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Gamma-ray spectrometric measurements of fission rate ratios between fresh and burnt fuel following irradiation in a zero-power reactor
Nuclear Instruments and Methods in Physics Research A 698 (2013) 72–80
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Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Gamma-ray spectrometric measurements of fission rate ratios between fresh and burnt fuel following irradiation in a zero-power reactor a,b,n,1 ¨ H. Krohnert , G. Perret a, M.F. Murphy a, R. Chawla a,b a b
Paul Scherrer Institut (PSI), CH-5232 Villigen, Switzerland ´ cole Polytechnique Fe´de´rale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland E
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 March 2012 Received in revised form 30 August 2012 Accepted 4 September 2012 Available online 11 September 2012
The gamma-ray activity from short-lived fission products has been measured in fresh and burnt UO2 fuel samples after irradiation in a zero-power reactor. For the first time, short-lived gamma-ray activity from fresh and burnt fuel has been compared and fresh-to-burnt fuel fission rate ratios have been derived. For the measurements, well characterized fresh and burnt fuel samples, with burn-ups up to 46 GWd/t, were irradiated in the zero-power research reactor PROTEUS. Fission rate ratios were derived based on the counting of high-energy gamma-rays above 2200 keV, in order to discriminate against the high intrinsic activity of the burnt fuel. This paper presents the measured fresh-to-burnt fuel fission rate ratios based on the 142La (2542 keV), 89Rb (2570 keV), 138Cs (2640 keV) and 95Y (3576 keV) high-energy gamma-ray lines. Comparisons are made with the results of Monte Carlo modeling of the experimental configuration, carried out using the MCNPX code. The measured fission rate ratios have 1s uncertainties of 1.7–3.4%. The comparisons with calculated predictions show an agreement within 1–3s, although there appears to be a slight bias ( 3%). & 2012 Elsevier B.V. All rights reserved.
Keywords: Light water reactor fuel Burnt fuel Fission rates Zero-power reactor Gamma-ray spectrometry Short-lived fission products MCNPX
1. Introduction The ongoing trend of increasing the initial fuel enrichment in order to obtain higher discharge burn-ups has led to more and more heterogeneous core configurations in modern light water reactors. As a consequence, a general need has been recognized for experimental data in the high burn-up range to validate the predictions of reactor physics code packages [1]. To provide such data, the Paul Scherrer Institute (PSI) and the Swiss association of nuclear utilities (swissnuclear) jointly launched the experimental program LIFE@PROTEUS [2] in 2006, the main goal being the investigation of mixed lattices of fresh and highly burnt fuel (burn-ups of up to 60 GWd/t) in the test zone of the zero-power research reactor PROTEUS at PSI. A key type of measurement to be made thereby is that of fission rate distributions across freshto-burnt fuel interfaces. One standard technique to determine fission rates is based on the measurement of the gamma-ray activity of fission products after irradiation [3]. So far, however, the measurements on burnt
n
Corresponding author. Tel.: þ41 56 310 2111; fax: þ 41 56 310 4527. ¨ E-mail address: [email protected] (H. Krohnert). 1 Present address: Swiss Federal Nuclear Safety Inspectorate, CH-5200 Brugg, Switzerland. 0168-9002/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nima.2012.09.008
fuel have been limited to commercial power reactors, where power distributions in fuel assemblies during the last weeks of operation were determined by measuring the 140La gamma-ray line at 1596 keV [4]. The measurement of fission rates in highly burnt fuel following an irradiation in a zero-power reactor requires, because of the low power, the development of a new experimental method that is able to discriminate against the high intrinsic gamma-ray and neutron background of burnt fuel. Two approaches are being investigated currently at PSI. One is based on the measurement of delayed neutrons from the irradiated fuel and has been presented elsewhere [5]. The other, which is the topic of this paper, is based on the detection of gamma-rays from short-lived fission products the energies of which are above the intrinsic background. During preliminary measurements, fresh fuel was irradiated in PROTEUS and several fission products with gamma-ray lines above 2200 keV were identified as potential candidates for the proposed new measurement technique [6]. Among them, the 142 La (2542 keV), 89Rb (2570 keV), 138Cs (2640 keV) and 95Y (3576 keV) gamma-ray lines were later measured in a fresh and a 36 GWd/t burnt UO2 sample. Each of these samples was irradiated at different lattice positions in the PROTEUS test zone, and ratios of fission rates between the different positions were derived [7]. These inter-position fission rate ratios had uncertainties
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of about 1–3% and 3–6% for the fresh and burnt fuel sample, respectively, the main contributions being the counting uncertainties for the different gamma-ray peaks. In the current paper, first results for inter-sample fission rate ratios between a fresh and two different burnt fuel samples (with burn-ups of 36 and 46 GWd/t, respectively) are presented. In comparison to the previously published inter-position fission rate ratios, the derivation of the present results has been considerably more challenging. This follows from the fact that various factors related to the counting efficiency of the detection system no longer cancel out and need to be accounted for explicitly for the two different fuel sample types. This paper is organized in the following way. In Section 2, the conducted experiments are described. Section 3 provides a description of the Monte Carlo (MCNPX) models that were used (a) to predict the inter-sample fission rate ratios, and (b) to estimate the solid angle and attenuation correction factors. The methodology to derive inter-sample fission rate ratios from the measured gamma-ray lines is presented in Section 4. Section 5 investigates the sensitivity of the results to certain specific experimental features. The calculation-to-experiment comparison is presented and discussed in Section 6, while Section 7 gives the final conclusions and recommendations for future experiments.
U T S R Q P O N M L K J I H G F E D C B A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Moderator
2. Experimental set-up and procedures
73
UO (5 wt%)
Irradiation position for fuel sample
Fig. 1. Layout of the PROTEUS test lattice.
This section provides a brief description of the conducted experiments, a detailed description given in [8]. 2.1. Experimental set-up The experiments were carried out at the PROTEUS zero-power research reactor. This critical facility is a multi-zone driven system featuring a central test zone ( 45 45 cm2), which can be loaded with the fuel configuration to be studied. The test zone itself is subcritical and is fed with neutrons from the surrounding annular driver zones. Fig. 1 shows the test zone configuration that was currently used [7]. The test lattice consisted of 5% enriched UO2 pins loaded in a pattern resembling that of a specific supercritical-water reactor (SCWR) assembly design. The test zone was filled with a H2O/D2O mixture to simulate water with a reduced density. As indicated earlier, three different fuel samples were used in the present experiments: a 3.5% enriched fresh UO2 sample, a 36 GWd/t burnt UO2 sample (initial enrichment 4.1%) and a 46 GWd/t burnt UO2 sample (initial enrichment 3.5%). All samples had been part of fuel pins irradiated in a Swiss PWR. The cooling time of the burnt samples was about 12.5 years. Each sample had a total pellet length of approximately 40 cm and a pellet diameter of about 0.91 cm. For the experiments, the fuel samples were placed into a specially designed transport flask. The latter was made of steel and had an outer diameter of about 70 cm. The samples were loaded into a rotary revolver at the center of the flask. Placed above the test zone of the reactor, within the reactor shielding, the flask also served as a sample changer for lowering the samples into the PROTEUS test lattice. For this purpose, the sample changer was equipped with a control unit to rotate the revolver hosting the samples in the flask, and to move the samples up and down. One at a time, the samples were inserted into different lattice positions for irradiation, and their gamma-ray activities were measured several minutes after the end of irradiation. The gamma-ray measurements took place directly within the steel body of the sample changer, using an HPGe detector (ORTEC model GEM-15180-P) that
was located in a cavity drilled into the steel body. The signals were processed by a DSPEC Plus multi-channel analyzer from ORTEC. A live-time spectrum and a so-called zero-dead-time (ZDT) spectrum were recorded in parallel. The latter spectrum is continuously corrected for dead-time losses on a channel-by-channel basis during data acquisition. Considering the rapidly changing count rates during the data acquisition, the ZDT option was particularly suitable for the current experiments. Demonstration of the reliability of the ZDT methodology for high dead times and strongly varying count rates has been reported elsewhere [9]. The acquired data were saved with the ORTEC software Gamma-Vision [10], while the software HyperLab [11] was used for the analysis of the ZDT spectra. Two different measurement positions were used for the fresh and the burnt fuel samples. As illustrated in Fig. 2, the fresh fuel sample was measured as close as possible to the detector, the distance between the sample and detector centers being about 20 cm. Due to their high intrinsic gamma-ray activity, the burnt fuel samples had to be moved to a position further away from the detector in order to keep the system dead time reasonably low. Consequently, the burnt samples were measured in a position below the detector, rather than in line with it, the distance between the top of the sample and the detector being about 26 cm. During the measurement of a given sample, the other burnt samples were moved to positions below the sample changer so as to avoid any interference from their intrinsic gamma-ray activity. 2.2. Irradiation and measurement conditions The irradiation and gamma-ray measurement conditions for the three samples are summarized in Table 1. The cooling time between irradiation and data acquisition corresponds to the time needed to withdraw the sample from the core and bring it into the measurement position. All times were measured with a precision of 1 s. The maximum dead times were the system dead times at the beginning of data acquisition (5 min after irradiation), while the minimum dead times refer to the values at the end of
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Radial position burnt sample
Radial position fresh sample
detector
detector
sample
sample
20cm
25cm Axial position burnt sample
Axial position fresh sample
sample
22cm
sample
detector
8cm
74
detector
Fig. 2. Fuel samples in their post-irradiation measurement positions in the transport flask.
Table 1 Reactor power (with nominal neutron flux value), irradiation time ti, cooling time tc, acquisition time ta, and maximum and minimum dead times (dT) for the conducted gamma-ray measurements. Sample
Reactor power (W)
n-flux (s 1 cm 2)
Lattice positions
ti (min)
tc (min)
ta (h)
Max. dT (%)
Min. dT (%)
Fresh UO2 36 GWd/t UO2 46 GWd/t UO2
100 800 800
5 108 4 109 4 109
M8, K7, L11 M8, K7, L11 I8
30 15 15
2–5 2–5 2–5
6 6 6
60 50 68
2 35 62
acquisition, when the count rate had already reached almost the background level. As mentioned above, the measurements took place inside the sample changer, within the reactor shielding. In spite of additional neutron shielding placed around the sample changer, a considerable fast neutron flux reached the detector during each irradiation and damaged the detector crystal, leading to a continuous worsening of the detector resolution. The total number of irradiations was thus limited. Accordingly, the experimental campaign focused on first irradiating the 36 GWd/t burnt fuel sample, and then the fresh sample, in the three lattice positions M8, K7 and L11. The 36 GWd/t burnt sample showed significantly lower count rates than the fresh sample because of its remote measurement position and its lower fissile content. To compensate for this, it was irradiated twice in each lattice position at a higher power than the fresh fuel sample, and the analysis was carried out on the sum of the recorded spectra. At the end of this set of irradiations, the detector resolution was still acceptable and, finally, the 46 GWd/t burnt fuel sample was irradiated twice in the position I8. The latter is equivalent to the position M8, both corresponding to the center of a moderator channel of the SCWRlike test lattice (see Fig. 1).
