nondestructive assay of spent nuclear fuel with gamma-ray spectroscopy

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Annals of Nuclear Energy 33 (2006) 427–438

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NUCLEAR ENERGY

Nondestructive assay of spent nuclear fuel withgamma-ray spectroscopy

Christofer Willman *, Ane Hakansson, Otasowie Osifo,Anders Backlin, Staffan Jacobsson Svard

Department of Radiation Sciences, Uppsala University, Box 535, SE-75121 Uppsala, Sweden

Received 21 October 2005; accepted 15 December 2005Available online 7 February 2006

Abstract

An important issue in nuclear safeguards is to verify operator-declared data of spent nuclear fuel. Various techniques have thereforebeen assigned for this purpose. A nondestructive approach is to measure the gamma radiation from spent nuclear fuel assemblies. Usingthis technique, parameters such as burnup and cooling time can be calculated or verified.

In this paper, we propose the utilization of gamma rays from 137Cs, 134Cs and 154Eu to determine the consistency of operator-declaredinformation. Specifically, we have investigated to what extent irradiation histories can be verified.

Computer simulations were used in order to determine limits for detecting small deviations from declared data. In addition, the tech-nique has been experimentally demonstrated on 12 PWR fuel assemblies.

A technique for determining burnup and cooling time for fuel assemblies where no operator-declared information is available is alsopresented. In such a case, the burnup could be determined with 1.6% relative standard deviation and the cooling time with 1.5%.� 2005 Elsevier Ltd. All rights reserved.

1. Introduction

The need for a robust nondestructive measurement tech-nique is generally recognized when spent fuel assembliesare to be verified experimentally for safeguards purposes.The term verification used in this paper is the procedurethat enables authorities to conclude if the provided declara-tions of specifically burnup, irradiation history and coolingtime are in agreement with the experimentally obtained, asmeasured on site.

Nondestructive verification of spent nuclear fuel assem-blies can be made by measuring the radiation emitted eitheras neutrons or gamma rays. In IAEA (2003), a number ofdifferent techniques used by IAEA for safeguarding spentfuel are described. The combined neutron and gamma-ray detector Fork (FDET) is a well known instrument thathas long been used for such purposes (Rinard and Bosler,

0306-4549/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.anucene.2005.12.005

* Corresponding author. Tel.: +46 18 471 5828; fax: +46 18 471 3513.E-mail address: [email protected] (C. Willman).

1988). These techniques can be used, among others, to ver-ify the discharge date of spent fuel assemblies and also forburnup verification. However, many different irradiationhistories can result in the same discharge burnup. A tech-nique that allows for verification of irradiation historywould therefore be of interest.

As mentioned in IAEA (2003), gamma-ray measurementis a useful technique for verification of spent nuclear fuel.Normally the intensity of 137Cs (T1/2 = 30.1 years) is usedas a measure of the burnup. In this paper we have investi-gated to what extent the measurement of other relativelylong-lived fission products can be of use for the verificationof also the irradiation history and cooling time. The addi-tional fission products studied are 134Cs (T1/2 = 2.1 years)and 154Eu (T1/2 = 8.6 years). Together with 137Cs, theseisotopes dominate the gamma-ray spectrum of spent fuelwith a cooling time of 10–20 years.

The present investigation has been made for PWR fuelassemblies with a cooling time of about 10 years, andinvolves both experimental measurements and computer

mailto:[email protected]

2500

]

ε = 3%

428 C. Willman et al. / Annals of Nuclear Energy 33 (2006) 427–438

simulations. In the experimental part, 12 PWR fuel assem-blies have been measured. The purpose was to determinethe accuracy that can be obtained in the correlationbetween fuel parameters and gamma-ray intensities. Inthe simulation part of the work, we have used the codeORIGEN-ARP to investigate to what extent the gamma-ray intensities can be used to reveal inconsistencies in thedeclared fuel data.

In particular, the intention has been to demonstrate atechnique to detect possible fuel assemblies that can be sub-ject to mistakes in the accountancy of the nuclear materialdue to e.g. human errors. Thus the scenario where an oper-ator deliberately tries to hide operations that are aimedtowards illegal activities is not primarily considered here.In countries like Sweden, where the fuel cycle follows theonce-through principle, such a technique would be of inter-est to implement prior to final deposition.

The technique described here is a further developed ver-sion of a technique described earlier (Hakansson et al.,1993), now including not only burnup and cooling timebut also a qualitative verification of the irradiation history.

The technique assumes that the operator can providerelevant data about the fuel assemblies. However, if fueldata are not available or incomplete, other techniques, ofwhich one is presented here, need to be used in order todetermine the fuel parameters experimentally (Hakanssonet al., 1993).

2. Isotope production in the fuel assembly during irradiation

The amount of fission products in spent nuclear fueldepends on various fuel parameters, which, in turn, dependon the physical conditions during reactor operation. Fuelparameters considered specifically in safeguards are pre-sented in Table 1.

The irradiation history is the detailed description onhow the reactor has been operated during the irradiationof a particular fuel assembly. Irradiation history and cool-ing time are the most dominant parameters that govern theconcentration of fission products in spent fuel at a givenmoment.

Table 1The fuel parameters often considered in gamma-ray measurements

Parameter Explanation

Burnup Total amount of energy produced in nuclear fuel,expressed in GWd/tUTypical values of spent fuel are 20–50 GWd/tU

Cooling time Period of time passed since the fuel assembly wastaken out of the reactor core. Cooling timesaccounted for in this paper range from 10 to 20years

Initial enrichment The content of 235U present in the fresh fuelassemblyTypical enrichments are 3–4%

Irradiation history Information on how the total burnup isdistributed in time

Typical values are included.

