Noble gas atmospheric monitoring at reprocessing facilities, Los Alamos National Laboratory document LA-UR-97-705, 1997. M. Ohkubo, Gaseous isotope correlation technique for safeguards at reprocessing facilities, IAEA report STR240, 1988. G.B. Hudson, Noble gas isotope measurements for spent nuclear fuel reprocessing, IAEA Task 90/0A211 Interim Report, 1993. C.W. Nahkleh, W.D. Stanbro, L.N. Hand, R.T. Perry, W.B. Wilson, B.L. Fearey, Noble-gas atmospheric monitoring for international safeguards at reprocessing facilities, Science and Global Security 6 (1997) 357. W.S. Charlton, Noble gas measurement and analysis technique for monitoring reprocessing facilities, Ph.D. Dissertation, Texas A&M University, Nuclear Engineering Department, August 1999. W.S. Charlton, W.D. Stanbro, B.L. Fearey, P.H. Hemberger, R.T. Perry, J. Poths, The use of stable noble gases to con®rm compliance with the ®ssile material cuto treaty, Presented at the Sixth International Conference on Facility Operations ± Safeguards Interface, September 20±24, Jackson Hole, WY, 1999. A.O. Nier, D.J. Schlutter, High-performance double-focusing mass spectrometer, Rev. Sci. Instrum. 56 (1985) 214. J. Poths, E.P. Chamberlin, A high eciency ion source for Kr and Xe isotropic measurements, Int. J. Mass Spec. Ion Process 146/147 (1995) 47. E.A. Villarino, R.J.J. StammÕler, A.A. Ferri, J.J. Casal, HELIOS: Angularly dependent collision probabilities, Nucl. Sci. Engrg. 112 (1992) 16. R.E. Alcoue, R.S. Baker, F.W. Brinkley, D.R. Marr, R.D. OÕDell, W.F. Walters, DANTSYS: A diusion accelerated neutral particle transport code system, Los Alamos National Laboratory document LA-12969-M, 1995. D.I. Poston, H.R. Trellue, UserÕs Manual, Version 1.00 for Monteburns, Version 3.01, Los Alamos National Laboratory document LA-UR-98-2718, 1998. W.S. Charlton, R.T. Perry, B.L. Fearey, T.A. Parish, Comparisons of HELIOS calculated isotope concentrations to measured values for several reactor systems, Los Alamos National Laboratory document LA-UR-98-4044, 1998. A. Leudet, A. Leuseur, Comportement des radionucleides gazeux degages pendant les operations initiales du retraitement, Commiss. Eur. Commun., EUR 7822 fr, 1982. R.J. Guenther, D.E. Blahnik, T.K. Campbell, U.P. Jenquin, J.E. Mendel, L.E. Thomas, C.K. Thornhill,
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W.S. Charlton et al. / Nucl. Instr. and Meth. in Phys. Res. B 168 (2000) 98±108 Characterization of spent fuel approved testing material ± ATM-103, Paci®c Northwest Laboratory report PNL5109-103, 1988. R.J. Guenther, D.E. Blahnik, U.P. Jenquin, J.E. Mendel, L.E. Thomas, C.K. Thornhill, Characterization of spent fuel approved testing material-ATM-104, Paci®c Northwest Laboratory report PNL-5109-104, 1991. R.J. Guenther, D.E. Blahnik, T.K. Campbell, U.P. Jenquin, J.E. Mendel, C.K. Thornhill, Characterization of spent fuel approved testing material-ATM-106, Paci®c Northwest Laboratory report PNL-5109-106, 1988. T. Adachi et al., Dissolution studies of spent nuclear fuels, Japan Atomic Energy Research Institute report JAERI-M 91-010, 1991. P. Barbero et al., Post-irradiation analysis of the Gundremmingen BWR spent fuel, Commiss. Eur. Commun., EUR 6301 en, 1979. M. Mogensen, Determination of ®ssion gas yields from isotope ratios, Int. J. Mass Spec. Ion. Phys. 48 (1983) 389. N. Larsen, H. Egsgaard, M. Mogensen, Mass spectrometric measurements of ®ssion gas from nuclear fuel, Int. J. Mass Spec. Ion. Phys. 48 (1983) 385. M. Mogensen, Determination of retained gas in irradiated fuel samples, RISO National Laboratory report RISO-M2352, 1982.