2.3. Measured gamma-ray activity from short-lived fission products As example, Fig. 3 shows recorded gamma-ray spectra of the three samples after an irradiation in the moderator channel position M8 (I8). In the high-energy region, gamma-ray lines from the freshly produced fission products 142La, 89Rb, 95Y, 138Cs and 84Br are clearly visible for all three samples. The intrinsic background of the burnt fuel samples below 2000 keV is seen to be quite dominating, the most prominent peaks being those from the long-lived fission products 154Eu and 137Cs. Apart from the fission product peaks, background peaks related to the activation of surrounding materials can be observed. The activation products 56 Mn and 116mIn are formed by (n,g) reactions on 55Mn and 115In in the steel of the sample changer and in the detector mount, respectively. The 1H (2223 keV) line corresponds to prompt gamma-rays from neutron captures in 1H which is present in the neutron shielding around the detector. Among the short-lived fission product peaks, only five have been considered for the present analysis of the measurements. These are 142La (2542 keV), 89Rb (2570 keV), 95Y (2632 keV), 138Cs (2640 keV) and 95Y (3576 keV). The other peaks suffered either from too low counting statistics or from interference with
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75
Fig. 3. Gamma-ray spectra of irradiated fresh, 36 GWd/t and 46 GWd/t burnt fuel samples; (a) energy region 0–2000 keV; (b) energy region 2000–4000 keV.
background peaks. The latter was particularly the case for 138Cs (2218 keV) interfering with the 1H (2223 keV) line, and for 142La (2398 keV) interfering with the 116mIn (2392 keV) line. For the further analysis, the counts of the two adjacent peaks 95 Y (2632 keV) and 138Cs (2640 keV) were summed. In the following, for the sake of convenience, the results for these two peaks are simply referred to as 138Cs (2640 keV).
3. MCNPX modeling Two Monte Carlo models have been employed in the frame of the present study, using MCNPX-2.5 [12] in conjunction with the JEFF-3.1 nuclear data library [13]. The first is a detailed model of the complete PROTEUS reactor, and the second is a model of the measurement set-up. 3.1. Whole-reactor model for fission rate calculations A 3D whole-reactor model of PROTEUS, with explicit representation of the individual fuel pins, was used to derive the freshto-burnt fuel fission rate ratios of interest. To this purpose, the three samples were modeled, one by one, in the given lattice positions, and the average number of fissions in the fuel was tallied suitably in each case. The fresh fuel sample was modeled according to its nominal specifications. Regarding the burnt fuel samples, their isotopic compositions were modeled according to post-irradiation examinations (PIEs) carried out previously at the PSI Hot Laboratory on adjacent fuel sections of the fuel pins from which the fuel samples had been cut [14]. In the MCNPX model, the fuel composition was considered homogenously distributed in both radial and axial directions. The 1s uncertainty on the calculated fission rates was about 0.15%, the uncertainties on the resulting calculated fission rate ratios being about 0.3%. The quoted uncertainties on the calculated fission
rate ratios are only statistical Monte Carlo uncertainties, being dependent on the number of simulated neutron histories. Apart from the total fission rates, the whole-reactor model served to calculate the contributions of the major fissioning isotopes (235U, 238U, 239Pu, 241Pu) to the total number of fissions. These isotopic fission contributions were needed for the derivation of the fission rate ratios from the measurements (see Section 4). Furthermore, the axial and radial fission profiles within the sample were tallied in terms of 20 axial regions and 6 concentric layers, respectively. The axial distribution was used as input for the MCNPX model of the measurement set-up (see next section), and the radial profile was used for the sensitivity study described in Section 5.2. 3.2. Model of the measurement station for solid angle and attenuation corrections A model of the measurement station was used to calculate the solid angle and attenuation correction factors, which were needed for the derivation of the experimental fission rate ratio values (see Section 4). The correction factors are defined as the fraction of gammarays emitted by the fuel sample that reach the detector without interacting in the sample changer or in the fuel sample itself. They were calculated by tallying the uncollided gamma-ray fluxes in the germanium crystal of the detector. The geometry and composition of the samples were modeled as described in Section 3.1. Each sample was modeled in its particular measurement position (see Fig. 2). For each energy of interest, i.e. 2542 keV, 2570 keV, 2640 keV and 3576 keV, a gamma-ray source was assigned to the samples according to the axial fission profile obtained with the whole-reactor model. The radial source distribution was assumed to be homogenous. The uncertainties on the correction factors were about 0.1% and 0.3% for sources in the fresh and burnt fuel measurement positions, respectively. Again, the quoted uncertainties are simply the statistical Monte Carlo uncertainties.
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4. Derivation of measured fission rate ratios In this paper, three fresh-to-36 GWd/t fuel fission rate ratios are presented, corresponding to the comparison made between the fresh and 36 GWd/t burnt samples for each of the three lattice positions M8, K7 and L11. The 46 GWd/t fuel sample was only irradiated in the lattice position I8, which is equivalent to position M8. Accordingly, only one fresh-to-46 GWd/t fuel fission rate ratio is presented. The methodology used to derive the inter-sample fission rate ratios is similar to that employed for the inter-position ratios reported earlier [7]. Given the different measurement positions for the fresh and the burnt fuel samples, however, an additional correction factor, taking into account the corresponding solid angle and gamma-ray attenuation effects during measurement, had to be introduced. 4.1. Methodology to derive fission rate ratios Each measured fresh-to-burnt fuel fission rate ratio was independently estimated with the four gamma-ray lines 142La (2542 keV), 89Rb (2570 keV), 138Cs (2640 keV) and 95Y (3576 keV). The fission rate ratio estimate FRR(Eg) based on a particular gamma-ray line of energy Eg can be written as follows: FRRðEg Þ ¼
Nnet,f attðEg Þb UbðEg ÞUC b U attðEg Þf UbðEg ÞUC f N net,b
ð1Þ
where the factors att(Eg) take into account corrections for the solid angle and the gamma-ray attenuation between the samples and the detector, and the subscripts f and b refer to the fresh and burnt fuel samples, respectively. Nnet is the net-count area of the gamma-ray line in the ZDT spectrum, b(Eg) is the gamma-ray intensity, and C is the correction for saturation and decay of the fission product. The efficiency of the gamma-ray detector is not present in Eq. 1, since the same gamma-ray line is considered for both the fresh and burnt fuel measurements. Note that if interfering gamma-ray peaks had to be considered, as was the case for 138Cs (2640 keV), the expression b(Eg) C in Eq. 1 had to be replaced by a sum of equivalent expressions, one for each contributing fission product [8]. Finally, the four individual estimates FRR(Eg) were compared for consistency and a standard weighted mean was derived to yield the final experimental value of the fission rate ratio. The procedure was repeated for each measured fresh-to-burnt fuel fission rate ratio. In the following, the determination of the individual parameters occurring in Eq. 1, as also their typical values, are discussed briefly. Uncertainties are quantified in Section 4.6. 4.2. Net-count areas Nnet The net-count areas in the ZDT spectra were obtained using the gamma-ray spectrum analysis code Hyperlab [11]. The spectrum fitting and deconvolution in Hyperlab are performed on a region-by-region basis with a semi-empirical fit function. The fit function accounts for the Gaussian peak shape and the background, as also for the low and high energy tailing of the peak. The various parameters of the fit function are determined with a standard least square method. The covariance matrix of the fitted parameters is also computed to estimate the uncertainty on the calculated net-peak areas. Due to the degrading detector resolution, the separation of strongly interfering peaks like 95Y (2632 keV) and 138Cs (2640 keV) became more and more error-prone. By summing the calculated net-count areas of the interfering peaks, as mentioned above, the potential error of attributing counts to a wrong
peak could be avoided. The estimated uncertainties of the netcount areas were combined applying the standard error propagation law. Typical net-count areas of the four investigated peaks were between 20,000 and 70,000 counts for the fresh fuel sample, between 3500 and 8000 counts for the 36 GWd/t burnt sample, and between 2500 and 6500 counts for the 46 GWd/t burnt sample (irradiation positions M8 and I8, respectively). 4.3. Solid Angle and attenuation correction factors att(Eg) As the fresh and burnt fuel samples were measured in different positions, the solid angle, and the attenuation of the gamma-rays between sample and detector were different in the two cases. This is accounted for in Eq. 1 by the ratio of the factors att(Eg)b and att(Eg)f. As described in Section 3, the factor att(Eg) was determined with MCNPX, being defined as the ratio of the number of uncollided gamma-rays arriving in the detector to the number emitted in the sample. For the fresh fuel sample, the tallied uncollided gamma-ray fluxes in the detector varied between 1.0 10 6 cm 2 per source gamma-ray with an energy of 2542 keV and 1.7 10 6 cm 2 per source gamma-ray with an energy of 3576 keV. Due to their specific measurement positions, which led to a lower solid angle and more shielding material between the detector and the samples, the corresponding results for the burnt fuel samples were lower. As an example, the tallied fluxes for the 36 GWd/t burnt sample varied between 4.2 10 8 cm 2 per source gammaray of 2542 keV and 8.9 10 8 cm 2 per source gamma-ray of 3576 keV. Thus, typical values of att(Eg)b/att(Eg)f were about 20–25, with a statistical Monte Carlo uncertainty of about 0.3%. This implies that 20–25 times more gamma-rays emitted from the fresh fuel measurement position reached the detector than from the burnt fuel measurement position, the self-absorption in the fresh and burnt fuel being similar. 4.4. Saturation and decay correction factors C Basic corrections for saturation and decay of fission products during and after irradiation can be found in the literature [15]. The simplest case for obtaining the saturation and decay correction is for the gamma-ray lines 142La (2542 keV), 89Rb (2570 keV) and 95Y (3576 keV). The corresponding correction factor is given by Eq. 2, relating the fission rate in the fuel sample during irradiation to the number of gamma-rays of a specific energy emitted by the considered fission product during the data acquisition. Y ind,2 i12 Ul1 UY cum,1 C¼ Uð1el2 ti ÞUel2 tc Uð1el2 ta Þ þ l2 l2 Uðl1 l2 Þ i12 Ul2 UY cum,1 Uð1el1 ti ÞUel1 tc Uð1el1 ta Þ þ ð2Þ l1 Uðl2 l1 Þ Ycum and Yind are the cumulative and independent effective fission yields, and l is the decay constant, the index 1 referring to the direct parent of the detected fission product and the index 2 to the fission product itself. The variables ti, tc and ta are the irradiation, cooling and acquisition times, respectively. In this simple case, the parent isotope decays only into the ground state of the fission product, the corresponding branching ratio being i12, and no isomeric state has to be considered. As mentioned, Eq. 2 can be applied in the case of the 142La (2542 keV), 89Rb (2570 keV) and 95Y (3576 keV) gamma-ray lines. The correction for the 138Cs (2640 keV) line is more complex because of the non-negligible isomeric state 138mCs [6]. All nuclear data were taken from the JEFF-3.1 nuclear data library [13]. The calculated values for saturation and decay
H. Kr¨ ohnert et al. / Nuclear Instruments and Methods in Physics Research A 698 (2013) 72–80
correction factors did not strongly differ between the three samples. Typically, the ratios ðbðEg ÞUC b Þ=ðbðEg ÞUC f Þ varied between 0.8 and 1.5.