Some fission products are produced directly in the fis-sion process and others are produced via fission followedby a series of neutron captures and beta decays. Whenthe fuel assembly has been taken out of the core, the unsta-ble fission products decay at different rates.

The production and decay of various isotopes form thebasis of the gamma-ray measurement technique. To give anunderstanding of the technique, a short account for howthe three mentioned isotopes are produced during reactoroperation is given in the following sections. In general,the enrichment has an influence on the buildup of isotopesin a nuclear fuel assembly. 137Cs is practically unaffected,but for 134Cs and 154Eu the initial enrichment is not negli-gible. In this paper it is just concluded that this influenceindicates a possibility to also verify the initial enrichment.In addition, for BWR fuel the production of 134Cs and154Eu is affected by the void fraction in the reactor. Noneof these effects are considered in this paper, but will be sub-ject for further studies.

The production of the three isotopes mentioned hasbeen investigated in simulations using ORIGEN-ARP.The irradiation of a PWR 17 · 17 fuel assembly was mod-elled for five consecutive cycles of 335 days each. Betweenthe irradiation cycles, a maintenance shutdown of 30 dayswas assumed. Ten different values of discharge burnupwere considered, ranging from 5 to 57 GWd/tU.

2.1. Production of 137Cs

The amount of 137Cs produced in the fuel depends on allfuel parameters accounted for in Table 1 in a relatively sim-ple manner. The fission yields for 235U, 239Pu and 241Pu areapproximately the same with 241Pu being slightly higher.

From the simulations, the isotopic content was extractedand it was inferred that the buildup of 137Cs deviates fromlinearity for a burnup in this range with less than 0.2% (1runcertainty of the linear slope coefficient, see Fig. 1).

0 20 40 600

500

1000

1500

2000

Burnup [GWd/tU]

Iso

top

ic c

on

ten

t [g

ram

/tU

Fig. 1. The buildup of 137Cs as calculated with ORIGEN-ARP in LWRfuel. The model used was PWR 17 · 17 fuel with an initial enrichment, e,of 3%.

C. Willman et al. / Annals of Nuclear Energy 33 (2006) 427–438 429

Due to its long half life and its linear dependence onburnup, 137Cs is relatively insensitive to irradiation history.

2.2. Production of 134Cs

The production of 134Cs is primarily governed by neu-tron capture in 133Cs, which, in turn, comes from 133Ithrough 133Xe. Since the 133I fission yields for 235U, 239Puand 241Pu are basically the same, 134Cs is not affected ofthe source of fission. Accordingly, the production of134Cs depends roughly quadratically on the neutron fluxdensity, and, as a consequence, the amount of 134Cs pro-duced depends roughly quadratically on the burnup. Thiseffect can be seen in Fig. 2.

0 20 40 600

50

100

150

200

250

300

Burnup [GWd/tU]

Iso

top

ic c

on

ten

t [g

ram

/tU

]

ε = 3%

Fig. 2. The buildup of 134Cs as calculated with ORIGEN-ARP in LWRfuel. The model used was PWR 17 · 17 fuel with an initial enrichment, e,of 3%.

0 20 40 600

10

20

30

40

50

Burnup [GWd/tU]

Iso

top

ic c

on

ten

t [g

ram

/tU

]

ε = 3%

Fig. 3. The buildup of 154Eu as calculated with ORIGEN-ARP in LWRfuel. The model used was PWR 17 · 17 fuel with an initial enrichment, e,of 3%.

Because the half life of 134Cs is comparatively short, themaximum cooling time of the fuel that can be considered isrestricted to about 20 years for 134Cs to be used.

2.3. Production of 154Eu

The buildup of 154Eu is the most complex of the threeisotopes considered here. It is produced directly from fis-sion only to a small extent. From the uranium loaded inthe core, a total of 20 reaction chains lead to the formationof 154Eu (Berndt, 1988). As with the case of 134Cs, theamount of 154Eu produced is a power function of burnup.In this work a quadratic function of burnup was usedwhich is a reasonably good description. The buildup of154Eu can be seen in Fig. 3.

3. Using gamma spectroscopy as a tool in safeguards

In this section, two different cases of safeguards verifica-tion of spent fuel are considered: (i) the operator-declaredirradiation history is available and needs to be verifiedand, (ii) only the fuel assembly type is known. The theoryof a gamma-spectroscopic verification technique for thetwo cases is presented together with a feasibility study ofthe technique.

To analyze and interpret the experimental data in thiswork, the following basic expression has been used

ix � ekxT ¼ F x; ð1Þwhere ix is the measured gamma-ray intensity and kx is thedecay constant of isotope x. T is the cooling time and Fx isa function of the isotopic content at discharge and variousexperimental parameters. The determination of Fx isdepending on whether the fuel parameters are to be verifiedsemi-empirically or determined empirically. The next twosections deal with this subject.

3.1. Semi-empiric verification of fuel parameters

If operator-declared information of the irradiation his-tory is available, the isotopic content can be calculatedby using various computer codes. In this paper, we haveillustrated the technique using the spent nuclear fuel codeSNF (Børresen et al., 2004). SNF is based on the fueldescription and history data generated in standard coresimulators, for instance, CASMO-4/SIMULATE-3 (Studs-vik Energiteknik, 1995; Edenius et al., 1995). In such a case(1) transforms to

ix � ekxT ¼ Kx � Ix. ð2ÞHere Kx is an experimental calibration constant and Ix isthe calculated isotopic content at fuel discharge.

The constant Kx can be determined by fitting a straightline to the experimental intensities, properly corrected forcooling time, as a function of the calculated isotopic con-tent. This should be done for a number of fuel assemblieswith well-known properties, here referred to as reference


assemblies. In such a way, generic relationships are estab-lished between the calculated isotopic content and theexperimental intensities. These relationships can be usedfor further measurements on fuel assemblies of the sametype as the reference assemblies.