[25] P. Barbero et al., Post irradiation analysis of the Obrigheim PWR spent fuel, Commiss. Eur. Commun. Nucl. Sci. Tech., EUR 6589 en, 1980. [26] J.C. Tait, I. Gauld, A.H. Kerr, Validation of the ORIGEN-S code for predicting radionuclide inventories in used CANDU fuel, J. Nucl. Mat. 223 (1995) 109. [27] J.C. Stachew, Isotopic analysis of natural UO2 fuel irradiated to 22,000 MWd/MTU. Theory vs experiment, Nucl. Appl. 4 (1968) 206. [28] A.M. Bresesti et al., Post-irradiation analysis of Trino Vercellese Reactor fuel elements, Commiss. Eur. Commun., EUR 4909 e, 1972. [29] P. Barbero et al., Post irradiation examination of the fuel discharged from the Trino Vercellese Reactor after the second irradiation cycle, Commiss. Eur. Commun., EUR 5605 e, 1977. [30] S.D. Atkin, Destructive examination of 3-cycle LWR fuel rods from Turkey Point Unit 3 for the climax-spent fuel test, Hanford Engineering Development Laboratory report HEDL-TME (1981) 80±89. [31] T. Bayes, An essay towards solving a problem in the doctrine of chances, Phil. Trans. Roy. Soc. 53 (1763) 370. [32] C.W. Nakhleh, Plausible inference and the interpretation of quantitative data, Los Alamos National Laboratory document LA-13412-MS, 1998.
www.elsevier.nl/locate/nimb
Operator declaration veri®cation technique for spent fuel at reprocessing facilities William S. Charlton a,*, Bryan L. Fearey a, Charles W. Nakhleh a, Theodore A. Parish b, Robert T. Perry a, Jane Poths a, John R. Quagliano a, William D. Stanbro a, William B. Wilson a a
NIS-7 Stafeguards Systems Group, Los Alamos National Laboratory, Mail Stom E 541, Los Alamos, NM 87545, USA b Texas A&M University, College Station, TX 77843, USA Received 9 March 1999; received in revised form 8 October 1999
Abstract A veri®cation technique for use at reprocessing facilities, which integrates existing technologies to strengthen safeguards through the use of environmental monitoring, has been developed at Los Alamos National Laboratory. This technique involves the measurement of isotopic ratios of stable noble ®ssion gases from on-stack emissions during reprocessing of spent fuel using high-precision mass spectrometry. These results are then compared to a database of calculated isotopic ratios using a data analysis method to determine speci®c fuel parameters (e.g., burnup, fuel type, reactor type, etc.). These inferred parameters can be used to verify operator declarations. The integrated system (mass spectrometry, reactor modeling, and data analysis) has been validated using on-stack measurements during reprocessing of fuel from a US production reactor. These measurements led to an inferred burnup that matched the declared burnup to within 3.9%, suggesting that the current system is sucient for most safeguards applications. Partial system validation using gas samples from literature measurements of power reactor fuel has been reported elsewhere. This has shown that the technique developed here may have some diculty distinguishing pressurized water reactor (PWR) from boiling water reactor (BWR) fuel; however, it consistently can distinguish light water reactor (either PWR or BWR) fuels from other reactor fuel types. Future validations will include advanced power reactor fuels (such as breeder reactor fuels) and research reactor fuels as samples become available. Ó 2000 Elsevier Science B.V. All rights reserved. Keywords: Spent fuel; Reprocessing; Mass spectrometry; Safeguards
1. Introduction
*
Corresponding author. Tel.: +505-665-8576; fax: +505667-7626. E-mail address: [email protected] (W.S. Charlton).