4.5. Effective fission yields Yind and Ycum The effective cumulative fission yields Ycum of the different isotopes were calculated according to Eq. 3 as the sum of the fission yields for the main fissioning isotopes 235U, 238U, 239Pu and 241 Pu, weighted by their isotopic fission contributions aU5, aU8, aP9 and aP1. Y ¼ aU5 UY th,U5 þ aU8 UY f ,U8 þ aP9 UY th,P9 þ aP1 UY th,P1
ð3Þ
with aU5 þ aU8 þaP9 þaP1 ¼ 1 The values aU5, aU8, aP9 and aP1 were obtained for each fuel sample, in each investigated lattice position, with the help of the MCNPX whole-reactor model, the statistical Monte Carlo uncertainty being less than 0.2% in each case. The MCNPX simulations also showed that, for each investigated case, more than 99% of the fissions in 235U, 239Pu and 241Pu occurred in the low energy range (0–0.1 keV), whereas more than 99% of the fissions in 238U occurred at high energies (9.1 keV–10 MeV). Accordingly, because of the rather weak dependence of the yields on energy, thermal fission yields alone could be used for fissions in 235U, 239Pu and 241 Pu, and fast fission yields could be used for fissions in 238U. Table 2 summarizes the calculated values of aU5, aU8, aP9 and aP1, obtained for the three samples irradiated in the moderator position M8(I8). Compared to the position M8(I8), the two lattice positions K7 and L11 had a less thermal neutron spectrum. Consequently, the fission contribution of 235U was reduced and that of 238U increased. However, the changes in these contributions were less than 4%. It is interesting to note that the fission contribution of 241Pu doubled in the 46 GWd/t sample, as compared to the 36 GWd/t sample, reaching more than 10%. The different isotopic fission contributions in the three samples are important because of their impact on the error propagation of the uncertainties on the fission yields. As seen in Eq. 2, independent fission yields are also required for the saturation and decay correction. Unfortunately, most of the independent fission yields of the investigated fission products are afflicted with extremely high uncertainties (e.g. 30–36% for Yind,th,U5 values for 95Y, 138Cs, 89Rb and 142La). To avoid these high uncertainties, the independent fission yields in Eq. 2 were replaced by the difference between the cumulative fission yields of the fission product and that of its parent weighted by the branching ratio i12. Nevertheless, the uncertainties on the fission yields remain one of the main contributing factors to the overall uncertainty on a given fission rate ratio (see following section).
77
uncertainties on the net-count areas, the statistical Monte Carlo uncertainties on the solid angle and attenuation corrections, and the uncertainties on all nuclear data such as fission yields, branching ratios, decay constants and gamma-ray intensities. All parameters were assumed to be independent and no covariance term was considered. The fission products emitting the measured gamma-ray lines pertain to different mass chains and their nuclear data are only weakly correlated among each other. It could not be excluded that the quoted cumulative fission yields of a considered fission product and its direct parent were correlated. However, this potential correlation could not be quantified in the present work. Since the times were recorded with a 1 s accuracy, the variables ti, tc and ta were considered as exact values. The statistical Monte Carlo uncertainties on the variables aU5, aU8, aP9 and aP1, calculated with MCNPX (see Section 3), were negligible and were not included in the uncertainty propagation. The uncertainties related to the fuel composition assumed in the calculations, however, were not negligible. These could not be quantified in the present work and were, instead, addressed with sensitivity studies [8], one of which is described in Section 5.1. The uncertainties on the net-count areas were determined, as mentioned previously, with the analysis software Hyperlab. The uncertainties on the nuclear data were taken from the JEFF-3.1 data library. Most of the nuclear data involved basically canceled out when taking fission rate ratios, so that, in general, the uncertainties on the nuclear data made a rather low contribution to the combined uncertainty. A notable exception was the uncertainty on the fission yields for 235U and 239Pu, which are summarized in Table 3. Table 4 shows the results of the uncertainty analysis for the freshto-36 GWd/t and the fresh-to-46 GWd/t fission rate ratios in the irradiation position M8(I8). For each gamma-ray line, the combined uncertainty of the derived fission rate ratio and its contributions are given. The latter correspond to the statistical uncertainties on the netcount areas, the uncertainties on the nuclear data and the Monte Carlo uncertainties on the MCNPX results. The combined uncertainty on each of the final fission rate ratio estimates, computed as a weighted mean, is also given in Table 4. In all cases, the uncertainties on the net-count areas represent the main contribution to the combined uncertainties. It should be noted, however, that the contribution from the nuclear data reached more than 1% for the fresh-to-46 GWd/t comparison. This resulted mainly from the uncertainties on the fission yields, the samples being of very different compositions with correspondingly large differences in isotopic fission contributions. This is important because, unlike the statistical uncertainties, the nuclear data uncertainties cannot be easily reduced in future experiments.
5. Sensitivity studies Table 2 Contributions aU5, aU8, aP9 and aP1 to the total number of fissions in the fuel samples irradiated in position M8(I8). Sample
aU5 (%)
aU8 (%)
aP9(%)
aP1(%)
Fresh 36 GWd/t 46 GWd/t
97.7 53.1 27.4
2.3 2.9 3.7
– 38.0 57.1
– 6.0 11.8
4.6. Uncertainty considerations The combined uncertainty on an independent estimate of a measured fission rate ratio, based on a particular gamma-ray line, was determined by applying the standard error propagation law. The uncertainties included in the error propagation were the
As mentioned earlier, the uncertainties considered for the MCNPX results are only the statistical Monte Carlo uncertainties. Uncertainties on the results related to the modeling of the geometry and the fuel composition have not been derived in a systematic way. Instead, they have been assessed separately with the help of sensitivity studies, which are presented in this section. 5.1. Axial burn-up profile of the 36 GWd/t burnt fuel sample An axial scan of the intrinsic gamma-ray activity of the burnt fuel pin, from which the 36 GWd/t sample was cut, indicated that the sample should have a significant axial burn-up gradient ( 10% over its 40 cm length). It was, however, hardly possible to quantify the exact axial burn-up profile, and thus the axial
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Table 3 Cumulative thermal fission yields of considered fission products in % and relative uncertainties [13]. Gamma-ray energy
Fission product
Ycum,th,U5
Ycum,th,P9
Parent isotope
Ycum,th,U5
Ycum,th,P9
2542 keV 2570 keV 2640 keV 3576 keV
142
5.86 4.69 6.69 6.47
4.97 1.68 5.94 4.82
142
5.80 4.43 6.41 5.28
4.68 1.42 5.02 3.23
La Rb 138 Cs 95 Y 89
(1.7%) (1.2%) (1.7%) (1.1%)
(1.1%) (1.9%) (2.7%) (2.0%)
Ba Kr 138 Xe 95 Sr 89
(1.7%) (1.4%) (1.8%) (2.2%)
(1.3%) (2.7%) (3.3%) (5.2%)
Table 4 Contributions to the combined uncertainties of measured inter-sample fission rate ratios. Counting uncert. (%)
Nuclear data uncert. (%)
Monte Carlo uncert. (%)
Combined uncert. (%)
Fresh-to-36 GWd/t fission rate ratio (M8) 142 La (2542 keV) 3.4 89 Rb (2570 keV) 5.2 138 Cs (2640 keV) 7.0 95 Y (3576 keV) 2.9 Weighted mean
0.7 0.5 1.0 0.8
0.3 0.3 0.3 0.3
3.5 5.2 7.1 3.1 2.0
Fresh-to-46 GWd/t fission rate ratio (M8,I8) 142 La (2542 keV) 5.6 89 Rb (2570 keV) 9.3 138 Cs (2640 keV) 30.2 95 Y (3576 keV) 4.6 Weighted mean
1.2 1.0 1.4 1.4
0.3 0.3 0.3 0.2
5.7 9.4 30.2 4.8 3.4
isotopic distributions, of the sample. Accordingly, the composition of the sample in MCNPX was assumed to be axially homogeneous, corresponding to the measured PIE results. The PIE had been performed on a fuel segment contiguous to the lower burn-up end of the sample, so that the overall burn-up of the sample modeled in MCNPX corresponded to a slight underestimation. The sensitivity of the calculated fission rate to the axial burnup profile was evaluated by repeating the fission rate calculation while assuming an increased sample burn-up of 5% and 10%, respectively. To this aim, a HELIOS pin-cell model of the fuel rod [16] was used for depleting the isotopic composition of the sample to the nominal burn-up, as also to 5% and 10% higher burn-up values. The calculated fission rates in the fuel sample with increased burn-ups were about 3% and 5% lower than those for the nominal burn-up, due to the reduced amounts of fissioning material in the fuel. This result has clearly to be taken into account when interpreting the comparison between measured and calculated fission rate ratios presented in Section 6. The change in the modeled sample composition also had an impact on the measured fission rate ratios. This is due to the change in the isotopic fission contributions aU5, aU8, aP9 and aP1, and to the resulting change of the effective fission yields used in the saturation corrections. A burn-up increase of 5% changed the fraction of fissions in 235U and 239Pu by 5.5% and þ3.5%, respectively. As a result, the measured fission rates based on the 89 Rb (2570 keV) peak were affected by about 2%, because of the very different fission yields for 235U and 239Pu. In comparison, the impact on the results based on the 142La (2542 keV), 138Cs (2640 keV) and 95Y (3576 keV) peaks was less than 0.7%, since the fission yields of these fission products do not strongly depend on the fissioning isotope. This result is of importance for future experiments in which the composition of the burnt fuel may not be known from PIE. In such a situation, it might be advisable not to include 89Rb in the quantitative analysis.
clearly a simplification with respect to burnt fuel samples, in which isotope densities can have significant radial variations. Sensitivity studies were carried out to quantify the impact of this simplification on the calculated fission rates in the burnt fuel samples, on the isotopic fission contributions (aU5, aU8, aP9, aP1), and on the attenuation corrections. HELIOS depletion calculations were used to obtain the radial number density distribution of each fissioning isotope for the 36 and 46 GWd/t samples. Six concentric layers of equal areas were considered for the purpose. As example, the radial number density distributions obtained for the 36 GWd/t sample are shown in Fig. 4. The radial distributions were then implemented into the samples in the MCNPX whole-reactor model. Each fissioning isotope was distributed according to its radial profile and scaled to conserve its total number density in the sample. The total fission rate in the 36 GWd/t sample, at a given irradiation position in the PROTEUS test lattice, changed only marginally (0.4%) by introducing the radially distributed isotopic composition. The same was the case for the isotopic fission contributions (less than 0.4% deviations). Very similar results were obtained for the 46 GWd/t sample. Using the whole-reactor model, the radial profile of the total fission rate during the PROTEUS irradiations was obtained for each sample (see Fig. 4). This was used as the gamma-ray source profile in the model of the sample changer. It was found that, for the investigated high-energy photons, the self-attenuation within the sample was the same (about 20%) with and without consideration of the radial gamma-ray source distribution, and that the calculated solid angle and attenuation correction factors did not change. Consequently, the simplification of employing a radially uniform sample composition in the MCNPX models is well justified.