Assuming that Kx has been established, a number ofconclusions can be drawn using the measured data andthe operator declarations. These conclusions are accountedfor below.

A test to conclude if one or more fuel parameters areincorrectly declared is to calculate the cooling time and com-pare with the declared cooling time. Due to its short half lifeand comparably strong dependence on power outtake, 134Csis the most suitable to use. Rearranging (2) we get

T 134 ¼1

k134ln

K134 � I134i134

� �. ð3Þ

The deviation from the declared cooling time, Tdecl, can bedenoted as

D134 ¼ T 134 � T decl. ð4ÞThe sensitivity of T134 on erroneous parameter declarationis investigated in Section 4. It can be noted that a signifi-cant deviation of T134 from declared cooling time doesnot necessarily mean that the cooling time is erroneouslydeclared. The error may also be in the other declaredparameters such as the irradiation history.

If the test above reveals a problem with the fuel declara-tion, it is of interest to be able to conclude which fuelparameter that may be erroneously declared. This necessi-tates a more elaborate treatment. The basic idea is thatwhenever the irradiation history is correctly declared, thecooling time, as calculated by solving for T in (2), shouldin principle give the same result regardless of the isotopeused. It should be noted that this conclusion is not depen-dent on neither actual nor declared cooling time.

To calculate T, it is however not feasible to solve (2) forT separately for 137Cs and 154Eu as the magnitude of 1/k137and 1/k154 give excessively large contributions to the uncer-tainties of the calculated cooling times. Instead, we hereutilize the combination of the intensities 134Cs + 137Csand 134Cs + 154Eu, respectively. Combining (2) for theseisotopes, the following two expressions are obtained

T 1 ¼1

k137 � k134ln

K137 � I137 � i134K134 � I134 � i137

� �;

T 2 ¼1

k154 � k134ln

K154 � I154 � i134K134 � I134 � i154

� �.

ð5Þ

It may now be argued that if the irradiation history is cor-rectly declared, then the following expression holds

jT 1 � T 2j < ðDT 1 þ DT 2Þ; ð6Þwhere DT1 and DT2 are the uncertainties of T1 and T2,respectively, see Section 4.

Since T1 and T2 are correlated, we put the correlationcoefficient to 1 and Eq. (6) is therefore a conservative esti-mate of the uncertainty of |T1 � T2|.

A drawback of the approach using T1 and T2 is that thestrong dependence of 134Cs on irradiation history is some-what relaxed by the influence of 137Cs and 154Eu in (5). Onemay thus expect a lowering of the sensitivity to detect erro-neously declared irradiation histories using this approachas compared to (3).

3.2. Empiric determination of fuel parameters

For a situation when the fuel parameters are consideredto be unavailable, burnup and cooling time may still beobtained (Hakansson et al., 1993) although with largeruncertainties. In such a situation (1) is written as

ix � ekxT ¼ Cxbjx . ð7Þ

Here, b is the burnup and jx assumes the value 1 for 137Cs,2 for 134Cs and about 2 or slightly less for 154Eu (Philipset al., 1980). Here, for 154Eu, j = 2 has been used. Cx areconstants that are determined by fitting a straight line toix � ekxT versus bjx for a number of reference assemblies ina similar way as in Section 3.1. See also Section 3.3 for de-tails regarding the calibration.

Specifically for 137Cs and 134Cs (or 154Eu), (7) yields

b ¼ i137 � ek137TC137

ð8Þ

and

b ¼ i134 � ek134TC134

� �12

. ð9Þ

By combining (8) and (9) and solving for burnup and cool-ing time, the following expressions are obtained (see alsoJansson, 2002)

b ¼ i134C134

C137

i137

� �k134k137

0@

1A

k1372k137�k134

; ð10Þ

T ¼ 1

k134 � 2k137ln

i137C137

� �2

� C134

i134

!. ð11Þ

It can be noted that any combination of two of the threeisotopes mentioned can be used. However, the combinationof 137Cs + 134Cs is expected to yield higher accuracy indetermining burnup and cooling time as compared to theother combinations. The reason is the large difference inhalf life of 134Cs as compared to 137Cs.

3.3. Calibration

The determination of the proportionality constant Kx of(2) includes the fitting of a line to ix � ekxT versus the isotopiccontent Ix. Accordingly, the accuracy of Kx is limited bythe accuracy with which the measurements and calcula-tions are performed as well as the number of reference fuelassemblies used. Mathematically, Kx is given by


Kx ¼PN

i¼1 Ix;i � hIxið Þix;i � ekxT iPNi¼1 Ix;i � hIxið Þ2

; ð12Þ

where N is the number of reference assemblies and ÆIxæ rep-resents the average value of Ix.

The coefficient Kx can be seen as the product of two fac-tors, A and B, where A depends on the geometry of themeasured fuel assembly and B depends on the propertiesof the detector and collimator arrangement.

Migration of primarily 137Cs and to some extent 134Cs inthe fuel rods, in principle, also contributes to A, see e.g.,Hsue et al. (1978) and Philips et al. (1980). Any significantmigration of 154Eu has on the other hand not beendetected. However, the effect of the migration of the threeisotopes was concluded to be smaller than the measure-ment uncertainty and was therefore omitted in thisanalysis.

The factor B is, in turn, a product of four factors gov-erned by

� The effective area of the assembly as seen from thedetector.

� The transmission of the radiation through the absorbingmedia between the fuel and the detector.

� The solid angle covered by the exposed part of the detec-tor as seen from the assembly through the collimator.