The discovery in 1991 of a large, clandestine weapons program in Iraq led to a call for improvements in international safeguards on nuclear facilities and materials. The International Atomic Energy Agency (IAEA) responded with an eort
0168-583X/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 0 6 3 3 - 3
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called ``Programme 93+2'' to develop new and more ecient safeguards techniques [1]. The product of this eort is known as the ``Model Protocol'' and is described in the IAEA document INFCIRC/540 [2]. INFCIRC/540 provides the basis for States to reach agreements with the IAEA on additional safeguards measures. Among the possible additions to safeguards contemplated in INFCIRC/540 is the use of environmental sampling. Large-scale reprocessing plants pose a particular challenge to IAEA safeguards [3]. One environmental monitoring (EM) technique that may prove widely applicable to the safeguarding of reprocessing facilities is the monitoring of atmospheric noble gas concentrations present in the facilityÕs stack gases [4]. Fissiogenic noble gases are not chemically bound in the spent nuclear fuel. Thus, they are readily released during reprocessing. These gases contain isotopes that allow for the extraction of information concerning reactor type, fuel type, burnup, and operational history. The two most prominent ®ssiogenic noble gases are Xe and Kr. Therefore, these two elements present the most useful signal for these EM techniques. The relative concentrations of the ®ssiogenically produced stable Xe and Kr isotopes depend on the neutron energy spectrum in the reactor, the ®ssioning isotopes, the power level, and the total number of ®ssions. Therefore, the Xe and Kr released from the fuel provide a unique signature of the fuel characteristics. Some previous attempts have been made to make use of these gaseous emissions; however, these studies proved inconclusive [5,6]. Los Alamos National Laboratory (LANL) has been studying advances in EM techniques for use in IAEA safeguards for several years [4,7]. This paper describes the development and application of a technique for estimating several characteristics of spent fuel (e.g., burnup and reactor type) being reprocessed [8]. This technique uses highprecision measurements of stable noble gas isotopic ratios in samples taken from a reprocessing plant exhaust stack. Using sophisticated data analysis techniques, these ratios are coupled with a database of calculated isotopic ratios to infer spent fuel parameters for fuel being reprocessed.
99
The information gained from this analysis could be used in an international safeguards regime to help verify declarations made by facility operators. This technique has been partially tested using literature measurements from power reactor fuels, and these validations are presented elsewhere [8,9]. The LANL technique is capable of performing two dierent forms of analysis: the forward and backward analyses. The forward analysis involves the determination and con®rmation of spent fuel burnup from a sample of gas released from reprocessed spent fuel when all information pertaining to the fuel is present (i.e., the reactor type, fuel type, fuel enrichment, operational history, etc.). The backward analysis involves the determination of spent fuel parameters from a gas sample collected during reprocessing of spent fuel when only minimal information is available about the reprocessed fuel. The backward analysis is signi®cantly more complicated and is the main thrust of the work presented in this report. 2. Proposed veri®cation procedure The proposed system couples a unique highprecision mass spectrometer with an extremely accurate ®ssiogenic gas database through the use of two data analysis techniques. The ®ssiogenic gas database contains Xe and Kr ®ssiogenic isotopic ratios as a function of burnup for an extensive set of fuel and reactor types. These ratios were calculated using a series of state-of-the-art reactor analysis codes, and the calculational accuracy has been benchmarked whenever possible [8]. The complete system integration can be seen in Fig. 1. The ®rst step in the use of this technique is to acquire a gas sample on-stack from the reprocessing facility during the dissolution of spent fuel. This gas sample can then be processed using the LANL mass spectrometry system to determine the Xe and Kr isotopic gas ratios due to ®ssion. The current LANL system has been fully developed for determining Xe isotopic ratios; however, the system is still being developed for use in measuring Kr isotopic ratios at comparable levels. These measured ratios (Xe, Kr, or both) are then
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3. Measurement system
Fig. 1. Veri®cation technique overview.
compared to the calculated database using sophisticated data analysis techniques. This results in a set of inferred spent fuel parameters that can include information such as burnup, reactor type, fuel type, and/or operational history. The technique developed here may be used to accurately analyze stable noble gases and characterize spent fuel from reprocessing facilities. Signi®cant advantages in the quantity and quality of inferred information accrue from using as many measured isotopic ratios as possible. The use of an extensive database and multiple data analysis methods results in a highly versatile technique. Also, since the gas samples can be taken on-stack (i.e., away from most of the reprocessing activities), the proposed method is non-invasive and thus free from the added costs and complexity that more intrusive sampling would entail. The technique described here is intended for use by inspectors to help verify operator declarations. This technique would not eliminate the need for standard IAEA inspections and would still require analysis of the facilities exhaust system to con®rm that the ®ssion gas has not been simply diverted away from the stack. The blending of fuels to hide the reprocessing of one low-burnup fuel would be dicult (but not impossible) for a facility to accomplish. This blending would likely result in an inferred burnup from the proposed technique that corresponded to some average of the fuels blended; however, this would most likely not correspond exactly to either of the fuels reprocessed and might alert the inspector of an inconsistency.