5.2. Radial profile of isotopes in the burnt fuel samples
The geometry of the fuel samples and their measurement positions within the sample changer have been modeled as accurately as possible. Nonetheless, it could not be excluded that the pellet stacks of the burnt fuel samples were shifted by a few
In MCNPX, the isotopic composition of a fuel sample was modeled homogeneously also in the radial direction. This is
5.3. Axial elevation of the fuel samples in the sample changer model
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Fission rate, number density (normalized to 1 in outer segment)
1.2
79
Total fissions
1.1
Fissions 235U
1.0
Number density 235U Fissions 239Pu
0.9
Number density 239Pu
0.8
Fissions 241Pu
0.7
Number density 241Pu
0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.1
0
0.2 0.3 Mid-radius of segment [cm]
0.4
Fig. 4. Number densities and fission radial distributions within the 36 GWd/t burnt fuel sample.
Table 5 Comparison of calculated and experimental inter-sample fission rate ratios (C/E values).
Fresh-to-36 GWd/t Fresh-to-46 GWd/t
M8(I8)
K7
L11
1.045 70.021 (2.0%) 1.012 70.034 (3.4%)
1.020 70.018 (1.8%)
1.031 7 0.018 (1.7%)
millimeters within their overcladding. In addition, the exact position of the sample within the sample changer is given with a precision of 71 mm. Given that the burnt fuel samples were measured below the detector, rather than in line with it (see Fig. 2), the calculated solid angle and attenuation correction factor for these samples has been found to be highly sensitive to an axial displacement. The calculated fission rates changed by about 1.5% and 8% for axial displacements as small as 1 and 5 mm, respectively.
6. Calculation-to-experiment comparisons and discussion The measured values of fresh-to-burnt fuel fission rate ratios were compared to the corresponding calculated results obtained with the whole-reactor MCNPX model described in Section 3. The comparisons between calculated (C) and experimental (E) intersample ratios are summarized in Table 5. The indicated uncertainties (1s) mainly reflect those on the net-count areas and on the nuclear data, the contributions of the statistical uncertainties in the MCNPX simulations being negligible (see Table 4). The net uncertainties are seen to be between about 2% on the C/Es for the fresh-to-36 Gwd/t fission rate ratios and 3.4% on the C/E for the fresh-to-46GWd/t fission rate ratio. For all three irradiation positions, the agreement between the measured and calculated fresh-to-36 GWd/t fission rate ratios is within 1–3 standard deviations. Nonetheless, the results predicted by MCNPX appear on average about 3% higher than the
measured values. Considering the observation made earlier with respect to the axial burn-up profile in the 36 GWd/t sample (see Section 5.1), the calculated fission rates in this sample should be about 3% lower than those reflected in Table 5 (assuming a 5% higher sample burn-up). This would increase the observed bias between experiment and calculation to about 6%. It is not easy, however, to identify the exact cause for such a bias. One possible explanation, as discussed below, could be a slight axial displacement of the 36 GWd/t sample within its overclad. As described earlier (Section 5.3), the exact position of the fuel during measurement was needed to accurately calculate the solid angle and attenuation correction factors. The sensitivity of the measured fission rate ratios to the modeled elevation of the burnt fuel samples was found to be quite high (as much as about 8% for a displacement of 5 mm). Consequently, a displacement of 3–4 mm of the 36 GWd/t fuel sample could account for a 6% discrepancy between calculated and measured results. To avoid such difficulties in future experiments, care should be taken to minimize the sensitivity of the measurements to the positioning of the samples and to ensure a relatively flat burn-up profile in the burnt fuel employed (at least in the measured part of the fuel samples). As seen from Table 5, the measured and calculated fresh-to-46 GWd/t fission rate ratios, which were derived for the equivalent irradiation positions M8 and I8, agreed within the 1s uncertainty of 3.4%. This demonstrates the possibility to extend the currently developed measurement technique to higher burn-ups.
7. Conclusions and outlook A new measurement technique, which uses high-energy gamma-rays emitted by freshly induced fission products, is being developed at the Paul Scherrer Institute (PSI) to determine fission rates in fresh and burnt nuclear fuel (re-)irradiated in a zeropower research reactor. To test this technique, gamma-ray spectrometry has been conducted on fresh and burnt UO2 fuel samples (burn-ups of 36 GWd/t and 46 GWd/t) irradiated in the PROTEUS zero-power reactor. Thereby, it has been possible to accurately
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measure the high-energy gamma-rays emitted by short-lived fission products, not only in fresh but also in burnt fuel with high intrinsic gamma-ray backgrounds. Based on gamma-ray lines emitted by the freshly induced fission products 142La, 89Rb, 138 Cs and 95Y, fission rate ratios have – for the first time – been derived comparing a fresh fuel sample to burnt (36 GWd/t and 46 GWd/t) fuel samples. Comparison with MCNPX predictions of the fission rate ratios showed a satisfactory agreement within 1–3s (see Table 5). The measured fresh-to-burnt fuel fission rate ratios have a 1s accuracy of 1.7–3.4%. The main contribution to the uncertainties being statistical, the improvement of the gamma-counting statistics has been noted as an important requisite for future experiments. One possibility is to further optimize the shielding against the fast neutron background from the reactor, which would allow longer irradiation times and especially improve the statistics for the somewhat longer-lived fission products 138Cs and 142La. Another possibility is the use of additional detectors or of a detector with a larger germanium crystal. The latter would have the advantage of an increased detection efficiency for high-energy gamma-rays relative to low energy ones, but it would require an optimized detector shielding to maintain acceptable system dead times. Fission rates derived from the 89Rb activity are quite sensitive to the relative contributions of 235U, 238U, 239Pu and 241Pu to the total number of fissions, whereas those based on 95Y, 142La and 138 Cs are not. The sensitivity to the exact isotopic composition of the fuel in the case of 89Rb was to be expected, because of its significantly different fission yields for 235U and 239Pu. Consequently, it might be advisable not to include 89Rb for experiments in which the composition of the burnt fuel samples is not well known. Another important observation in the context of the present experiments is that, because of the different counting geometries employed for the fresh and burnt samples, the experimental results have been found to be highly sensitive to slight axial displacements of the burnt fuel during data acquisition. In future experiments, this high sensitivity can be reduced relatively easily, by optimizing the filter between sample and detector such that a more favorable measurement position can be used for all samples. Finally, the contribution of nuclear-data related uncertainties to the net uncertainty on derived fission rate ratios has been seen to be in the range 0.5–1.4%. In contrast to the statistical uncertainties, this specific contribution cannot be improved unless new and more accurate fission yield measurements are carried out.
Consequently, this will probably be the main constraint to the achievable precision in future experiments.
Acknowledgments This work has been carried out in the framework of LIFE@PROTEUS, a joint research program. The authors thank J.-M. Cavedon and M. Zimmermann (PSI), J. Krouthe´n (Axpo AG), F. Jatuff and ¨ W. Sauser (Kernkraftwerke Gosgen), U. Georg (Kernkraftwerke ¨ Mulhleberg), H.-D.Berger (AREVA-NP), and U. Bergmann (Westinghouse Electric Sweden) for their support of the program. Special thanks are also due to M. Fassbind, M.W. Zimmermann, and A. Stephan for their excellent maintenance and operation of the reactor.
References [1] NEA, Very High Burn-ups in Light Water Reactors, NEA Report No. 6224, ISBN 92-64-02303-8, 2006. [2] M.F. Murphy et al., Large-Scale Irradiated Fuel Experiments at PROTEUS research program, PHYSOR 2010, Pittsburgh, Pennsylvania, USA, 9–14 May 2010. [3] U. Bergmann, et al., Nuclear Instruments Methods A 556 (2006) 331. [4] P. Jansson, et al., Nuclear Science Engineering 152 (2006) 76. [5] K. Jordan, G. Perret, Nuclear Instruments Methods A 634 (2011) 91. ¨ [6] H. Krohnert et al., Measurement of fission rate ratios in fresh UO2 fuel utilising short-lived high-energy gamma activity, PHYSOR 2008, Interlaken, Switzerland, CD-ROM, ISBN 978-3-9521409-5-6, 14–19 September 2008. ¨ [7] H. Krohnert, et al., Nuclear Instruments Methods A 624 (2010) 101. ¨ [8] H. Krohnert, Fission rates measured using high-energy gamma-rays from short half-life fission products in fresh and spent nuclear fuel, Ph.D. dissertation, Ecole Polytechnique Fe´de´rale de Lausanne, Switzerland, 2011. [9] M. Blaauw, Journal of Radioanalytical Nuclear Chemistry 257 (3) (2003) 457. [10] ORTEC, Gamma-Vission-32, Gamma-ray Spectrum Analysis and MCA Emulator, A66-B32 user’s Manual, 2003. [11] HyperLabs Software, HyperLab 2005 Gamma Spectroscopy Software System, Manuals, 2005. [12] D.B. Pelowitz, MCNPX User’s Manual Version 2.5.0, Los Alamos National Laboratory Report LA-CP-05-0369, 2005. [13] A. Koning et al., The JEFF-3.1 Nuclear Data Library, in JEFF Report 21, NEA No.6190, ISBN 92-64-02314-3, 2006. [14] P. Grimm et al., Burnup Calculations and Chemical Analysis of Irradiated Fuel Samples Studied in LWR-PROTEUS Phase II, PHYSOR 2006, Vancouver, Canada, CD-ROM, ISBN 0-89448-697-7, 10–14 September 2006. [15] G. Gilmore, J.D. Hemingway, Practical Gamma-ray Spectrometry, ISBN 0-47195-150-1, 1995. ¨ [16] H. Krohnert, Analysis of the nuclide composition of highly-burnt PWR fuel examined in connection with the LWR PROTEUS Phase II project with the ¨ W¨arme- und Brennstofftechnik, Technische spectral code HELIOS, Institut fur ¨ Braunschweig, Diploma thesis, 2006. Universitat
Contents lists available at SciVerse ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Gamma-ray spectrometric measurements of fission rate ratios between fresh and burnt fuel following irradiation in a zero-power reactor a,b,n,1 ¨ H. Krohnert , G. Perret a, M.F. Murphy a, R. Chawla a,b a b
Paul Scherrer Institut (PSI), CH-5232 Villigen, Switzerland ´ cole Polytechnique Fe´de´rale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland E
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 March 2012 Received in revised form 30 August 2012 Accepted 4 September 2012 Available online 11 September 2012
The gamma-ray activity from short-lived fission products has been measured in fresh and burnt UO2 fuel samples after irradiation in a zero-power reactor. For the first time, short-lived gamma-ray activity from fresh and burnt fuel has been compared and fresh-to-burnt fuel fission rate ratios have been derived. For the measurements, well characterized fresh and burnt fuel samples, with burn-ups up to 46 GWd/t, were irradiated in the zero-power research reactor PROTEUS. Fission rate ratios were derived based on the counting of high-energy gamma-rays above 2200 keV, in order to discriminate against the high intrinsic activity of the burnt fuel. This paper presents the measured fresh-to-burnt fuel fission rate ratios based on the 142La (2542 keV), 89Rb (2570 keV), 138Cs (2640 keV) and 95Y (3576 keV) high-energy gamma-ray lines. Comparisons are made with the results of Monte Carlo modeling of the experimental configuration, carried out using the MCNPX code. The measured fission rate ratios have 1s uncertainties of 1.7–3.4%. The comparisons with calculated predictions show an agreement within 1–3s, although there appears to be a slight bias ( 3%). & 2012 Elsevier B.V. All rights reserved.