� The intrinsic efficiency of the detector, i.e., the probabil-ity that a gamma quantum of a certain energy, hittingthe detector, will result in the storing of a full-energyevent in the detector system.

Consequently, Kx needs to be reestablished every timethe detector or the measurement geometry is changed. Italso follows that Kx must be established for each fuel typeof interest.

As a measure of the overall uncertainty of Kx obtainedin this work, the standard deviation of Kx for each assem-bly was calculated. The result can be seen in Table 7.

The constant Cx of (7) was treated in a correspondingway as Kx. Here, the accuracy with which the burnup ofthe reference assemblies was declared is a determining fac-tor. In the same spirit as in estimating the accuracy of Kx,we here adopted average values obtained from experi-ments, see Fig. 9. As the irradiation history was not takeninto account in the determination of Cx, one expects largerrelative uncertainties of Cx as compared to Kx. The stan-dard deviation of the data in Fig. 9 indicates an accuracyof Cx within 2% (1r). See Table 8 for details.

It can be noted that the efficiency of a detector normallyvaries with energy and, accordingly, a correction for thismust be done when absolute measurements are to be per-formed. However, the method described here relies on rel-ative measurements which is manifested through thecalibration constants Kx and Cx. These constants includeall relevant information about the detector efficiency. Aspecific efficiency calibration is thus not necessary in theevaluation of (2) and (7).

3.4. Accuracy considerations

The key factor in the accuracy of the method is how wellthe gamma-ray intensity of the three isotopes can be mea-sured. For this work, the net count rates i137, i134 and i154were measured with typical statistical accuracies of0.05%, 0.15% and 0.15%, respectively, for fuel assemblieswith cooling times of about 10 years. A larger contributionto the overall accuracy is due to the consistency with whichthe fuel assemblies were positioned in the measurement fix-ture. This contribution was estimated to be in the order of1–2% for the three isotopes.

The accuracy of the isotopic concentration, Ix, dependson the code used. From Sanders and Gauld (2003) it isinferred that the depletion code ORIGEN-ARP calculatesIx with a standard deviation of 0.5%, 2.2% and 3.2% for137Cs, 134Cs and 154Eu, respectively. For the SNF code usedhere, it is reasonable to expect an uncertainty of the sameorder or better since SNF utilizes more detailed core phys-ics calculations.

Applying the above values to (3) shows that the uncer-tainty of T134 is 27 days (1r). If a verification measurementis performed on a fuel assembly yielding a value of D134

that is not significantly larger (less than 3 or 4r, say) thismay be interpreted as a correct declaration of that fuelassembly.

Furthermore, using the above accuracies in conjunctionwith (5) yields DT1 = 9 days and D T2 = 22 days. Accord-ingly, (6) may thereby be rewritten as |T1 � T2| < 31 days(1r). This means that if the difference between T1 and T2

is small enough, one may expect the irradiation history tobe correctly declared provided that D134 meets therequirements.

For (10) and (11) it can be shown that an uncertainty ofone percent of the measured intensities of 137Cs and 134Csgives us an uncertainty in T of 28 days. In the same man-ner, the relative difference of the calculated b is 1.2% fora measured intensity uncertainty of one percent in thetwo isotopes.

For fuel assemblies with cooling times exceeding about20 years the combination 137Cs + 154Eu is however the onlyapplicable to use since most of the 134Cs has decayed bythen. When using this combination, the uncertainty in T

is 235 days and the uncertainty in b is 2.4% assumingone percent uncertainty for each of the two measuredintensities.

One may also note that the radial burnup distributionmay influence the measured gamma-ray intensities. To esti-mate this influence, a two-step calculation was made. Firstthe burnup of each fuel rod in a former standard AA8 · 8 BWR fuel assembly, with an initial enrichment of2.82%, was calculated for six values of the total burnupusing the CASMO 2.3 code (Kurcyusz, 1995). In this way,different stages of the assembly’s irradiation history weresimulated. In the second step these burnup values wereintroduced into a code, which calculates the total gamma-ray intensity emitted from the fuel assembly, taking into

10 15 20 251.000

1.005

1.010

1.015

1.020

Burnup [GWd/tU]

Rel

ativ

e in

ten

sity

of

137 C

s

Fig. 4. Calculated relative gamma-ray intensities of 137Cs as a function ofburnup. The intensities from an AA 8 · 8 fuel assembly of 2.82% initialenrichment were normalized to a fuel assembly with a flat radial burnupdistribution. This figure illustrates that the correction for various radialburnup distributions is relatively small.

Table 2Values of D134 and T1 and T2 obtained in simulations where the actualburnup per power cycle is 5.5 GWd/tU instead of the reference case of5 GWd/tU

Tx Cooling time (years)

T134 3449T1 3546T2 3627

D134 �201 days|T1 � T2| 81 days

The values should be compared to the experimental accuracies of 27 daysand 31 days for D134 and for the difference in T1 and T2, 1r, respectively.The simulated cooling time was 3650 days.

Table 3Three different irradiation histories resulting in the same discharge burnupquoted in GWd/tU

Cycle Fuelref Fuelalt1 Fuelalt2

Burnup (GWd/tU)

1 5 – –2 5 6 –3 5 6 7.54 5 6 7.55 5 6 7.56 5 6 7.5P

Burnup 30 30 30

T134 – 3569 3483T1 – 3576 3498T2 – 3557 3461

D134 – �81 days �167 days|T1 � T2| – 19 days 37 days

Fuelref is the reference history and Fuelalt1 and Fuelalt2 are the two alter-native histories. The simulated cooling time in each case was 3650 days.


account self-absorption within the fuel assembly andabsorption in the surrounding water.

