Estimation of isotopic composition of plutonium from thermal reactors by neutron coincidence counting through isotopic correlation technique

DOI: 10.1007/s10967-007-7192-1 Journal of Radioanalytical and Nuclear Chemistry, Vol. 278, No.1 (2008) 137–149

0236–5731/USD 20.00 Akadémiai Kiadó, Budapest © 2008 Akadémiai Kiadó, Budapest Springer, Dordrecht

Estimation of isotopic composition of plutonium from thermal reactors by neutron coincidence counting through isotopic correlation technique

Pradeep Kumar,* Dipti Shah, K. L. Ramakumar Radioanalytical Chemistry Division, Radiochemistry and Isotope Group, Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India

(Received December 24, 2007)

Correlations have been established between %Eff 240Pu and various plutonium isotopes formed in thermal reactors. Based on these correlations, a method has been developed for the estimation of isotopic composition of plutonium obtained from thermal reactors. The method is simple, fast, non-destructive and finds application for the verification of plutonium isotopic composition in the finished products of known plutonium content. The method could be applied in the nuclear fuel fabrication to verify and confirm the fissile content (239Pu+241Pu) specification. It has also been shown that in principle, similar correlations could be established for Pu obtained from different thermal reactor fuels with reactor specific fitting parameters.

Introduction

During the irradiation of the nuclear fuel in a nuclear reactor, besides nuclear fission, the isotopic composition of nuclear fuel viz. uranium and plutonium undergoes complex changes, i.e., the depletion of 235U, production of 236U, 239Pu, 240Pu, 241Pu, 242Pu, etc. These changes and transmutations are regular, inherently related to one another and can be represented by linear expressions, which forms the basis of Isotopic Correlation Technique (ICT).1–3 These isotopic correlations could function as useful tools to verify internal consistency of the isotopic data, and for the estimation of the burnup of the fuel, which indirectly indicates to the amount of Pu produced. Since long, the potential application of the ICT has been recognized for the independent verification of nuclear material. A large number of isotopic correlations have been reported in the literature.4–14 Among the various isotopic correlations, those involving the heavy element isotopes have been extensively investigated and found reliable. Isotopic Correlation Technique has been widely employed by the International Atomic Energy Agency (IAEA) for the verification of declared values at the various stages of nuclear fuel cycle. Some of the important applications of the ICT are: independent verification of plutonium, verification of substitution of fuel assemblies, confirmation of the consistency in the measured data, identification of the fuel and the reactor type.

The Pu isotopic composition is a function of various factors like reactor type, burnup, fuel type, initial fuel composition, neutron flux and neutron absorption cross sections, etc. Most of the isotopic correlations reported in the literature are between various Pu isotopes versus burnup or among various Pu isotopes. DE REGGE and BODEN15 have derived expressions between the isotopic composition of Pu and burnup for the Pu from thermal

* E-mail: [email protected]

reactors (pressurized water reactors). These correlations are based on the equations for the formation and depletion of various Pu isotopes formed in thermal reactors.

During the course of plutonium based nuclear fuel fabrication, it is desirable to verify the isotopic composition of Pu as well as the fissile content (239Pu+241Pu) in the finished products such as fuel pins, fuel pellets etc. A simple and reliable ICT might be an attractive proposition for this purpose. Non-destructive assay (NDA) techniques are available for the estimation of Pu employing neutron coincidence counting through the determination of Eff 240Pu content. It was thought desirable to establish correlations between %Eff 240Pu and various Pu isotopes. The availability of such correlations would greatly reduce the necessity of other non-destructive techniques such as gamma-spectrometry for the estimation of Pu isotopic composition. However, establishment of such correlations requires the knowledge of large number of parameters such as Pu amount, Pu isotopic composition, neutron absorption cross section, neutron flux and irradiation time. However, for a particular reactor type and fuel, the isotopic composition depends upon the extent of burnup.