Keywords: Light water reactor fuel Burnt fuel Fission rates Zero-power reactor Gamma-ray spectrometry Short-lived fission products MCNPX
1. Introduction The ongoing trend of increasing the initial fuel enrichment in order to obtain higher discharge burn-ups has led to more and more heterogeneous core configurations in modern light water reactors. As a consequence, a general need has been recognized for experimental data in the high burn-up range to validate the predictions of reactor physics code packages [1]. To provide such data, the Paul Scherrer Institute (PSI) and the Swiss association of nuclear utilities (swissnuclear) jointly launched the experimental program LIFE@PROTEUS [2] in 2006, the main goal being the investigation of mixed lattices of fresh and highly burnt fuel (burn-ups of up to 60 GWd/t) in the test zone of the zero-power research reactor PROTEUS at PSI. A key type of measurement to be made thereby is that of fission rate distributions across freshto-burnt fuel interfaces. One standard technique to determine fission rates is based on the measurement of the gamma-ray activity of fission products after irradiation [3]. So far, however, the measurements on burnt
n
Corresponding author. Tel.: þ41 56 310 2111; fax: þ 41 56 310 4527. ¨ E-mail address: [email protected] (H. Krohnert). 1 Present address: Swiss Federal Nuclear Safety Inspectorate, CH-5200 Brugg, Switzerland. 0168-9002/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nima.2012.09.008
fuel have been limited to commercial power reactors, where power distributions in fuel assemblies during the last weeks of operation were determined by measuring the 140La gamma-ray line at 1596 keV [4]. The measurement of fission rates in highly burnt fuel following an irradiation in a zero-power reactor requires, because of the low power, the development of a new experimental method that is able to discriminate against the high intrinsic gamma-ray and neutron background of burnt fuel. Two approaches are being investigated currently at PSI. One is based on the measurement of delayed neutrons from the irradiated fuel and has been presented elsewhere [5]. The other, which is the topic of this paper, is based on the detection of gamma-rays from short-lived fission products the energies of which are above the intrinsic background. During preliminary measurements, fresh fuel was irradiated in PROTEUS and several fission products with gamma-ray lines above 2200 keV were identified as potential candidates for the proposed new measurement technique [6]. Among them, the 142 La (2542 keV), 89Rb (2570 keV), 138Cs (2640 keV) and 95Y (3576 keV) gamma-ray lines were later measured in a fresh and a 36 GWd/t burnt UO2 sample. Each of these samples was irradiated at different lattice positions in the PROTEUS test zone, and ratios of fission rates between the different positions were derived [7]. These inter-position fission rate ratios had uncertainties
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of about 1–3% and 3–6% for the fresh and burnt fuel sample, respectively, the main contributions being the counting uncertainties for the different gamma-ray peaks. In the current paper, first results for inter-sample fission rate ratios between a fresh and two different burnt fuel samples (with burn-ups of 36 and 46 GWd/t, respectively) are presented. In comparison to the previously published inter-position fission rate ratios, the derivation of the present results has been considerably more challenging. This follows from the fact that various factors related to the counting efficiency of the detection system no longer cancel out and need to be accounted for explicitly for the two different fuel sample types. This paper is organized in the following way. In Section 2, the conducted experiments are described. Section 3 provides a description of the Monte Carlo (MCNPX) models that were used (a) to predict the inter-sample fission rate ratios, and (b) to estimate the solid angle and attenuation correction factors. The methodology to derive inter-sample fission rate ratios from the measured gamma-ray lines is presented in Section 4. Section 5 investigates the sensitivity of the results to certain specific experimental features. The calculation-to-experiment comparison is presented and discussed in Section 6, while Section 7 gives the final conclusions and recommendations for future experiments.
U T S R Q P O N M L K J I H G F E D C B A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Moderator
2. Experimental set-up and procedures
73
UO (5 wt%)
Irradiation position for fuel sample
Fig. 1. Layout of the PROTEUS test lattice.
This section provides a brief description of the conducted experiments, a detailed description given in [8]. 2.1. Experimental set-up The experiments were carried out at the PROTEUS zero-power research reactor. This critical facility is a multi-zone driven system featuring a central test zone ( 45 45 cm2), which can be loaded with the fuel configuration to be studied. The test zone itself is subcritical and is fed with neutrons from the surrounding annular driver zones. Fig. 1 shows the test zone configuration that was currently used [7]. The test lattice consisted of 5% enriched UO2 pins loaded in a pattern resembling that of a specific supercritical-water reactor (SCWR) assembly design. The test zone was filled with a H2O/D2O mixture to simulate water with a reduced density. As indicated earlier, three different fuel samples were used in the present experiments: a 3.5% enriched fresh UO2 sample, a 36 GWd/t burnt UO2 sample (initial enrichment 4.1%) and a 46 GWd/t burnt UO2 sample (initial enrichment 3.5%). All samples had been part of fuel pins irradiated in a Swiss PWR. The cooling time of the burnt samples was about 12.5 years. Each sample had a total pellet length of approximately 40 cm and a pellet diameter of about 0.91 cm. For the experiments, the fuel samples were placed into a specially designed transport flask. The latter was made of steel and had an outer diameter of about 70 cm. The samples were loaded into a rotary revolver at the center of the flask. Placed above the test zone of the reactor, within the reactor shielding, the flask also served as a sample changer for lowering the samples into the PROTEUS test lattice. For this purpose, the sample changer was equipped with a control unit to rotate the revolver hosting the samples in the flask, and to move the samples up and down. One at a time, the samples were inserted into different lattice positions for irradiation, and their gamma-ray activities were measured several minutes after the end of irradiation. The gamma-ray measurements took place directly within the steel body of the sample changer, using an HPGe detector (ORTEC model GEM-15180-P) that
was located in a cavity drilled into the steel body. The signals were processed by a DSPEC Plus multi-channel analyzer from ORTEC. A live-time spectrum and a so-called zero-dead-time (ZDT) spectrum were recorded in parallel. The latter spectrum is continuously corrected for dead-time losses on a channel-by-channel basis during data acquisition. Considering the rapidly changing count rates during the data acquisition, the ZDT option was particularly suitable for the current experiments. Demonstration of the reliability of the ZDT methodology for high dead times and strongly varying count rates has been reported elsewhere [9]. The acquired data were saved with the ORTEC software Gamma-Vision [10], while the software HyperLab [11] was used for the analysis of the ZDT spectra. Two different measurement positions were used for the fresh and the burnt fuel samples. As illustrated in Fig. 2, the fresh fuel sample was measured as close as possible to the detector, the distance between the sample and detector centers being about 20 cm. Due to their high intrinsic gamma-ray activity, the burnt fuel samples had to be moved to a position further away from the detector in order to keep the system dead time reasonably low. Consequently, the burnt samples were measured in a position below the detector, rather than in line with it, the distance between the top of the sample and the detector being about 26 cm. During the measurement of a given sample, the other burnt samples were moved to positions below the sample changer so as to avoid any interference from their intrinsic gamma-ray activity. 2.2. Irradiation and measurement conditions The irradiation and gamma-ray measurement conditions for the three samples are summarized in Table 1. The cooling time between irradiation and data acquisition corresponds to the time needed to withdraw the sample from the core and bring it into the measurement position. All times were measured with a precision of 1 s. The maximum dead times were the system dead times at the beginning of data acquisition (5 min after irradiation), while the minimum dead times refer to the values at the end of
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Radial position burnt sample
Radial position fresh sample
detector
detector
sample
sample
20cm
25cm Axial position burnt sample
Axial position fresh sample
sample
22cm
sample
detector
8cm
74
detector
Fig. 2. Fuel samples in their post-irradiation measurement positions in the transport flask.
Table 1 Reactor power (with nominal neutron flux value), irradiation time ti, cooling time tc, acquisition time ta, and maximum and minimum dead times (dT) for the conducted gamma-ray measurements. Sample
Reactor power (W)
n-flux (s 1 cm 2)
Lattice positions
ti (min)
tc (min)
ta (h)
Max. dT (%)
Min. dT (%)
Fresh UO2 36 GWd/t UO2 46 GWd/t UO2
100 800 800
5 108 4 109 4 109
M8, K7, L11 M8, K7, L11 I8
30 15 15
2–5 2–5 2–5
6 6 6
60 50 68
2 35 62
acquisition, when the count rate had already reached almost the background level. As mentioned above, the measurements took place inside the sample changer, within the reactor shielding. In spite of additional neutron shielding placed around the sample changer, a considerable fast neutron flux reached the detector during each irradiation and damaged the detector crystal, leading to a continuous worsening of the detector resolution. The total number of irradiations was thus limited. Accordingly, the experimental campaign focused on first irradiating the 36 GWd/t burnt fuel sample, and then the fresh sample, in the three lattice positions M8, K7 and L11. The 36 GWd/t burnt sample showed significantly lower count rates than the fresh sample because of its remote measurement position and its lower fissile content. To compensate for this, it was irradiated twice in each lattice position at a higher power than the fresh fuel sample, and the analysis was carried out on the sum of the recorded spectra. At the end of this set of irradiations, the detector resolution was still acceptable and, finally, the 46 GWd/t burnt fuel sample was irradiated twice in the position I8. The latter is equivalent to the position M8, both corresponding to the center of a moderator channel of the SCWRlike test lattice (see Fig. 1).