One of the most important portions of this veri®cation method is the measurement system. Determining spent fuel parameters from noble gas emissions requires highly precise and accurate measurements of the isotopic ratios of the ®ssion gases. The LANL technique makes use of a unique, high-precision mass spectrometer (described below) that allows for high-accuracy isotopic ratio determination even for samples with a low signalto-noise ratio. Compared to the background-air, the concentration of the ®ssion gases on-stack at a reprocessing facility is low. This necessitates the use of a high-precision instrument that will allow for the extraction of the ®ssiogenic component with a high degree of accuracy. The most valuable isotopic ratios for use in this technique are 131 Xe/134 Xe, 132 Xe/134 Xe, 83 Kr/86 Kr and 84 Kr/86 Kr. 134 Xe and 86 Kr have been chosen as the normalizing isotopes due to their larger ®ssion yield and limited dependence on operational parameters. Additional isotopic ratios, that have much smaller ®ssiogenic components (e.g., 130 Xe/134 Xe and 82 Kr/86 Kr), can still prove useful in these analyses. Also, since the 135 Xe neutron absorption cross section is so large (2.6 ´ 106 barns), the 136 Xe/134 Xe isotopic ratio contains information regarding the operational history of the fuel and may be used to determine factors such as power level and percent downtime. The use of the 136 Xe/134 Xe isotopic ratio has been explored to a limited extent, allowing only for qualitative comments regarding operational history. In the future, more eort will be expended on this subject to extend its use into determining quantitative information such as percent downtime and/or power level. The current measurement system is capable of accurately determining Xe isotopic ratios. Xe was the initial focus in this study because of its generally larger ®ssion yields and smaller backgroundair concentration. Kr isotopes appear with a much higher concentration in natural air and have slightly smaller ®ssion yields; thus, the measurement instrumentÕs precision must be excellent to acquire valuable information on ®ssiogenic Kr gases. The addition to the LANL instrument of
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detectors to determine Kr isotopic ratios is in process. 3.1. Sampling This technique makes use of gas samples taken on-stack at reprocessing facilities, ordinarily via isostatic sampling. The measurement system typically requires liter-sized gas samples that can be acquired using standard evacuated bottles. Generally, the dilution of the radioisotopes in the stack gases results in samples that present no radiological hazard and can be handled and transported without any special procedures. It may be possible to make use of the existing air-handling system at a given reprocessing facility to increase the ease with which these samples can be taken. Exact sampling protocol will likely be determined on a case-by-case basis. The LANL technique allows for the direct removal of background-air from the ®ssiogenic-gas-containing sample (see Section 5.1 below); however, it is also recommended that background-air samples be acquired to aid in con®rmation of the removal of the natural-air contaminant. 3.2. Mass spectroscopy There are two principal challenges associated with Xe mass spectrometry for this project. First, the xenon isotopic composition in stack gas samples must be analyzed with high accuracy to extract the ®ssiogenic Xe signature in the presence of the more abundant atmospheric Xe, which fortunately has a dierent isotopic composition. The second challenge is to develop robust sample analysis methods that will enable rapid, routine analysis of numerous stack gas samples. These two goals are met through a new plasma-source, multicollector mass spectrometer developed at LANL. This spectrometer provides Xe isotopic analysis on liter-sized air samples with a reproducibility of 0.05% in the isotopic ratios (at ambient air concentrations of 0.087 ppm). An analysis takes less than 30 min and does not require concentration of Xe in the sample. Rapidity of analysis, simplicity of procedure, and modest required sample size are some of this systemÕs major advantages compared
101
to other state-of-the-art, dynamic, gas mass spectrometers, although the accuracy of this system may be less. This mass spectrometer utilizes the Mattauch± Herzog geometry [10], with the Xe multi-collector located at a 24 cm radius in the extended focal plane of the magnet. High ionization eciency is achieved by a 2.45 GHz microwave plasma ion source operated at low pressure (2.6 ´ 10ÿ5 atm of Ar) [11]. Ions are accelerated through 8 kV from the ion source, pass through a quadrupole triplet lens system for beam shaping and into the instrument. Detection is through simultaneous collection of masses 129±136 with Faraday cups. To ®t the tight spacing and tolerances (a 0.9 mm centerto-center spacing per mass unit and a slit width of 0.046 mm), the collectors are assembled as a stack of metalized ceramic plates with a nine-slit mask mounted in front. This collector assembly is located at the focal plane within the gap of the analyzed magnet, which provides excellent secondary electron supression. Simultaneous detection of the Xe isotopes yields two primary advantages: (1) increased accuracy by compensating for ¯uctuations in ion beam intensity due to instability in the plasma source and (2) excellent duty cycle and thus sample utilization. The associated gas-handling system (Fig. 2) and protocol to run the samples are simple by design. An air-like sample ¯ows through a getter and into the ion source at a rate controlled by the leak valve and monitored on the pressure transducer. The
Fig. 2. Mass spectrometry and gas handling system.