In a thermal reactor, 239Pu is formed from 238U by (n,γ) reaction followed by two successive β–-decays. The other Pu isotopes are formed from 239Pu by successive neutron capture reactions:

( )

( ) ( ) ( ) PuPuPu

PuNpUU242γn,241γn,240γn,

239β239β239γn,238

⎯⎯ →⎯⎯⎯ →⎯⎯⎯ →⎯

⎯→⎯⎯→⎯⎯⎯ →⎯−−

(1)

While deriving the expressions for various Pu isotopes versus burnup, DE REGGE and BODEN15 have not mentioned the expression for 238Pu formation. The probable reason might be apparent from the isotopic composition consideration of Pu obtained from thermal

PRADEEP KUMAR et al.: ESTIMATION OF ISOTOPIC COMPOSITION OF PLUTONIUM FROM THERMAL REACTORS

138

reactors, as the percentage of 238Pu in Pu produced is very small (<0.2% of Pu). However, the expression for Eff 240Pu content includes the contribution from 238Pu isotope. As 238Pu contributes significantly towards spontaneous fission events, while deriving the theoretical expression for Eff 240Pu, in addition to the expressions derived by DE REGGE and BODEN, expression for 238Pu production is also required. Moreover, unlike other plutonium isotopes, production of 238Pu is a complex process involving two independent nuclear reactions:

PuNpNp

UU

238238)(n,237

237)(n,

(n,2n)238

⎯⎯→⎯⎯⎯ →⎯

⎯⎯→⎯⎯⎯ ⎯← ⎯⎯ →⎯

−

−

βγ

βγ (2)

PuNpNp

UUU

238238)(n,237

237)(n,236)(n,235

⎯⎯→⎯⎯⎯ →⎯

⎯⎯→⎯⎯⎯→⎯⎯⎯→⎯−

−

βγ

βγγ

(3)

Theoretical basis for isotopic correlations

Neutron coincidence counting and Eff 240Pu

In Pu bearing materials the contribution to neutrons arises from the following sources:16

(1) Spontaneous fission (SF) of even-even isotopes of Pu (238Pu, 240Pu, 242Pu).

(2) Alpha-particle induced reactions with light elements in the matrix (O, F, C, N, etc).

(3) Neutron induced fission of fissile isotopes (239Pu, 241Pu) at higher Pu amount.

(4) Background neutrons. In Table 1 the spontaneous fission neutrons emitted

per gram per second from various plutonium isotopes are listed. From the table, it is evident that the major contributors for spontaneous fission events are the even-even isotopes of Pu, i.e., 240Pu, 238Pu, 242Pu. The neutron coincidence counting (NCC) measures the spontaneous fission neutrons. However, NCC is unable to provide information about the isotope of origin of neutron. Since neutron multiplicity is different for different Pu isotopes, the spontaneous fission neutron count rate would depend upon plutonium isotopic composition. For convenience, it is customary to normalize the spontaneous fission neutron contribution from various Pu isotopes in terms of 240Pu, mainly because 240Pu is the major contributor towards spontaneous fission events. Accordingly, a plutonium

lot of particular isotopic composition, could be characterized by its %Eff 240Pu (X) content; defined as:16

X = 2.43 [238Pu]+[240Pu]+1.69 [242Pu] (4) where [238Pu], [240Pu] and [242Pu] are the weight percentages of the respective Pu isotopes in the Pu lot. The quantity of “%Eff 240Pu content” is very useful as it can be determined by the neutron coincidence counting and is a measure of spontaneous fission neutrons emitted from 100 gram of Pu. For isotopically well characterized sample, by determining its Eff 240Pu content by neutron coincidence counting, Pu amount can be estimated. Conversely, for a sample of known Pu amount, its Eff 240Pu content can be determined by the neutron coincidence counting. In the present study, for a sample of known plutonium amount, by determining its %Eff 240Pu content, the plutonium isotopic composition has been estimated employing the Isotopic Correlation Technique.