The calculations were limited to 137Cs because itsgamma-ray energy of 662 keV is the lowest considered inthis study and is expected to show the largest effect dueto the radial burnup distribution. Fig. 4 shows the relativeintensities of 137Cs from these calculations. The intensitieshave been normalized to intensities corresponding to ahypothetic fuel assembly with a flat burnup distribution.

It is seen that the ratio only slightly deviates from unityand that the radial distribution tends to level out as theburnup increases. From this investigation it may be con-cluded that regular burnup distributions are not expectedto affect the results in a mentionable way.

4. A feasibility study using simulated irradiation histories

In this section, a study is presented where various simu-lated irradiation histories have been investigated in order todeduce the detection limits of the technique describedabove. The reference assumption was that an investigatedPWR 17 · 17 fuel assembly with an initial enrichment of3.1% had been irradiated for 6 power cycles, each lasting335 days followed by a maintenance shutdown period of30 days. The burnup per power cycle was 5 GWd/tU result-ing in a discharge burnup of 30 GWd/tU. The feasibilitystudy comprises the calculation of relevant intensities fromthis fuel assembly and comparisons of these with the corre-sponding intensities from fuel assemblies with similar butnot entirely equal irradiation histories. The declared coolingtime was set to 10 years (3650 days) throughout the study.

4.1. Erroneously declared discharge burnup

In the first scenario, it was assumed that the operator bymistake had delivered data from another fuel assembly than

the one that was measured. The number of power cycleswas still 6 but the burnup per power cycle was 5.5 GWd/tU instead of 5 GWd/tU resulting in a declared final bur-nup of 33 GWd/tU. The results are presented in Table 2.

From Table 2 it is seen that the deviation of T134 fromthe simulated cooling time, D134, is about 200 days, whichis in the order of 7 standard deviations from expected.Thus D134 indicates a clear mismatch between declaredand actual fuel parameters. To be able to judge whetherthe cooling time or the irradiation history is erroneouslydeclared, the difference |T1 � T2| was calculated. As shownin Table 2, the value obtained is almost 3 times larger thanthe standard deviation of 31 days. Taking that as a signif-icant deviation one may conclude that the irradiation his-tory was erroneously declared in this case.

4.2. Erroneously declared number of cycles

In a second scenario, two alternative irradiation histo-ries were simulated, each resulting in the same dischargeburnup as the reference case. These were compared to thereference irradiation history, see Table 3.

Table 5Each row represents an alternative irradiation history where the fuelassembly has been out of core for 1–5 years before the last irradiationcycle

Out of core(years)

T134

(days)T1

(days)T2

(days)D134

(days)|T1 � T2|(days)

1 3806 3797 3829 156 332 3946 3925 3988 296 633 4059 4024 4112 409 884 4146 4096 4204 496 1085 4213 4146 4271 563 125

For each case, the calculated values of D134 and |T1 � T2| are presented.


In Table 3, the reference irradiation history is denotedFuelref while the two alternative irradiation histories aredenoted Fuelalt1 and Fuelalt2. The declared and actual dis-charge burnup was considered to be equal.

In Table 3,D134 is about 3 and 6 standard deviations fromexpected, respectively. However, if (5) is applied to thesecases the difference in |T1 � T2| is 18 days and37days, respec-tively. These two cases thus represent scenarios that can bedetected but where the conclusion whether the irradiationhistory or cooling time is not correctly declared is dubious.

For the third scenario, shown in Table 4, two real casesof irradiation histories have been simulated. One assemblyhas been irradiated for five power cycles, which is consid-ered here to be the declared history, Fueldecl. The other fuelassembly, Fuelalt, has been irradiated for four power cyclesand is here assumed to have been exchanged with thedeclared fuel assembly.

The deviation D134 is 193 days, which is about 7 stan-dard deviations from expected. It thus represents clear evi-dence that the fuel assembly is not correctly declared.However, also in this case it can be seen that the difference|T1 � T2| = 17 is below the stated detection limit of 31 days.

4.3. Nondeclared outtake

The last scenario represents a case where the fuel assem-bly was taken out of the core before the last power cycle,left out for 1–5 years and eventually put back in foranother irradiation cycle. The burnup for each irradiationcycle was 5 GWd/tU, see Table 5. These irradiation histo-ries were compared to the reference irradiation history.Also in this case, D134 and the time difference |T1 � T2| werecalculated as displayed in Table 5.

Using D134, all scenarios are revealed. By using the dif-ference |T1 � T2|, it is seen in Table 5 that a nondeclaredouttake of two years or more results in conclusive informa-tion that the irradiation history was erroneously declared.

Table 4Two real-case irradiation histories with the acquired burnup per cycle

Cycle Fueldecl Fuelalt

Burnup (GWd/tU)

1 6.89 –2 10.42 10.273 7.87 10.044 6.94 7.625 3.34 7.71P

Burnup 35.46 35.64

T134 – 3457T1 – 3466T2 – 3449

D134 – �193 days|T1 � T2| – 17 days

Here it is assumed that these two fuel assemblies have been exchanged sothat the declared irradiation history is not correct, although the dischargeburnup is similar. It can be noted that the experimental parameter D134

clearly indicates the erroneous declaration.

4.4. Conclusion of the feasibility study

According to the feasibility study, the technique pre-sented here has a potential to reveal, within reasonable lim-its, erroneous declarations of irradiation history. It mayalso be concluded that the technique is especially sensitiveto incorrectly declared cooling times, the uncertainty of 27days, 1r, for the cooling time determination indicates thatsmall cooling time deviations may be detected.

This study is based on that 134Cs is available and accord-ingly, the technique may be used for fuel assemblies with acooling time of maximum 20 years.