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getter removes all reactive gases, so that the sample enters the ion source as Ar with traces of other noble gases (100 and 10 ppm of Kr and Xe, respectively). The Ar naturally present in air provides the pressure needed to sustain the plasma. Once an ion beam is established with the sample, the peak shape and sensitivity are optimized with the quadrupole triplet lens system and steering electrodes. Data are then collected for the six stable, heavy Xe isotopes (129 Xe, 130 Xe, 131 Xe, 132 Xe, 134 Xe and 136 Xe) and associated baselines over a period of time to monitor mass-bias eects and acquire adequate statistical data. Unknown sample analysis is alternated with Xe analysis on ambient air samples to provide data for the mass-bias correction and relative collector eciencies. The ®ssiogenic component is then calculated based on the dierence between the sample and the measured air value (see Section 5.1). A further advantage of this system is minimal cross-talk between samples (or ``memory eect''). No signi®cant memory eect was detected when switching between atmospheric samples and ®ssiogenic samples that had up to a 50% overabundance of 136 Xe/132 Xe compared to the atmospheric value. Keeping the Xe in a matrix (air or Ar) appears to help reduce sorption of Xe on the walls of the vacuum system. 4. Reactor modeling The calculated database of Xe and Kr isotopic ratios as a function of spent fuel characteristics has been created using a series of state-of-the-art reactor analysis codes (including HELIOS [12], DANT/CINDER [13] and MCNP/ORIGEN [14]). These codes allow for the calculation of Xe and Kr isotopic ratios as a function of burnup for essentially all types of reactors [including pressurized water reactors (PWRs), boiling water reactors (BWRs), Canadian deuterium±uranium reactors (CANDUs), graphite moderated reactors (e.g., HTGRs and RBMKs), and liquid metal fast breeder reactors (LMFBRs)]. These codes have recently been benchmarked for this work using previous measurements from the literature to determine the codesÕ accuracy in calculating ®ssion
noble gas concentrations in spent nuclear fuel for as many reactor types as were available. The existing code systems can generate ®ssion noble gas isotopic ratios for any existing reactor and fuel type to within 2% for a wide range of burnups. The database of isotopic ratios was created as a function of burnup, reactor type, and fuel type. Below is a brief description of the models used in performing these calculations, some of the benchmark results, and comparisons of noble gas isotopic ratios for several reactor systems. 4.1. Calculational model Through the use of numerical experiments and reactor benchmarks, it was determined that accurate assembly-level calculations can be performed using a modi®ed pin cell (see below) [15]. The use of a pin cell calculation, as opposed to an assembly calculation, signi®cantly decreases the required computing time and allows for an increase in the number of datapoints available in the database. The pin cell that was used was modi®ed so that the fuel-to-moderator ratio was identical to that existing in the assembly. The pin cell model consisted of nine ¯at-¯ux fuel regions for the burnup calculations. The power reactor calculations were performed with burnup step sizes of 100 MWd/ MTU for burnups between 0 and 1000 MWd/ MTU and 1000 MWd/MTU for burnups between 1000 and 50 000 MWd/MTU. Larger burnup step sizes yielded the same degree of accuracy in the calculation, but 1000 MWd/MTU was chosen to allow for more accurate interpolations in the database of isotopic ratios. The production reactor fuel calculations were performed with burnup step sizes of 10 MWd/MTU for burnups between 0 and 400 MWd/MTU and 100 MWd/MTU for burnups between 400 and 5000 MWd/MTU. Radial leakage from the full core calculation and reactivity control characteristics (control rod level and chemical shim concentrations) were shown to have a negligible eect (<0.08%) on the resultant ®ssion product noble gas isotopic ratios. Changes in power level signi®cantly aected only the 136 Xe/ 134 Xe isotopic ratio, while all other values remained essentially unchanged.