Expressions for Pu isotopes versus %Eff 240Pu

The formation of various isotopes of Pu in a thermal reactor could be expressed by the simple relationships15 of the following type:

)(49

)(49

49 4928 tt eBeAN ϕσϕσ −− += (5.1)

)(40

)(40

)(40

40 404928 ttt eCeBeAN ϕσϕσϕσ −−− ++= (5.2)

)(

41)(

41

)(41

)(41

41

4140

4928

tt

tt

eDeC

eBeANϕσλϕσ

ϕσϕσ

+−−

−−

++

++= (5.3)

)(

42)(

42)(

42

)(42

)(42

42

424140

4928

ttt

tt

eEeDeC

eBeANϕσϕσλϕσ

ϕσϕσ

−+−−

−−

+++

++= (5.4)

where N indicates the amount (atoms per unit volume) of the isotope formed. The first digit in the index refers to (Z-90), where Z denotes the atomic number. The second digit in the index refers to (A-230), where A denotes the mass number. The symbols σ, ϕ, t, σc refer to absorption cross section, neutron flux, time of irradiation and capture cross section, respectively, and A, B, C, D and E are coefficients defined by DE REGGE and BODEN.15 In the present work, based on the same analogy of Pu isotope formation, the equation for 238Pu production has been derived (Annex-I) taking into account its two routes of production:

t

tt

eBA

eBeANϕσ

ϕσϕσ

48

2825

24848

484848

)( −

−−

+−

−+= (6.1)


139

Table 1. Spontaneous fission neutron yields of plutonium isotopes16

Plutonium isotope

S.F. half-life, year

Neutrons/g/s S.F. neutron multiplicity

Induced fission neutron multiplicity

238Pu 4.77.1010 2480 2.21 2.91 239Pu 5.48.1015 0.0218 2.16 2.88 240Pu 1.16.1011 1022 2.16 2.80 241Pu 2.5.1015 0.05 2.25 2.80 242Pu 6.84.1010 1720 2.15 2.81

Substituting θ = φ t , and the values of 48N, 40N and

42N from Eqs (5.1), (5.2), (5.4), in Eq. (4), the %Eff 240Pu, denoted by X, could be expressed as:

)

(69.1

)(

))(

(43.2

4241

404928

404928

48

2825

42)(

42

424242

404040

24848

4848

θσθσλ

θσθσθσ

θσθσθσ

θσ

θσθσ

−+−

−−−

−−−

−

−−

++

++++

++++

++−

−+=

eEeD

eCeBeA

eCeBeA

eBA

eBeAX

(7.1)

The exponential term in Eq. (7.1) can be expanded, recalling that the Maclaurin series for the exponential function ex is:

K+++++=!4!3!21

1432 xxxxex (7.2)

As the quantity σθ is very small (~10–2), the higher power terms (square and above) could be neglected and the Eq. (7.1) can be simplified into Eq. (7.3):

X = AX–BXθ (7.3)

where AX = [A40+B40+C40+1.69(A42+B42+C42+D42+E42)] BX = [2.43A48(σ25–2σ48)+2.43B48(σ28–2σ48)+ +A40σ28+B40σ49+C40σ40+1.69A42σ28+1.69B42σ49+ +1.69C42σ40 + 1.69D42(λ+σ41) + 1.69E42σ42]

From Eq. (7.3), the θ can be expressed in terms of X

as:

X

XB

XA )( −=θ (7.4)

On substituting the above value of θ into Eq. (5.1) and expanding by employing the Maclaurin series for the exponential function ex (neglecting higher power terms, square and above), 239Pu percentage could be expressed as linear expression in terms of %Eff 240Pu as (Annex-II):

XN 494949 βα += (8.1)

where

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

X

X

X

XB

ABB

AA 4949

284949 11 σσα (9.1)

XB

BA )( 4949284949

σσβ += (9.2)