2.3. Measured gamma-ray activity from short-lived fission products As example, Fig. 3 shows recorded gamma-ray spectra of the three samples after an irradiation in the moderator channel position M8 (I8). In the high-energy region, gamma-ray lines from the freshly produced fission products 142La, 89Rb, 95Y, 138Cs and 84Br are clearly visible for all three samples. The intrinsic background of the burnt fuel samples below 2000 keV is seen to be quite dominating, the most prominent peaks being those from the long-lived fission products 154Eu and 137Cs. Apart from the fission product peaks, background peaks related to the activation of surrounding materials can be observed. The activation products 56 Mn and 116mIn are formed by (n,g) reactions on 55Mn and 115In in the steel of the sample changer and in the detector mount, respectively. The 1H (2223 keV) line corresponds to prompt gamma-rays from neutron captures in 1H which is present in the neutron shielding around the detector. Among the short-lived fission product peaks, only five have been considered for the present analysis of the measurements. These are 142La (2542 keV), 89Rb (2570 keV), 95Y (2632 keV), 138Cs (2640 keV) and 95Y (3576 keV). The other peaks suffered either from too low counting statistics or from interference with
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75
Fig. 3. Gamma-ray spectra of irradiated fresh, 36 GWd/t and 46 GWd/t burnt fuel samples; (a) energy region 0–2000 keV; (b) energy region 2000–4000 keV.
background peaks. The latter was particularly the case for 138Cs (2218 keV) interfering with the 1H (2223 keV) line, and for 142La (2398 keV) interfering with the 116mIn (2392 keV) line. For the further analysis, the counts of the two adjacent peaks 95 Y (2632 keV) and 138Cs (2640 keV) were summed. In the following, for the sake of convenience, the results for these two peaks are simply referred to as 138Cs (2640 keV).
3. MCNPX modeling Two Monte Carlo models have been employed in the frame of the present study, using MCNPX-2.5 [12] in conjunction with the JEFF-3.1 nuclear data library [13]. The first is a detailed model of the complete PROTEUS reactor, and the second is a model of the measurement set-up. 3.1. Whole-reactor model for fission rate calculations A 3D whole-reactor model of PROTEUS, with explicit representation of the individual fuel pins, was used to derive the freshto-burnt fuel fission rate ratios of interest. To this purpose, the three samples were modeled, one by one, in the given lattice positions, and the average number of fissions in the fuel was tallied suitably in each case. The fresh fuel sample was modeled according to its nominal specifications. Regarding the burnt fuel samples, their isotopic compositions were modeled according to post-irradiation examinations (PIEs) carried out previously at the PSI Hot Laboratory on adjacent fuel sections of the fuel pins from which the fuel samples had been cut [14]. In the MCNPX model, the fuel composition was considered homogenously distributed in both radial and axial directions. The 1s uncertainty on the calculated fission rates was about 0.15%, the uncertainties on the resulting calculated fission rate ratios being about 0.3%. The quoted uncertainties on the calculated fission
rate ratios are only statistical Monte Carlo uncertainties, being dependent on the number of simulated neutron histories. Apart from the total fission rates, the whole-reactor model served to calculate the contributions of the major fissioning isotopes (235U, 238U, 239Pu, 241Pu) to the total number of fissions. These isotopic fission contributions were needed for the derivation of the fission rate ratios from the measurements (see Section 4). Furthermore, the axial and radial fission profiles within the sample were tallied in terms of 20 axial regions and 6 concentric layers, respectively. The axial distribution was used as input for the MCNPX model of the measurement set-up (see next section), and the radial profile was used for the sensitivity study described in Section 5.2. 3.2. Model of the measurement station for solid angle and attenuation corrections A model of the measurement station was used to calculate the solid angle and attenuation correction factors, which were needed for the derivation of the experimental fission rate ratio values (see Section 4). The correction factors are defined as the fraction of gammarays emitted by the fuel sample that reach the detector without interacting in the sample changer or in the fuel sample itself. They were calculated by tallying the uncollided gamma-ray fluxes in the germanium crystal of the detector. The geometry and composition of the samples were modeled as described in Section 3.1. Each sample was modeled in its particular measurement position (see Fig. 2). For each energy of interest, i.e. 2542 keV, 2570 keV, 2640 keV and 3576 keV, a gamma-ray source was assigned to the samples according to the axial fission profile obtained with the whole-reactor model. The radial source distribution was assumed to be homogenous. The uncertainties on the correction factors were about 0.1% and 0.3% for sources in the fresh and burnt fuel measurement positions, respectively. Again, the quoted uncertainties are simply the statistical Monte Carlo uncertainties.
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4. Derivation of measured fission rate ratios In this paper, three fresh-to-36 GWd/t fuel fission rate ratios are presented, corresponding to the comparison made between the fresh and 36 GWd/t burnt samples for each of the three lattice positions M8, K7 and L11. The 46 GWd/t fuel sample was only irradiated in the lattice position I8, which is equivalent to position M8. Accordingly, only one fresh-to-46 GWd/t fuel fission rate ratio is presented. The methodology used to derive the inter-sample fission rate ratios is similar to that employed for the inter-position ratios reported earlier [7]. Given the different measurement positions for the fresh and the burnt fuel samples, however, an additional correction factor, taking into account the corresponding solid angle and gamma-ray attenuation effects during measurement, had to be introduced. 4.1. Methodology to derive fission rate ratios Each measured fresh-to-burnt fuel fission rate ratio was independently estimated with the four gamma-ray lines 142La (2542 keV), 89Rb (2570 keV), 138Cs (2640 keV) and 95Y (3576 keV). The fission rate ratio estimate FRR(Eg) based on a particular gamma-ray line of energy Eg can be written as follows: FRRðEg Þ ¼
Nnet,f attðEg Þb UbðEg ÞUC b U attðEg Þf UbðEg ÞUC f N net,b
ð1Þ
where the factors att(Eg) take into account corrections for the solid angle and the gamma-ray attenuation between the samples and the detector, and the subscripts f and b refer to the fresh and burnt fuel samples, respectively. Nnet is the net-count area of the gamma-ray line in the ZDT spectrum, b(Eg) is the gamma-ray intensity, and C is the correction for saturation and decay of the fission product. The efficiency of the gamma-ray detector is not present in Eq. 1, since the same gamma-ray line is considered for both the fresh and burnt fuel measurements. Note that if interfering gamma-ray peaks had to be considered, as was the case for 138Cs (2640 keV), the expression b(Eg) C in Eq. 1 had to be replaced by a sum of equivalent expressions, one for each contributing fission product [8]. Finally, the four individual estimates FRR(Eg) were compared for consistency and a standard weighted mean was derived to yield the final experimental value of the fission rate ratio. The procedure was repeated for each measured fresh-to-burnt fuel fission rate ratio. In the following, the determination of the individual parameters occurring in Eq. 1, as also their typical values, are discussed briefly. Uncertainties are quantified in Section 4.6. 4.2. Net-count areas Nnet The net-count areas in the ZDT spectra were obtained using the gamma-ray spectrum analysis code Hyperlab [11]. The spectrum fitting and deconvolution in Hyperlab are performed on a region-by-region basis with a semi-empirical fit function. The fit function accounts for the Gaussian peak shape and the background, as also for the low and high energy tailing of the peak. The various parameters of the fit function are determined with a standard least square method. The covariance matrix of the fitted parameters is also computed to estimate the uncertainty on the calculated net-peak areas. Due to the degrading detector resolution, the separation of strongly interfering peaks like 95Y (2632 keV) and 138Cs (2640 keV) became more and more error-prone. By summing the calculated net-count areas of the interfering peaks, as mentioned above, the potential error of attributing counts to a wrong
peak could be avoided. The estimated uncertainties of the netcount areas were combined applying the standard error propagation law. Typical net-count areas of the four investigated peaks were between 20,000 and 70,000 counts for the fresh fuel sample, between 3500 and 8000 counts for the 36 GWd/t burnt sample, and between 2500 and 6500 counts for the 46 GWd/t burnt sample (irradiation positions M8 and I8, respectively). 4.3. Solid Angle and attenuation correction factors att(Eg) As the fresh and burnt fuel samples were measured in different positions, the solid angle, and the attenuation of the gamma-rays between sample and detector were different in the two cases. This is accounted for in Eq. 1 by the ratio of the factors att(Eg)b and att(Eg)f. As described in Section 3, the factor att(Eg) was determined with MCNPX, being defined as the ratio of the number of uncollided gamma-rays arriving in the detector to the number emitted in the sample. For the fresh fuel sample, the tallied uncollided gamma-ray fluxes in the detector varied between 1.0 10 6 cm 2 per source gamma-ray with an energy of 2542 keV and 1.7 10 6 cm 2 per source gamma-ray with an energy of 3576 keV. Due to their specific measurement positions, which led to a lower solid angle and more shielding material between the detector and the samples, the corresponding results for the burnt fuel samples were lower. As an example, the tallied fluxes for the 36 GWd/t burnt sample varied between 4.2 10 8 cm 2 per source gammaray of 2542 keV and 8.9 10 8 cm 2 per source gamma-ray of 3576 keV. Thus, typical values of att(Eg)b/att(Eg)f were about 20–25, with a statistical Monte Carlo uncertainty of about 0.3%. This implies that 20–25 times more gamma-rays emitted from the fresh fuel measurement position reached the detector than from the burnt fuel measurement position, the self-absorption in the fresh and burnt fuel being similar. 4.4. Saturation and decay correction factors C Basic corrections for saturation and decay of fission products during and after irradiation can be found in the literature [15]. The simplest case for obtaining the saturation and decay correction is for the gamma-ray lines 142La (2542 keV), 89Rb (2570 keV) and 95Y (3576 keV). The corresponding correction factor is given by Eq. 2, relating the fission rate in the fuel sample during irradiation to the number of gamma-rays of a specific energy emitted by the considered fission product during the data acquisition. Y ind,2 i12 Ul1 UY cum,1 C¼ Uð1el2 ti ÞUel2 tc Uð1el2 ta Þ þ l2 l2 Uðl1 l2 Þ i12 Ul2 UY cum,1 Uð1el1 ti ÞUel1 tc Uð1el1 ta Þ þ ð2Þ l1 Uðl2 l1 Þ Ycum and Yind are the cumulative and independent effective fission yields, and l is the decay constant, the index 1 referring to the direct parent of the detected fission product and the index 2 to the fission product itself. The variables ti, tc and ta are the irradiation, cooling and acquisition times, respectively. In this simple case, the parent isotope decays only into the ground state of the fission product, the corresponding branching ratio being i12, and no isomeric state has to be considered. As mentioned, Eq. 2 can be applied in the case of the 142La (2542 keV), 89Rb (2570 keV) and 95Y (3576 keV) gamma-ray lines. The correction for the 138Cs (2640 keV) line is more complex because of the non-negligible isomeric state 138mCs [6]. All nuclear data were taken from the JEFF-3.1 nuclear data library [13]. The calculated values for saturation and decay
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correction factors did not strongly differ between the three samples. Typically, the ratios ðbðEg ÞUC b Þ=ðbðEg ÞUC f Þ varied between 0.8 and 1.5.