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Table 1 Reactor systems from the literature used in reactor physics benchmarking Reactor name
Reactor type
Burnup range (MWd/MTU)
Borsselle [16] Calvert Clis [17±19] Garigliano [6] Genkai [20] Gundremmingen [21] Halden [22±24] Mihama [20] Obrigheim [25] Pickering [26] Shippingport [27] Trino Vercellese [28,29] Turkey Point [30]
PWR PWR BWR PWR BWR HBWR PWR PWR CANDU PWR PWR PWR
31 000±32 000 18 680±46 460 9800±14 480 29 440±38 700 14 390±25 900 15 040±28 600 6900±21 200 15 600±36 260 9200 2414±22 000 3399±27 758 30 510±31 560
4.2. Calculation benchmarks To verify the accuracy of the calculated database, the reactor physics code systems were benchmarked to various measurements from the literature. Table 1 contains a list of all reactor systems used in the benchmarking process, as well as the reactor types, burnup ranges for the spent fuel, and the information reported in the literature. As can be seen, a fairly extensive set of reactors was used to perform the benchmarking calculations. The only reactor system of importance missing from this group is graphite-moderated reactors (e.g., HTGR and RBMK reactors). These systems will be benchmarked to the database as measurements of their fuel become available. In general, it was found that the calculated isotopic ratios for Xe and Kr compared to the literature measurements within 2%. Detailed descriptions of the results from these benchmarks can be found elsewhere [15]. These literature measurements have been used only to benchmark the accuracy of the calculated database; however, in the future they may also be used to aid in validating the proposed monitoring system (i.e., data analysis and reactor simulation).
Heavy metal isotopics reported
Noble gas isotopics reported
as a function of burnup for several reactor systems. The results chosen are representative of their particular class of reactor (e.g., PWR or BWR). Figs. 3 and 4 illustrate the dierences expected for various reactors. As can be seen in Fig. 3, the 131 Xe/134 Xe ratio is fairly invariant for dierent reactor systems. This is due to the small changes in the 131 Xe ®ssion yield with changes in energy and ®ssioning isotope and the large eect of the 131 Xe absorption cross section. Conversely, as seen in Fig. 4, the 132 Xe/134 Xe isotopic ratio varies up to 25% with changes in reactor type. Similar behavior is found for the Kr isotopes. These results show that the 131 Xe/134 Xe ratio provides a direct indication of whether a repro-
4.3. Reactor type comparisons Using selected results from the database, comparisons were made for calculated isotopic ratios
Fig. 3. 131 Xe/134 Xe isotopic ratio versus burnup for various reactor systems.
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5.1. Background-air correction
Fig. 4. 132 Xe/134 Xe isotopic ratio versus burnup for various reactor systems.
cessed fuel is of low burnup or high burnup regardless of the reactor type that produced the fuel. The other isotopic ratios yield information suggesting the actual spent fuel characteristics (such as reactor type and fuel enrichment). These results also illustrate the need for an extremely accurate measurement system and calculated database to allow for con®dent determination of spent fuel characteristics (e.g., for PWR versus BWR analysis). This demonstrates that non-rigorous reactor physics calculations and standard commercial mass spectrometers are insucient to achieve discrimination (as well as being limited in their ability to remove background-air contributions). 5. Data analysis LANL has developed the means to perform both forward and reverse analysis on the resultant measurements using a coupled Bayesian and Principal Component Analysis/Principal Component Regression (PCA/PCR) analysis tool. With these two techniques combined, the integrated system is signi®cantly more robust (able to analyze more diverse data sets). These techniques are crucial to the determination of reactor type, fuel type, and burnup. The data analysis tool automatically yields combined uncertainties using all available information. Descriptions of the two analysis techniques and the background-air correction are given below.