Similarly, linear expressions could be established for 240Pu, 241Pu, 242Pu, 238Pu from Eqs (5.2), (5.3), (5.4) and (6.1):

XN 404040 βα += (8.2)

XN 414141 βα += (8.3)

XN 424242 βα += (8.4)

XN 484848 βα += (8.5)

where

⎥⎥⎦

⎤⎟⎟⎠

⎞⎜⎜⎝

⎛−+

⎢⎢⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛−+⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

X

X

X

X

X

X

BAC

BAB

BAA

4040

4940

284040

1

11

σ

σσα

(9.3)

XB

CBA )( 40404940284040

σσσβ ++= (9.4)

⎥⎥⎦

⎤⎟⎟⎠

⎞⎜⎜⎝

⎛ +−+⎟⎟

⎠

⎞⎜⎜⎝

⎛−+

⎢⎢⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛−+⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

X

X

X

X

X

X

X

X

BAD

BAC

BAB

BAA

)(11

11

4141

4041

4941

284141

σλσ

σσα

(9.5)

XBDDCBA )( 414141404049402840

40σλσσσ

β++++

=

=(9.6)

⎥⎥⎦

⎤⎟⎟⎠

⎞⎜⎜⎝

⎛ σ−+

+⎟⎟⎠

⎞⎜⎜⎝

⎛ σ+λ−+⎟⎟

⎠

⎞⎜⎜⎝

⎛ σ−+

⎢⎢⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛ σ−+⎟⎟

⎠

⎞⎜⎜⎝

⎛ σ−=α

X

X

X

X

X

X

X

X

X

X

BAE

BAD

BAC

BAB

BAA

4242

4142

4042

4942

284242

1

)(11

11

(9.7)


140

XBEDDCBA )( 4242414141404049402840

42σσλσσσ

β+++++=

=(9.8)

X

XB

ABA )]2()2([ 28484825484848

σσσσα −+−= (9.9)

XB

BA )]2()2([ 48284848254848

σσσσβ −+−= (9.10)

Experimental

To determine the plutonium isotopic composition of a sample by the Isotopic Correlation Technique, a prior knowledge of %Eff 240Pu is essential. The %Eff 240Pu can be determined by neutron coincidence counting system by measuring the neutron coincidence count rate.

Neutron coincidence counting system

Sorting out of spontaneous fission neutrons through coincidence counting was suggested and used by JACQUESSON.17 Subsequently, the idea of coincidence counting was conceived and developed at NRL and Los Alamos laboratories.18–20 BÖHNEL21 developed a shift-register based neutron coincidence counting unit in 1975. The neutron coincidence counting finds wide ranging applications such as quality control of finished products, nuclear materials accounting, process control and safeguards by IAEA.22–27 DIERCKX and HAGE, SHER, CEO and THOMSON, JAMES et al., GRABBER, HANNA, FATTAHM have carried out significant work in the field of neutron coincidence counting.28–35

A block diagram of the neutron coincidence counting system is shown in Fig. 1. The system comprises of a neutron detection assembly, pre-amplifier, amplifier, high voltage unit, coincidence unit and a triple scaler. The neutron detection assembly consists of High Density Polyethylene matrix (0.92 g/cm3) having a cylindrical cavity (well) of 15 cm diameter and 50 cm depth at the center for holding samples as well as achieving high neutron detection efficiency. Sixteen 3He

detectors are arranged in a circular array of 25 cm diameter so as surround the cavity. The detectors are of cylindrical shape having 2.5 cm diameter and 50 cm height, filled with 3He gas at a pressure of 4 atmosphere. The neutrons emitted from plutonium bearing sample, (kept inside cavity) are thermalized by the High Density Polyethylene matrix prior to their detection. Owing to

finite dimensions of the detection assembly, the relative detection probability for the thermalized neutrons diminishes as a function of time owing to leakage and absorption. Therefore, for time-correlated fission neutrons, the detection probability would be finite within the die-away time (average life-time of neutrons in the system). On the other hand, for time-uncorrelated (α,n) reaction neutrons and background neutrons (random), the relative detection probability is independent of the specific time intervals. Rossi-alpha distribution developed by PACILIO36 is very helpful for quantifying the time-correlated neutrons. The distribution is obtained by recording arrival time of successive pulses (neutron detection event) with respect to an arbitrary pulse. For random events, the distribution is constant with respect to time. If both fission neutrons and (α,n) reaction neutrons together are present, then the Rossi-alpha distribution can be represented by the following equation:

⎟⎠⎞

⎜⎝⎛−

+= Tt

AtS Re)( (10)

where S(t) is the height of the distribution at time t. The terms A, R and T denote the accidental (random) count rate, the real coincidence count rate and the die-away time of the system, respectively. The combined output from all neutron detectors are connected in parallel, through an amplifier which is fed to the shift-register based coincidence unit. The coincidence unit sorts out the spontaneous fission neutrons by exploiting the time correlation as per Eq. (10). In the coincidence unit, the number of neutrons following each neutron are sampled at two equal gates separated by a long delay (several times of the die-away time). In the first gate (prompt gate) time-correlated and random neutrons to the triggering neutron pulse are counted, in the second gate (delayed gate) random neutrons with respect to the triggering neutron pulse are counted. The subsequent arriving neutron pulses are subjected to the coincidence analysis and the contents of prompt gate and delayed gate are continuously displayed on the coincidence unit, whereas the accumulated counts of these gates and gross counts are displayed on the triple scaler unit. The net difference in the counts of prompt and delayed gate is the time-correlated coincidence counts. The coincidence counts are the measure of spontaneous fission neutrons which are related to the Eff 240Pu content of the plutonium bearing sample.


141

Fig. 1. Block diagram of neutron coincidence counting setup

Determination of the Pu isotopic composition

Pu isotopic composition can be calculated from Eqs (8.1) to (8.5) by substituting the value of %Eff 240Pu obtained from NCC. The values of coefficients αi and βi in Eqs (8.1) to (8.5) were determined from the slopes and intercepts of the graphs of %Eff 240Pu versus percentage of plutonium isotope. For the plutonium obtained form Indian Pressurized Heavy Water Reactors (PHWRs), the graphs for isotopes 239Pu, 240Pu, 242Pu, 238Pu are shown in Fig. 2a, Fig. 2b, Fig. 2c and Fig. 2d, respectively. The graphs are linear as predicted by Eqs (8.1) to (8.5). From the graphs the values of the coefficients αi and βi were obtained by subjecting the graph data to least square fitting. From the graphs following equations were obtained:

239Pu (%) = –0.986 X + 97.533 (11.1) 240Pu (%) = 0.741 X + 4.082 (11.2) 242Pu (%) = 0.136 X–2.171 (11.3) 238Pu (%) = 0.011 X–0.158 (11.4)

where X represents the %Eff 240Pu. The isotopic

composition of an unknown sample, of known Pu amount, could be calculated by substituting the value of %Eff 240Pu into Eqs (11.1) to (11.4). The %Eff 240Pu content of a plutonium sample was determined by comparing sample’s neutron coincidence count rate with an isotopically characterized standard of known Pu amount. The 241Pu (%) was calculated by the difference, i.e.:

241Pu (%)= {100–(239Pu(%)+240Pu(%)+ +242Pu(%)+238Pu(%))}.

Results and discussion

The present method is a non-destructive method to determine the plutonium isotopic composition. The method has many special features: provides rapid information on the Pu isotopic composition of the large size finished product samples like pellets, pins, fuel bundles, etc. The method is versatile with respect to sample composition and configuration. However, a prior knowledge of the plutonium amount is the prerequisite.