5. Experimental study

5.1. Mechanical arrangement

The experimental equipment used to collect the data inthis paper is schematically shown in Fig. 5. This type ofinstallation is present in all Swedish BWR nuclear power

Fig. 5. A schematic view of the gamma-scanning setup.

0 1 2 310

0

102

104

106

Energy [MeV]

Nu

mb

er o

f co

un

ts

137Cs

134Cs154Eu

Fig. 6. A typical spectrum of one corner of a fuel assembly with a burnupof 47 GWd/tU and a cooling time of 12 years. The peak around 2.7 MeVis the pulser peak used for dead-time correction.


plants and at the interim storage facility CLAB. The mea-surements presented in this paper were performed at thelatter facility.

Prior to measurement, the spent fuel assembly is posi-tioned into a fixture that can be elevated and rotated rela-tive to a horizontal collimator slit mounted in the poolwall. The collimator is made from two massive, 200 mmin diameter, steel half cylinders sandwiching a thin horizon-tal steel plate where a routing defines the collimator slit.The collimator height can be varied between one and fivemillimeters by changing between different slit plates. Thecollimator has a length of 120 cm and the detector is placedapproximately 246 cm from the center of the fuel assembly.Between the center of the fuel assembly and the pool wallthere is about 50 cm of water (Jansson, 2002).

The fuel assembly can be positioned laterally and angu-larly within a few millimeters and one degree, respectively.The fuel assembly is rotated so that a corner faces thecollimator. By scanning the corners of the assembly, thepositioning error in the measured intensity is minimized(Tarvainen et al., 1992). In this procedure, the fuel assem-bly is scanned by registering the gamma-ray spectrum asthe fuel assembly is moved vertically in front of thecollimator slit. Typically, the speed of the elevator is setso that it takes about 200 s for the whole fuel assemblyto pass the collimator slit. The assembly is then turned90� so that the next corner of the fuel assembly faces thedetector and the measurement procedure is repeated. Thusall four corners are scanned and eventually summed for theevaluation. In total, the measurement time is roughly20 min per fuel assembly.

5.2. The detector system

To detect the radiation emanating from the decay ofdifferent isotopes in the fuel, a high-resolution gamma-ray spectroscopy system should be considered. For fuelassemblies with long cooling times, the intensity of134Cs is weak in comparison with the 137Cs intensity.Therefore, the system should be able to measure weakintensities in the presence of strong intensities. Also, inorder to keep the measuring times reasonably short, theperformance of the detector should be optimized withrespect to two aspects.

� The peak-to-Compton ratio should be as high as possi-ble. This requirement implies the use of a comparablylarge detector.

� The system should be able to operate at as high countrates as possible.

As stated above, a large detector should be used in orderto fulfill the requirements. The size of the detector usedhere corresponded to �80% relative efficiency.

The detector used was equipped with a transistor resetpreamplifier which is a preamplifier type intended for highcounting rate applications.

The detector was irradiated radially since it was con-cluded that the peak area was less sensitive to count ratevariations using such a geometry as compared to a geome-try with axial irradiation (Bjorkholm and Dyring, 1990). Ingeneral, a 4 mm lead plate sandwiched with a 1 mm copperplate was used to filter out the comparatively strong inten-sity of low energy scattered photons.

5.3. Measurement and analysis

As discussed in Section 5.1, the fuel assemblies werescanned with one corner at the time facing the detector.Furthermore, the measurement of each corner of the fuelassembly was divided into 210 subspectra, each represent-ing a fuel length of about 2 cm and corresponding to ameasuring time of about 1 s.

During the measurements, high counting rates wereencountered, up to 100,000 counts per second (cps). Inaddition, the counting rates varied significantly and there-fore a proper dead-time correction of the spectra wasrequired.

In this work, each subspectrum was corrected fordead-time using the pulser method. Artificial pulses wereinjected into the detector system from an external pulsegenerator with a well-defined event rate. By formingthe ratio between the number of pulses injected duringthe measuring time for each subspectrum and the actualnumber of counts in the pulser peak in the spectrum, adead-time correction factor was obtained for each sub-spectrum. The content of each channel of a subspectrumwas multiplied with the corresponding dead-time correc-tion factor in order to get properly dead-time correctedspectra.

Finally, all subspectra were added together yielding atotal spectrum of each corner of the fuel assembly. Fromthis total spectrum, the net count rates of 137Cs, 134Cs


and 154Eu were extracted. An example of a total spectrumis presented in Fig. 6.

The peak at 0.662 MeV in Fig. 6 emanates fromthe decay of 137Cs while the peak at 0.795 MeV corre-sponds to 134Cs. The intensity corresponding to 154Eucan be found at 1.275 MeV and the large peak at2.7 MeV is the pulser peak. In Fig. 7, a typical axial pro-file of 137Cs is shown for a scanned PWR 17 · 17 fuelassembly. Each point in the figure corresponds to theevaluation of one subspectrum. The positions of thespacers of the fuel can be seen as dips in the intensitydistribution.

As the 137Cs intensity is proportional to burnup it can beconcluded that this particular fuel assembly had a relativelyuniform axial burnup profile.

Shown in Fig. 8 are the intensity profiles for 134Cs and154Eu obtained from the same fuel assembly.

0 50 100 1500

2000

4000

6000

8000

10000

12000

Axial position

Nu

mb

er o

f co

un

ts

Fig. 7. The axial profile of 137Cs. The lower part of the fuel is to left in thefigure.