Because any realistically acquired samples will contain both a ®ssiogenic component and a natural-air component, the sampleÕs measured isotopic ratios will consist of a combination of the ®ssiogenic and atmospheric-air noble gases. Because some noble gas isotopes (for instance, 129 Xe and 80 Kr) are not produced in signi®cant quantities via ®ssion, these measured non-®ssiogenic isotopes can be used to remove the background-air contaminant. This requires using known natural abundances of the Xe and Kr isotopes in air (either assumed or measured). If the abundances of all measured noble gas isotopes in atmospheric-air (relative to the abundance of the non-®ssiogenic isotope) are known, then the ®ssiogenic component of that isotope can be determined using x x x Nf;u Nm;u Nm;air ÿ ; 129 129 129 Nm;u Nm;air Nm;air
1
x is the ®ssiogenic component of where Nf;u the concentration of isotope x in the unknown 129 is the concentration of the nonsample, Nm;air ®ssiogenic isotope (in this case 129 Xe) in atmox is the measured concentration of spheric-air, Nm;u 129 ®ssiogenic isotope x in the unknown sample, Nm;u is the measured concentration of the non-®ssiox is the genic isotope in the unknown sample, Nm;air concentration of ®ssiogenic isotope x in atmospheric-air. Considering the element Xe with normalizing isotope 134 Xe and non-®ssiogenic isotope 129 Xe, the isotopic ratio of interest is given by x 129 x 129 x Nm;u =Nm;u ÿ Nm;air =Nm;air Nf;u : 2 134 Nf;u 134 =N 129 ÿ N 134 =N 129 Nm;u m;u m;air m;air
Thus, given a measurement of the isotope of interest and the normalizing isotope relative to 129 Xe in the unknown sample and in atmospheric-air, the background-air contaminant can be removed directly. A similar technique can be used for the Kr gases using 78 Kr and/or 80 Kr as the gas lacking a signi®cant ®ssiogenic component.
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where Rm is the set of all measured ratios or
5.2. Bayesian analysis The Bayesian analysis technique is based on BayesÕ theorem, which relates the probability that the hypothesis is true, given the data, to the probability that we would observe the measured data if the hypothesis were true. In simplest terms, BayesÕ theorem can be seen as [31] prob hypothesisjdata; I / prob datajhypothesis; I prob hypothesisjI;
3
where the standard probability theory notation has been used. In this analysis, BayesÕ theorem is utilized by comparing each of the models (Mj ) in the calculated database and determining which model is most likely to correctly represent the reprocessed fuel. This is achieved by ®rst converting each measured isotopic ratio Rm i to a burnup value for each model through interpolation in the calculated database. A combined average burnup (Bj ) is then created for each model (Mj ) based on all the ratios. The calculated ratios Rci based on the average burnup (Bj ) for each model (Mj ) can then be determined. Using these calculated ratios and the maximum entropy formulation, the probability that a given model at the modelÕs average burnup would result in the observance of the measured ratio is generated using the following equation: p Rm i jMj ; Bj ; I
105
1 ri Mj ; Bj ÿ 2 ! c ÿ Rm i ÿ Ri Mj ; Bj ; exp 2r2i Mj ; Bi 4
where ri (Mj ,Bj ) is the standard deviation of the calculated isotopic ratio. These are calculated for each model in the database. Each model can then be compared to some nominal model using a version of BayesÕ theorem [32] p Mj ; Bj jRm ; I p Mj ; Bj jI Y p Rm i jMj ; Bj ; I ; BjR m ; I p M; BjI p M; p Rm i jM; B; I
m m Rm Rm 1 ; R2 ; R3 ; . . .:
6
Based on the values calculated using Eq. (5), the most appropriate model and burnup value for the observed data can be inferred. It should be noted that these decisions are computationally intensive and that as the calculated database becomes more comprehensive (i.e., more models are added), the computational time for this analysis increases. It may be appropriate in the future to alter the existing format of the database to allow for faster computations on more portable machines. 5.3. Principal component analysis/principal component regression (PCA/PCR) Principal component analysis (PCA) attempts to ®nd the eigenvalues and eigenvectors of the covariance matrix of all the mass spectrometric isotopic ratios in the calibration set by employing a singular value decomposition (SVD). SVD performs the following: Xmn Umm Smn Vnn0 ;
7
where X is the experimental data matrix of m mass spectra of n channels, S is a diagonal matrix of positive square roots of eigenvalues, and V 0 contains the eigenvectors of X 0 X . Note that X 0 X is the covariance matrix and the prime (0 ) denotes a matrix transpose. The results of the PCA model allow the analyst to classify or identify which of the modeled reactors is most likely related to an arbitrary unknown mass spectral signature at future times. Once this categorization is made, the burnup rate for the identi®ed reactor can be determined from a regression equation using principal component regression (PCR). This involves the following: 0 0 Xmn Vnk0 Tkm Tmk ; Vkn Xmm
8
Qkp Dkk Tkm Ymp ;
9
Amp Pmn Vnk0 Qkp ;
10
i
5
106