142

Fig. 2a, 2b, 2c, 2d. Correlation graphs for Pu from Indian PHWR

For Pu estimation non-destructive methods like

neutron coincidence counting, gamma-spectroscopy, calorimetry are normally employed. However, these methods need the knowledge of isotopic composition of plutonium for which other expensive techniques such as thermal ionization mass spectrometry is employed. Destructive analytical techniques such as electro-analytical techniques based on potentiometric/ampero-metric end point detection are preferred for this purpose as they require only a few mg of sample and give precision and accuracy better than 0.5%. Moreover, the knowledge of isotopic composition is not required. Pu content obtained using these electroanalytical techniques, the isotopic composition could be rapidly estimated by neutron coincidence counting thus eliminating the need of thermal ionization mass spectrometry. The method is very useful for nuclear fuel production plants where the quick verification of fissile content is desirable, e.g., in MOX fuel for thermal reactors, where the plutonium % is based on the fissile (239Pu+241Pu) content of the plutonium lot.

One unique feature of the method is that by determining a single parameter only, the percentage of all the five isotopes of Pu formed in the thermal reactor could be estimated. Also, the determination of coefficients αi and βi [Eqs (8.1) to (8.5)] requires the knowledge of a large number of parameters. However, from the graphs (Figs 2a to 2d) the values of the coefficients αi and βi can be obtained, thus avoiding the knowledge of large number of parameters.

The graphs obtained by plotting the experimentally observed data (% of isotope versus %Eff 240Pu) are linear having correlation coefficients better than 0.98. These graphs matches with the trend predicted by Eqs (8.1) to (8.5) thus giving full credence to the hypothesis. The observed data reveals that 239Pu (%) declines linearly with increasing %Eff 240Pu, while the percentage of other isotopes rises linearly with increasing %Eff 240Pu. This behavior emanates from the fact that in a reactor as the irradiation progresses, more and more 239Pu gets converted into higher Pu isotopes.


143

In the plutonium obtained from thermal reactors, 239Pu is present in highest percentage followed by 240Pu, 241Pu, 242Pu. In Indian PHWRs the burnup witnessed by the fuel is in the vicinity of 7000 MWd/t. At such burnup levels, the 239Pu ranges between 71% to 77%, 240Pu between 18% to 24%, 241Pu between 3% to 5%, 242Pu between 2% to 4% and 238Pu<0.3%.

The isotopic composition of a few representative samples as determined by neutron coincidence counting (NCC) is shown in Table 2 and that obtained from thermal ionization mass spectrometry (TIMS) is also included for comparison. For various Pu isotopes the ratios of percentage by NCC and that by TIMS are also listed for comparison purpose. For 239Pu, 240Pu, 241Pu, 242Pu, 238Pu the ratios are (0.998±0.003), (0.999±0.004), (1.007±0.088), (1.014±0.045), (1.004±0.072) respectively. For fissile content (239Pu+241Pu ) the ratio is nearly 1.

The results gained by the present method are sufficiently accurate to be applied in nuclear fuel cycle exploiting the associated advantages of the method. One such application of the method is the rapid verification of the fissile content specification of Pu lots. For experiments on plutonium recycling in thermal reactors,

mixed oxide (MOX) fuel for boiling water reactor (BWR) was producted. In MOX fuel, plutonium oxide is mixed with uranium oxide. The plutonium percentage in MOX fuel depends on the fissile content (239Pu+241Pu). During the MOX fuel production a rapid verification of fissile content of Pu lots was required. The Pu used in MOX fuel production was obtained from the reprocessing of irradiated fuel from PHWR. The specification for the fissile content was (77±2.5)%. As evident from Table 2, the present method could be successfully applied for the verification of the fissile content of a Pu lot. The fissile content values obtained by ICT are in excellent agreement with the values determined by TIMS.

241Pu is a beta-emitter; it decays to 241Am and has a short half-life (14.4 years). It is most likely that over long periods, the decay of 241Pu might alter the %Eff 240Pu content leading to error in the estimation of isotopic composition. Hence, correction for 241Pu decay needs to be applied to old Pu lots. The calculated change in isotopic composition and %Eff 240Pu with time for a particular Pu lot is listed in Table 3. 241Pu is most severely affected.