4.5. Effective fission yields Yind and Ycum The effective cumulative fission yields Ycum of the different isotopes were calculated according to Eq. 3 as the sum of the fission yields for the main fissioning isotopes 235U, 238U, 239Pu and 241 Pu, weighted by their isotopic fission contributions aU5, aU8, aP9 and aP1. Y ¼ aU5 UY th,U5 þ aU8 UY f ,U8 þ aP9 UY th,P9 þ aP1 UY th,P1
ð3Þ
with aU5 þ aU8 þaP9 þaP1 ¼ 1 The values aU5, aU8, aP9 and aP1 were obtained for each fuel sample, in each investigated lattice position, with the help of the MCNPX whole-reactor model, the statistical Monte Carlo uncertainty being less than 0.2% in each case. The MCNPX simulations also showed that, for each investigated case, more than 99% of the fissions in 235U, 239Pu and 241Pu occurred in the low energy range (0–0.1 keV), whereas more than 99% of the fissions in 238U occurred at high energies (9.1 keV–10 MeV). Accordingly, because of the rather weak dependence of the yields on energy, thermal fission yields alone could be used for fissions in 235U, 239Pu and 241 Pu, and fast fission yields could be used for fissions in 238U. Table 2 summarizes the calculated values of aU5, aU8, aP9 and aP1, obtained for the three samples irradiated in the moderator position M8(I8). Compared to the position M8(I8), the two lattice positions K7 and L11 had a less thermal neutron spectrum. Consequently, the fission contribution of 235U was reduced and that of 238U increased. However, the changes in these contributions were less than 4%. It is interesting to note that the fission contribution of 241Pu doubled in the 46 GWd/t sample, as compared to the 36 GWd/t sample, reaching more than 10%. The different isotopic fission contributions in the three samples are important because of their impact on the error propagation of the uncertainties on the fission yields. As seen in Eq. 2, independent fission yields are also required for the saturation and decay correction. Unfortunately, most of the independent fission yields of the investigated fission products are afflicted with extremely high uncertainties (e.g. 30–36% for Yind,th,U5 values for 95Y, 138Cs, 89Rb and 142La). To avoid these high uncertainties, the independent fission yields in Eq. 2 were replaced by the difference between the cumulative fission yields of the fission product and that of its parent weighted by the branching ratio i12. Nevertheless, the uncertainties on the fission yields remain one of the main contributing factors to the overall uncertainty on a given fission rate ratio (see following section).
77
uncertainties on the net-count areas, the statistical Monte Carlo uncertainties on the solid angle and attenuation corrections, and the uncertainties on all nuclear data such as fission yields, branching ratios, decay constants and gamma-ray intensities. All parameters were assumed to be independent and no covariance term was considered. The fission products emitting the measured gamma-ray lines pertain to different mass chains and their nuclear data are only weakly correlated among each other. It could not be excluded that the quoted cumulative fission yields of a considered fission product and its direct parent were correlated. However, this potential correlation could not be quantified in the present work. Since the times were recorded with a 1 s accuracy, the variables ti, tc and ta were considered as exact values. The statistical Monte Carlo uncertainties on the variables aU5, aU8, aP9 and aP1, calculated with MCNPX (see Section 3), were negligible and were not included in the uncertainty propagation. The uncertainties related to the fuel composition assumed in the calculations, however, were not negligible. These could not be quantified in the present work and were, instead, addressed with sensitivity studies [8], one of which is described in Section 5.1. The uncertainties on the net-count areas were determined, as mentioned previously, with the analysis software Hyperlab. The uncertainties on the nuclear data were taken from the JEFF-3.1 data library. Most of the nuclear data involved basically canceled out when taking fission rate ratios, so that, in general, the uncertainties on the nuclear data made a rather low contribution to the combined uncertainty. A notable exception was the uncertainty on the fission yields for 235U and 239Pu, which are summarized in Table 3. Table 4 shows the results of the uncertainty analysis for the freshto-36 GWd/t and the fresh-to-46 GWd/t fission rate ratios in the irradiation position M8(I8). For each gamma-ray line, the combined uncertainty of the derived fission rate ratio and its contributions are given. The latter correspond to the statistical uncertainties on the netcount areas, the uncertainties on the nuclear data and the Monte Carlo uncertainties on the MCNPX results. The combined uncertainty on each of the final fission rate ratio estimates, computed as a weighted mean, is also given in Table 4. In all cases, the uncertainties on the net-count areas represent the main contribution to the combined uncertainties. It should be noted, however, that the contribution from the nuclear data reached more than 1% for the fresh-to-46 GWd/t comparison. This resulted mainly from the uncertainties on the fission yields, the samples being of very different compositions with correspondingly large differences in isotopic fission contributions. This is important because, unlike the statistical uncertainties, the nuclear data uncertainties cannot be easily reduced in future experiments.
5. Sensitivity studies Table 2 Contributions aU5, aU8, aP9 and aP1 to the total number of fissions in the fuel samples irradiated in position M8(I8). Sample
aU5 (%)
aU8 (%)
aP9(%)
aP1(%)
Fresh 36 GWd/t 46 GWd/t
97.7 53.1 27.4
2.3 2.9 3.7
– 38.0 57.1
– 6.0 11.8
4.6. Uncertainty considerations The combined uncertainty on an independent estimate of a measured fission rate ratio, based on a particular gamma-ray line, was determined by applying the standard error propagation law. The uncertainties included in the error propagation were the
As mentioned earlier, the uncertainties considered for the MCNPX results are only the statistical Monte Carlo uncertainties. Uncertainties on the results related to the modeling of the geometry and the fuel composition have not been derived in a systematic way. Instead, they have been assessed separately with the help of sensitivity studies, which are presented in this section. 5.1. Axial burn-up profile of the 36 GWd/t burnt fuel sample An axial scan of the intrinsic gamma-ray activity of the burnt fuel pin, from which the 36 GWd/t sample was cut, indicated that the sample should have a significant axial burn-up gradient ( 10% over its 40 cm length). It was, however, hardly possible to quantify the exact axial burn-up profile, and thus the axial
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Table 3 Cumulative thermal fission yields of considered fission products in % and relative uncertainties [13]. Gamma-ray energy
Fission product
Ycum,th,U5
Ycum,th,P9
Parent isotope
Ycum,th,U5
Ycum,th,P9
2542 keV 2570 keV 2640 keV 3576 keV
142
5.86 4.69 6.69 6.47
4.97 1.68 5.94 4.82
142
5.80 4.43 6.41 5.28
4.68 1.42 5.02 3.23
La Rb 138 Cs 95 Y 89
(1.7%) (1.2%) (1.7%) (1.1%)
(1.1%) (1.9%) (2.7%) (2.0%)
Ba Kr 138 Xe 95 Sr 89
(1.7%) (1.4%) (1.8%) (2.2%)
(1.3%) (2.7%) (3.3%) (5.2%)
Table 4 Contributions to the combined uncertainties of measured inter-sample fission rate ratios. Counting uncert. (%)
Nuclear data uncert. (%)
Monte Carlo uncert. (%)
Combined uncert. (%)
Fresh-to-36 GWd/t fission rate ratio (M8) 142 La (2542 keV) 3.4 89 Rb (2570 keV) 5.2 138 Cs (2640 keV) 7.0 95 Y (3576 keV) 2.9 Weighted mean
0.7 0.5 1.0 0.8
0.3 0.3 0.3 0.3
3.5 5.2 7.1 3.1 2.0
Fresh-to-46 GWd/t fission rate ratio (M8,I8) 142 La (2542 keV) 5.6 89 Rb (2570 keV) 9.3 138 Cs (2640 keV) 30.2 95 Y (3576 keV) 4.6 Weighted mean
1.2 1.0 1.4 1.4
0.3 0.3 0.3 0.2
5.7 9.4 30.2 4.8 3.4
isotopic distributions, of the sample. Accordingly, the composition of the sample in MCNPX was assumed to be axially homogeneous, corresponding to the measured PIE results. The PIE had been performed on a fuel segment contiguous to the lower burn-up end of the sample, so that the overall burn-up of the sample modeled in MCNPX corresponded to a slight underestimation. The sensitivity of the calculated fission rate to the axial burnup profile was evaluated by repeating the fission rate calculation while assuming an increased sample burn-up of 5% and 10%, respectively. To this aim, a HELIOS pin-cell model of the fuel rod [16] was used for depleting the isotopic composition of the sample to the nominal burn-up, as also to 5% and 10% higher burn-up values. The calculated fission rates in the fuel sample with increased burn-ups were about 3% and 5% lower than those for the nominal burn-up, due to the reduced amounts of fissioning material in the fuel. This result has clearly to be taken into account when interpreting the comparison between measured and calculated fission rate ratios presented in Section 6. The change in the modeled sample composition also had an impact on the measured fission rate ratios. This is due to the change in the isotopic fission contributions aU5, aU8, aP9 and aP1, and to the resulting change of the effective fission yields used in the saturation corrections. A burn-up increase of 5% changed the fraction of fissions in 235U and 239Pu by 5.5% and þ3.5%, respectively. As a result, the measured fission rates based on the 89 Rb (2570 keV) peak were affected by about 2%, because of the very different fission yields for 235U and 239Pu. In comparison, the impact on the results based on the 142La (2542 keV), 138Cs (2640 keV) and 95Y (3576 keV) peaks was less than 0.7%, since the fission yields of these fission products do not strongly depend on the fissioning isotope. This result is of importance for future experiments in which the composition of the burnt fuel may not be known from PIE. In such a situation, it might be advisable not to include 89Rb in the quantitative analysis.
clearly a simplification with respect to burnt fuel samples, in which isotope densities can have significant radial variations. Sensitivity studies were carried out to quantify the impact of this simplification on the calculated fission rates in the burnt fuel samples, on the isotopic fission contributions (aU5, aU8, aP9, aP1), and on the attenuation corrections. HELIOS depletion calculations were used to obtain the radial number density distribution of each fissioning isotope for the 36 and 46 GWd/t samples. Six concentric layers of equal areas were considered for the purpose. As example, the radial number density distributions obtained for the 36 GWd/t sample are shown in Fig. 4. The radial distributions were then implemented into the samples in the MCNPX whole-reactor model. Each fissioning isotope was distributed according to its radial profile and scaled to conserve its total number density in the sample. The total fission rate in the 36 GWd/t sample, at a given irradiation position in the PROTEUS test lattice, changed only marginally (0.4%) by introducing the radially distributed isotopic composition. The same was the case for the isotopic fission contributions (less than 0.4% deviations). Very similar results were obtained for the 46 GWd/t sample. Using the whole-reactor model, the radial profile of the total fission rate during the PROTEUS irradiations was obtained for each sample (see Fig. 4). This was used as the gamma-ray source profile in the model of the sample changer. It was found that, for the investigated high-energy photons, the self-attenuation within the sample was the same (about 20%) with and without consideration of the radial gamma-ray source distribution, and that the calculated solid angle and attenuation correction factors did not change. Consequently, the simplification of employing a radially uniform sample composition in the MCNPX models is well justified.