0 50 100 1500

200

400

600

800

1000

Axial position

Nu

mb

er o

f co

un

ts

a b

Fig. 8. Illustration of the measured axial profiles of the (a) 134Cs and (b) 154Euthe figures is only about one second, the statistical properties of each data po

5.4. Experimental results

The experimental study was performed on 12 fuelassemblies of the PWR 17 · 17 type coming from theSwedish nuclear power plant Ringhals 3. The assemblieswere evaluated with respect to the count rates of 137Cs,134Cs and 154Eu. Table 6 lists some of the properties of thefuel assemblies.

5.4.1. Determination of calibration constants

Due to that no particular reference assemblywas assignedfor this study, it was assumed that the whole data set couldmake up the reference. Accordingly, the calibration con-stants, Kx for the case with available operator-declared dataand Cx for the case with no operator-declared data, weredetermined as an average of the complete data set. The con-stants Kx can be seen in Table 7.

0 50 100 1500

200

400

600

800

Axial position

Nu

mb

er o

f co

un

ts

intensities. It can be noted that since the measuring time for each point inint are relatively poor, and the values will therefore fluctuate accordingly.

Table 6The fuel assemblies included in the experimental study

FuelId

Enrichment(%)

Burnup(GWd/tU)

Declared T

(days)

0C9 3.101 38.65 39681C2 3.101 33.38 39721C5 3.101 38.66 39672C2 3.101 36.61 39683C1 3.101 36.69 39683C5 3.101 38.55 39683C9 3.101 36.64 39684C4 3.101 33.39 39724C7 3.101 38.56 39680E2 3.103 41.67 31960E6 3.103 36.00 31981E5 3.103 34.57 3196

Of these fuel assemblies, 10 had similar irradiation cycles (four consecutivecycles) and two fuel assemblies had three consecutive irradiation cycles(0E6 and 1E5).

Table 7The calibration constants Kx as determined in this work for the fuelassemblies described in Table 6

Isotope Kx (cps/g)

137Cs 22.1 ± 0.3134Cs 500.1 ± 5.7154Eu 109.1 ± 1.0

Table 8The calibration constants Cx as determined in this work

Isotope C137 (cps/(GWd/tU)) C134,C154 (cps/(GWd/tU)2)

137Cs 366 ± 5 –134Cs – 26.2 ± 0.7154Eu – 1.0 ± 0.04

For C137, j = 1 was used while for C134 and C154, j = 2 was used.

Table 9The experimental results obtained according to the equations described inSection 3.1

Fuel Id Declared T

(days)T134

(days)T1

(days)T2

(days)D134

(days)|T1 � T2|(days)

0C9 3968 3980 3976 3961 12 151C2 3972 3990 3974 4004 18 301C5 3967 3961 3965 3943 �6 222C2 3968 3972 3966 3965 4 13C1 3968 3971 3968 3970 3 23C5 3968 3951 3957 3943 �17 143C9 3968 3967 3967 3958 �1 94C4 3972 3966 3956 3987 �6 314C7 3968 3951 3967 3940 �17 270E2 3196 3181 3216 3182 �15 340E6 3198 3206 3200 3220 8 201E5 3196 3213 3197 3233 17 36


The relation between measured intensity, corrected forcooling time, versus declared burnup is shown in Fig. 9for the three isotopes. Here, j = 2 was used for 134Cs and154Eu, as accounted for in Section 3.2.

0 10 20 30 40 500

5000

10000

15000

20000

Burnup [GWd/tU]

137 C

s in

ten

sity

[cp

s]

(a ) 137 Cs

0 300 6000

300

600

900

1200

1500

1800

Burn

154 E

u in

ten

sity

[cp

s]

Fig. 9. The measured intensities, corrected for declared cooling time, versus dethat 154Eu is actually not a purely quadratic function of burnup.

The constants Cx of (7) were determined as an averageof the data set and are shown in Table 8. It can be seen thatthe relative uncertainties of Cx for this particular data setare 1.4%, 2.7% and 4.0% for 137Cs, 134Cs and 154Eu, respec-

0 300 600 900 1200 1500 18000

10000

20000

30000

40000

50000

Burnup2 [(GWd/tU)2]

134 C

s in

ten

sity

[cp

s]

(b) 134 Cs

900 1200 1500 1800

up2 [(GWd/tU)2]

(c) 154 Eu

clared burnup. For 134Cs and 154Eu the burnup is squared. It can be noted


tively (1r). The values of Cx were then used to calculate T

and b for each fuel assembly using (10) and (11).

5.4.2. Verification of fuel assemblies with declared

irradiation histories

The data from the assemblies were evaluated accordingto (3) and (5). The differences |T1 � T2| and D134 were cal-culated and evaluated as described in Section 3.1. Table 9shows the result of this exercise.

As Table 9 shows, neither |T1 � T2| nor D134 indicate anyerrors in the declaration of the fuel assemblies.

Table 10Calculated burnup using the two combinations of 137Cs + 134Cs and137Cs + 154Eu

FuelId

Calculatedb 137Cs + 134Cs(GWd/tU)

Deviationfromdeclaredburnup(GWd/tU)

Calculatedb 137Cs + 154Eu(GWd/tU)

Deviationfromdeclaredburnup(GWd/tU)

0C9 38.19 �0.46 38.48 �0.171C2 32.82 �0.56 31.47 �1.911C5 38.56 �0.10 39.17 0.512C2 36.32 �0.29 36.13 �0.483C1 36.41 �0.29 36.18 �0.523C5 38.61 0.06 39.12 0.573C9 36.56 �0.04 36.64 0.014C4 33.02 �0.37 31.74 �1.654C7 38.93 0.37 39.87 1.320E2 43.52 1.85 46.17 5.040E6 36.18 0.18 35.89 �0.111E5 34.56 �0.01 33.65 �0.92

Relative standarddeviation

1.6% 4.6%

Also shown are the deviations from declared burnup. The relative stan-dard deviation obtained by using the two combinations is 1.6% and 4.6%,respectively.