Table 2. Isotopic composition of Pu from Indian PHWR (in atom %) by neutron coincidence counting and mass spectrometry (TIMS)

Lot No. Method and bias 239Pu, % 240Pu, % 241Pu, % 242Pu, % 238Pu, % (239Pu+241Pu), % PK-1 TIMS 75.36 21.051 2.617 0.886 0.089 77.98 NCC 75.09 20.961 2.923 0.933 0.097 78.01 Ratio 0.996 0.996 1.117 1.053 1.089 1.000 PK-2 TIMS 74.94 21.27 2.696 0.978 0.114 77.64 NCC 74.65 21.288 2.965 0.993 0.102 77.62 Ratio 0.996 1.001 1.100 1.015 0.895 0.999 PK-3 TIMS 77.23 19.698 2.312 0.702 0.072 79.54 NCC 76.81 19.664 2.753 0.694 0.077 79.56 Ratio 0.995 0.998 1.191 0.989 1.069 1.0003 PK-4 TIMS 74.94 21.27 2.696 0.978 0.114 77.63 NCC 74.65 21.28 2.965 0.993 0.102 77.63 Ratio 0.996 1.0004 1.099 1.015 0.895 1.000 PK-5 TIMS 75.89 20.437 2.627 0.948 0.096 78.53 NCC 75.56 20.606 2.876 0.867 0.092 78.43 Ratio 0.996 1.008 1.095 0.915 0.958 0.999 PK-6 TIMS 73.57 22.267 2.959 1.085 0.115 76.53 NCC 73.55 22.118 3.074 1.145 0.114 76.62 Bias –0.03 –0.15 0.12 0.06 0.00 0.09 Ratio 0.999 0.993 1.039 1.055 0.991 0.999 PK-7 TIMS 75.84 20.449 2.827 0.771 0.083 78.66 NCC 75.88 20.361 2.844 0.822 0.088 78.73 Ratio 1.001 0.996 1.006 1.066 1.060 1.001 PK-8 TIMS 77.23 19.698 2.312 0.702 0.072 79.54 NCC 76.81 19.664 2.753 0.694 0.077 79.56 Bias –0.42 –0.03 0.44 –0.01 0.01 0.02 Ratio 0.995 0.998 1.191 0.989 1.069 1.0003 PK-9 TIMS 75.84 20.449 2.832 0.791 0.091 78.67 NCC 75.84 20.398 2.573 0.829 0.089 78.66 Ratio 1.000 0.998 0.909 1.048 0.978 0.9998 PK-10 TIMS 71.83 23.496 3.15 1.395 0.1294 74.98 NCC 72.01 23.430 3.160. 1.386 0.134 75.18 Ratio 1.003 0.997 1.003 0.994 1.039 1.003


144

Equations (11.1) to (11.4) are for Pu from Indian PHWRs where natural uranium oxide is employed as fuel. For other types of fuel, e.g., mixed oxide (U, Pu)O2, enriched uranium oxide, the logic should hold good, i.e., linear correlations between isotopic composition and %Eff 240Pu should be obtained, only the values of coefficients could differ. To verify this logic, from the plutonium isotopic composition reported in the literature, the correlation graphs were constructed and the values of coefficients (αi, βi) were obtained. In Table 4, plutonium isotopic composition as determined by thermal ionization mass spectrometry, at various burnup levels in pressurized water reactor (PWR) is shown.15

The correlation graphs based on the isotopic composition data in Table 4, are shown Figs 3a to 3d. The correlations are linear upto burnup level of 43950 MWd/t.

The isotopic composition of plutonium (by TIMS) from YANKEE ROWE core, a PWR, is listed in Table 5.37 This PWR is enriched uranium fuelled. The fuel has witnessed the exposure level of 30,000 MWd/t. The correlation graphs based on the isotopic composition data in Table 5, are shown Figs 4a to 4d. The correlat-ions are linear upto the burnup level of 30,000 MWd/t.