5.2. Radial profile of isotopes in the burnt fuel samples
The geometry of the fuel samples and their measurement positions within the sample changer have been modeled as accurately as possible. Nonetheless, it could not be excluded that the pellet stacks of the burnt fuel samples were shifted by a few
In MCNPX, the isotopic composition of a fuel sample was modeled homogeneously also in the radial direction. This is
5.3. Axial elevation of the fuel samples in the sample changer model
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Fission rate, number density (normalized to 1 in outer segment)
1.2
79
Total fissions
1.1
Fissions 235U
1.0
Number density 235U Fissions 239Pu
0.9
Number density 239Pu
0.8
Fissions 241Pu
0.7
Number density 241Pu
0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.1
0
0.2 0.3 Mid-radius of segment [cm]
0.4
Fig. 4. Number densities and fission radial distributions within the 36 GWd/t burnt fuel sample.
Table 5 Comparison of calculated and experimental inter-sample fission rate ratios (C/E values).
Fresh-to-36 GWd/t Fresh-to-46 GWd/t
M8(I8)
K7
L11
1.045 70.021 (2.0%) 1.012 70.034 (3.4%)
1.020 70.018 (1.8%)
1.031 7 0.018 (1.7%)
millimeters within their overcladding. In addition, the exact position of the sample within the sample changer is given with a precision of 71 mm. Given that the burnt fuel samples were measured below the detector, rather than in line with it (see Fig. 2), the calculated solid angle and attenuation correction factor for these samples has been found to be highly sensitive to an axial displacement. The calculated fission rates changed by about 1.5% and 8% for axial displacements as small as 1 and 5 mm, respectively.
6. Calculation-to-experiment comparisons and discussion The measured values of fresh-to-burnt fuel fission rate ratios were compared to the corresponding calculated results obtained with the whole-reactor MCNPX model described in Section 3. The comparisons between calculated (C) and experimental (E) intersample ratios are summarized in Table 5. The indicated uncertainties (1s) mainly reflect those on the net-count areas and on the nuclear data, the contributions of the statistical uncertainties in the MCNPX simulations being negligible (see Table 4). The net uncertainties are seen to be between about 2% on the C/Es for the fresh-to-36 Gwd/t fission rate ratios and 3.4% on the C/E for the fresh-to-46GWd/t fission rate ratio. For all three irradiation positions, the agreement between the measured and calculated fresh-to-36 GWd/t fission rate ratios is within 1–3 standard deviations. Nonetheless, the results predicted by MCNPX appear on average about 3% higher than the
measured values. Considering the observation made earlier with respect to the axial burn-up profile in the 36 GWd/t sample (see Section 5.1), the calculated fission rates in this sample should be about 3% lower than those reflected in Table 5 (assuming a 5% higher sample burn-up). This would increase the observed bias between experiment and calculation to about 6%. It is not easy, however, to identify the exact cause for such a bias. One possible explanation, as discussed below, could be a slight axial displacement of the 36 GWd/t sample within its overclad. As described earlier (Section 5.3), the exact position of the fuel during measurement was needed to accurately calculate the solid angle and attenuation correction factors. The sensitivity of the measured fission rate ratios to the modeled elevation of the burnt fuel samples was found to be quite high (as much as about 8% for a displacement of 5 mm). Consequently, a displacement of 3–4 mm of the 36 GWd/t fuel sample could account for a 6% discrepancy between calculated and measured results. To avoid such difficulties in future experiments, care should be taken to minimize the sensitivity of the measurements to the positioning of the samples and to ensure a relatively flat burn-up profile in the burnt fuel employed (at least in the measured part of the fuel samples). As seen from Table 5, the measured and calculated fresh-to-46 GWd/t fission rate ratios, which were derived for the equivalent irradiation positions M8 and I8, agreed within the 1s uncertainty of 3.4%. This demonstrates the possibility to extend the currently developed measurement technique to higher burn-ups.
7. Conclusions and outlook A new measurement technique, which uses high-energy gamma-rays emitted by freshly induced fission products, is being developed at the Paul Scherrer Institute (PSI) to determine fission rates in fresh and burnt nuclear fuel (re-)irradiated in a zeropower research reactor. To test this technique, gamma-ray spectrometry has been conducted on fresh and burnt UO2 fuel samples (burn-ups of 36 GWd/t and 46 GWd/t) irradiated in the PROTEUS zero-power reactor. Thereby, it has been possible to accurately
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measure the high-energy gamma-rays emitted by short-lived fission products, not only in fresh but also in burnt fuel with high intrinsic gamma-ray backgrounds. Based on gamma-ray lines emitted by the freshly induced fission products 142La, 89Rb, 138 Cs and 95Y, fission rate ratios have – for the first time – been derived comparing a fresh fuel sample to burnt (36 GWd/t and 46 GWd/t) fuel samples. Comparison with MCNPX predictions of the fission rate ratios showed a satisfactory agreement within 1–3s (see Table 5). The measured fresh-to-burnt fuel fission rate ratios have a 1s accuracy of 1.7–3.4%. The main contribution to the uncertainties being statistical, the improvement of the gamma-counting statistics has been noted as an important requisite for future experiments. One possibility is to further optimize the shielding against the fast neutron background from the reactor, which would allow longer irradiation times and especially improve the statistics for the somewhat longer-lived fission products 138Cs and 142La. Another possibility is the use of additional detectors or of a detector with a larger germanium crystal. The latter would have the advantage of an increased detection efficiency for high-energy gamma-rays relative to low energy ones, but it would require an optimized detector shielding to maintain acceptable system dead times. Fission rates derived from the 89Rb activity are quite sensitive to the relative contributions of 235U, 238U, 239Pu and 241Pu to the total number of fissions, whereas those based on 95Y, 142La and 138 Cs are not. The sensitivity to the exact isotopic composition of the fuel in the case of 89Rb was to be expected, because of its significantly different fission yields for 235U and 239Pu. Consequently, it might be advisable not to include 89Rb for experiments in which the composition of the burnt fuel samples is not well known. Another important observation in the context of the present experiments is that, because of the different counting geometries employed for the fresh and burnt samples, the experimental results have been found to be highly sensitive to slight axial displacements of the burnt fuel during data acquisition. In future experiments, this high sensitivity can be reduced relatively easily, by optimizing the filter between sample and detector such that a more favorable measurement position can be used for all samples. Finally, the contribution of nuclear-data related uncertainties to the net uncertainty on derived fission rate ratios has been seen to be in the range 0.5–1.4%. In contrast to the statistical uncertainties, this specific contribution cannot be improved unless new and more accurate fission yield measurements are carried out.
Consequently, this will probably be the main constraint to the achievable precision in future experiments.
Acknowledgments This work has been carried out in the framework of LIFE@PROTEUS, a joint research program. The authors thank J.-M. Cavedon and M. Zimmermann (PSI), J. Krouthe´n (Axpo AG), F. Jatuff and ¨ W. Sauser (Kernkraftwerke Gosgen), U. Georg (Kernkraftwerke ¨ Mulhleberg), H.-D.Berger (AREVA-NP), and U. Bergmann (Westinghouse Electric Sweden) for their support of the program. Special thanks are also due to M. Fassbind, M.W. Zimmermann, and A. Stephan for their excellent maintenance and operation of the reactor.
References [1] NEA, Very High Burn-ups in Light Water Reactors, NEA Report No. 6224, ISBN 92-64-02303-8, 2006. [2] M.F. Murphy et al., Large-Scale Irradiated Fuel Experiments at PROTEUS research program, PHYSOR 2010, Pittsburgh, Pennsylvania, USA, 9–14 May 2010. [3] U. Bergmann, et al., Nuclear Instruments Methods A 556 (2006) 331. [4] P. Jansson, et al., Nuclear Science Engineering 152 (2006) 76. [5] K. Jordan, G. Perret, Nuclear Instruments Methods A 634 (2011) 91. ¨ [6] H. Krohnert et al., Measurement of fission rate ratios in fresh UO2 fuel utilising short-lived high-energy gamma activity, PHYSOR 2008, Interlaken, Switzerland, CD-ROM, ISBN 978-3-9521409-5-6, 14–19 September 2008. ¨ [7] H. Krohnert, et al., Nuclear Instruments Methods A 624 (2010) 101. ¨ [8] H. Krohnert, Fission rates measured using high-energy gamma-rays from short half-life fission products in fresh and spent nuclear fuel, Ph.D. dissertation, Ecole Polytechnique Fe´de´rale de Lausanne, Switzerland, 2011. [9] M. Blaauw, Journal of Radioanalytical Nuclear Chemistry 257 (3) (2003) 457. [10] ORTEC, Gamma-Vission-32, Gamma-ray Spectrum Analysis and MCA Emulator, A66-B32 user’s Manual, 2003. [11] HyperLabs Software, HyperLab 2005 Gamma Spectroscopy Software System, Manuals, 2005. [12] D.B. Pelowitz, MCNPX User’s Manual Version 2.5.0, Los Alamos National Laboratory Report LA-CP-05-0369, 2005. [13] A. Koning et al., The JEFF-3.1 Nuclear Data Library, in JEFF Report 21, NEA No.6190, ISBN 92-64-02314-3, 2006. [14] P. Grimm et al., Burnup Calculations and Chemical Analysis of Irradiated Fuel Samples Studied in LWR-PROTEUS Phase II, PHYSOR 2006, Vancouver, Canada, CD-ROM, ISBN 0-89448-697-7, 10–14 September 2006. [15] G. Gilmore, J.D. Hemingway, Practical Gamma-ray Spectrometry, ISBN 0-47195-150-1, 1995. ¨ [16] H. Krohnert, Analysis of the nuclide composition of highly-burnt PWR fuel examined in connection with the LWR PROTEUS Phase II project with the ¨ W¨arme- und Brennstofftechnik, Technische spectral code HELIOS, Institut fur ¨ Braunschweig, Diploma thesis, 2006. Universitat