Table 11Calculated cooling time using the two combinations of 137Cs + 134Cs and137Cs + 154Eu

FuelId

CalculatedT 137Cs + 134Cs(days)

Deviation fromdeclared T

(days)

CalculatedT 137Cs + 154Eu(days)

Deviationfromdeclared T

(days)

0C9 3987 19 4106 1381C2 3905 �67 3237 �7351C5 3986 19 4237 2702C2 3952 �16 3867 �1013C1 3954 �14 3854 �1143C5 3982 14 4193 �2253C9 3960 �8 3995 �274C4 3895 �77 3267 �7054C7 4002 34 4382 4140E2 3327 131 4453 12570E6 3197 �1 3067 �1311E5 3164 �32 2739 �457

Relative standarddeviation

1.5% 15.5%

Also shown are the deviations from declared cooling time. The relativestandard deviation is 1.5% and 15.5%, respectively, using the twocombinations.

5.4.3. Independent experimental determination of burnup and

cooling time

The case where no operator-declared information isavailable can be treated according to the discussion in Sec-tion 3.2. It can be noted that the discussion requires thatthe type of fuel assembly may be identified.

The experimentally determined burnup and cooling timeare summarized in Tables 10 and 11.

From the values given in Table 10 it is inferred that theburnup can be determined with a relative uncertainty of1.6% when using the combination of the 137Cs and 134Csintensities. Using the combination of the 137Cs and 154Euintensities yields a relative standard deviation of 4.6%.The corresponding relative uncertainties of the determinedcooling times are 1.5% and 15.5%, respectively, as shown inTable 11.

6. Summary

There have been two purposes of this work:

(1) To show that spectroscopic measurements of gamma-rays can be used to verify a given declaration of a fuelassembly. In particular, verification of the irradiationhistory was of specific interest in this study.

(2) To calculate the basic fuel parameters burnup andcooling time if the fuel assembly declaration is missing.

A feasibility study was made using simulated data inorder to see how the technique would respond to differenterrors in the declaration of the fuel assemblies. It was con-cluded that a feasible procedure is to evaluate the isotopiccontent of 137Cs, 134Cs and 154Eu.

The technique has been demonstrated experimentally on12 PWR fuel assemblies from the Swedish power plantRinghals 3. The assemblies had different cooling time, bur-nup and irradiation history. The experimental results forthe irradiation history measurements could all be verified.

For the case where no operator-declared informationwas assumed to be available the burnup and cooling timecould be calculated with a relative standard deviation of1.2% and 1.5%, respectively.

Acknowledgments

The authors thank the staff at CLAB for good coopera-tion and valuable assistance during the experiments. SigurdBørresen at Studsvik Scandpower is acknowledged for hishelp with the SNF data and Ewa Kurcyusz at VattenfallBransle AB for her help with the CASMO calculations.

This work was kindly financed by the Swedish NuclearPower Inspectorate (SKI).

References

Berndt, R., 1988. Verification of spent PWR fuel data using the 154Eu,134Cs and 137Cs activities. Kernenergie 31, 59–63.


Bjorkholm, P., Dyring, A., 1990. A study of high count rate gammaspectrometry system for burnup measurements. Master’s Thesis,Institute of Technology, Uppsala University, Uppsala, Sweden.

Børresen, S., Bahadir, T., Kruners, M., 2004. Validation of CMS/SNFcalculations against preliminary CLAB decay heat measurements.

Edenius, M., Ekberg, K., Forssen, B., Knott, D., 1995. CASMO-4, a fuelassembly burn-up program: user’s manual. STUDSVIK/SOA-95/1.

Hakansson, A., Backlin, A., Hildingsson, L., Danielsson, N., 1993.Results of spent-fuel NDA with HRGS. In: Proceedings of the 15thAnnual Esarda Meeting, Rome, Italy.

Hsue, S., Crane Jr., W.T., Lee, J.C., 1978. Nondestructive assay methodsfor irradiated nuclear fuels. Report LA-6923 (ISPO-9), Los AlamosNational Laboratory.

IAEA, 2003. Safeguards techniques and equipment. International NuclearVerification Series No. 1 (Revised).

Jansson, P., 2002. Studies of nuclear fuel by means of nuclear spectro-scopic methods. Ph.D. Thesis, Department of Radiation Sciences,Uppsala University, Uppsala, Sweden.

Kurcyusz, E., 1995. private communication.Philips, J., Halbig, J., Lee, D., Beach, E., Bement, T., Dermendjiev, E.,

Hatcher, C., Kaieda, K., Medina, E., 1980. Application of nonde-structive gamma-ray and neutron techniques for the safeguarding ofirradiated fuel materials. Report LA-8212 (ISPO-77), Los AlamosNational Laboratory.

Rinard, P., Bosler, G., 1988. March. Safeguarding LWR spent fuel withthe fork detector. Technical Report LA-11096-MS (ISPO-281), LosAlamos National Laboratory.

Sanders, C.E., Gauld, I.C., 2003. Isotopic analysis of high-burnup PWRspent fuel samples from the Takahama-3 reactor. Technical ReportORNL/TM–2001/259, Oak Ridge National Laboratory.

Studsvik Energiteknik, A.B., 1995. SIMULATE-3. Advanced three-dimensional two-group reactor analysis code. STUDSVIK/SOA-95/15-REV 0.

Tarvainen, M., Backlin, A., Hakansson, A., 1992. Calibration of the TVOspent BWR reference fuel assembly. Technical Report STUK-YTO-TR 37, Finnish Centre for Radiation and Nuclear Safety (STUK).

nondestructive assay of spent nuclear fuel with gamma-ray spectroscopy

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