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where k is chosen by the analyst from the PCA model, Tkm are matrixes of scores, and Ymp are the known reference burnup rates associated with the m mass spectra. The index p only runs to one because we are only trying to predict one dependent variable: the burnup rate. In general, p is greater than one if a plurality of dependent variables needs to be predicted. Dkk is a diagonal matrix of reciprocal eigenvalues, Qkp are the chemical loadings (i.e., how the burnup rates look in the reduced k-dimensional coordinate system), Pmn are the unknown validation spectra to be predicted, and Amp is the predicted quantity (e.g., burnup). The scores, which are related to the eigenvalues, contain information on how spectral samples relate to each other for a given kth dimension. Eq. (8) essentially projects the mass spectra into the modi®ed coordinate system, Eq. (9) transforms the associated reference burnup rates into the same new coordinate system, and Eq. (10) is the regression equation permitting prediction of burnup rates. There are some practical advantages to using principal components as opposed to other statistical tools. These include increased applicability with low signal-to-noise ratios, allowing replicates in the model, producing eigenvectors that may have physically meaningful patterns to an expert, and reducing the number of independent variables needed for graphical diagnostics. To some degree PCA/PCR complements the Bayesian analysis technique mentioned above. This use of complementary techniques adds to the robustness of the proposed system. 6. System validation The proposed technique has been validated using on-stack measurements taken during the reprocessing of spent fuel from a US production reactor. The samples were acquired during the dissolution of weapons-grade spent fuel with a declared burnup of 178 MWd/MTU. The complete system generated an inferred burnup of 171 13 MWd/MTU and correctly matched the measured samples to the reactor type (see Fig. 5). Thus, the inferred burnup was in error by only
Fig. 5. Measured 131 Xe/134 Xe isotopic ratio versus burnup for a US production reactor compared to the HELIOS calculated result (inferred fuel burnup using the LANL technique and the declared fuel burnup are shown).
3.9%, which is most likely within the uncertainty of the declared burnup. This fuel represents a good test of the system because of the small signal-tonoise ratio in low-burnup fuel and the increased diculty in modeling this reactor. On the other hand, from an analysis of Figs. 3 and 4, the production reactor stable noble gas isotopic ratios are clearly dierent from those of any other fuel at low burnup values. Therefore, it is unlikely that the analysis would incorrectly determine the reactor type for this fuel dissolution. This validation demonstrates the accuracy of this technique; however, the ability of this technique to distinguish between dierent power reactor fuels has not been fully tested (especially for PWR versus BWR). Full system tests for power reactor fuels (including on-stack sample collection) will require the cooperation of a commercial reprocessing facility; this is being explored. Current eorts are also being made to acquire samples from other spent fuel operations, research reactor storage facilities, and other sources to aid in the system viability demonstration. This validation shows that the current techniqueÕs accuracy is sucient for many safeguards applications (e.g., distinguishing between low-and high-burnup fuels). However, continued validation for other power and production reactor fuel is necessary to demonstrate the robustness of this technique.
W.S. Charlton et al. / Nucl. Instr. and Meth. in Phys. Res. B 168 (2000) 98±108
7. Conclusions Los Alamos National Laboratory has been actively studying techniques for strengthening safeguards at reprocessing facilities through environmental monitoring techniques. The method proposed here involves the integration of a high-precision mass spectrometer, several reactor analysis codes, and sophisticated data analysis techniques. The integrated system allows for the determination of speci®c fuel parameters such as burnup and reactor type. The complete methodology has been benchmarked for on-stack samples acquired during reprocessing of fuel from a US production reactor. These measurements led to an inferred burnup that matched the declared burnup to within 3.9%. Future work is necessary to demonstrate the robustness of this system for production, power, and research reactor fuels. Also, advances are needed in the database, data analysis tools, and user interface to increase its portability and usability by inspectors. Currently, the database is stored as a series of text ®les at LANL and could be placed into a more sophisticated and accessible format. The data analysis tools requires some degree of integration and increased portability if they are to be easily usable by inspectors (currently the codes are only available at LANL). Acknowledgements The authors would like to thank Holly R. Trellue and David I. Poston for their eorts in helping run the Monteburns code system. Also, thanks must be given to Rudi J.J. StammÕler and Aldo Ferri for aiding in the use of HELIOS. Los Alamos National Laboratory is operated by the University of California for the US Department of Energy under contract W-7405-ENG-36.
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