In the Table 6, the coefficients α, β and the correlation coefficients are compared for isotopic correlations for the above-mentioned three types of fuels, i.e., natural uranium oxide, MOX and enriched uranium oxide.

For 239Pu and 240Put the correlation coefficients are greater then 0.99. For 242Pu and 238Pu the correlation coefficients are between 0.95 and 0.99.

This is probably due to the fact that the 239Pu and 240Pu are present at higher percentage whereas 238Pu and 242Pu are present at lower percentage. The linearity in correlations is maintained at higher burnup levels also, i.e., 30,000 MWd/t for Yankee Rowe and 43950 MWd/t for PWR (BR3 reactor). Thus the isotopic correlation concept holds good for natural uranium, enriched uranium, mixed uranium-plutonium fuelled thermal reactors. The present study offers a simple and non-destructive technique for quick estimation of isotopic composition of plutonium obtained from thermal reactors. It should, however, be mentioned that correlations have to be established for Pu obtained from different reactor systems. A prerequisite is the knowledge of total Pu content, which can easily be estimated by established electrochemical techniques.38

Table 3. Change in Pu isotopic composition and %Eff 240Pu with time

Time, year 241Pu, % Pu, % 238Pu, % 239Pu, % 240Pu, % 242Pu, % %Eff 240Pu 0 2.617 100 0.089 75.361 21.051 0.886 22.76 1 2.494 99.88 0.089 75.453 21.077 0.887 22.79 2 2.377 99.76 0.089 75.541 21.102 0.888 22.82 3 2.265 99.65 0.089 75.626 21.125 0.889 22.84 4 2.159 99.54 0.089 75.707 21.148 0.890 22.87 5 2.057 99.44 0.090 75.784 21.169 0.891 22.89 6 1.961 99.34 0.090 75.858 21.190 0.892 22.92 7 1.868 99.25 0.090 75.928 21.210 0.893 22.94 8 1.781 99.16 0.090 75.996 21.229 0.893 22.96 9 1.697 99.08 0.090 76.060 21.246 0.894 22.98

10 1.617 99.00 0.090 76.121 21.264 0.895 22.99

Table 4. Plutonium isotopic composition at various burnup levels in PWR employing plutonium based fuel15

Burn up, MWd/t 238Pu, % 239Pu, % 240Pu, % 241Pu, % 242Pu, % %Eff 240Pu – 0.018 91.3 7.870 0.790 0.041 7.983 – 0 88.2 10.300 1.300 0.2 10.638

12950 0.129 77.806 17.152 4.52 0.393 18.130 19350 0.15 72.263 21.472 5.474 0.641 22.920 27900 0.294 68.091 22.669 7.891 1.056 25.168 25700 0.309 64.944 25.148 8.336 1.263 28.033 33050 0.318 61.051 28.503 8.537 1.591 31.965 33500 0.431 59.793 27.745 10.160 1.871 31.954 36350 0.455 49.518 36.712 10.366 2.948 42.800 43950 0.661 41.162 40.852 12.592 4.733 50.457


145

Fig. 3a, 3b, 3c, 3d. Correlation graphs for Pu from PWR

Table 5. Plutonium isotopic composition for Yankee Rowe core VII38

Batch No. Initial 235U, % 238Pu, % 239Pu, % 240Pu, % 241Pu, % 242Pu, % %Eff 240Pu 12 4.935 0.888 74.649 11.022 9.094 1.346 15.455 11 4.935 0.916 73.949 14.309 9.397 1.43 18.952

9 4.935 0.945 73.74 14.369 9.486 1.46 19.133 10 4.935 0.938 73.757 14.343 9.505 1.46 19.090

1 4.935 0.905 73.979 14.286 9.413 1.417 18.880 8 4.935 1.063 72.505 14.777 10.01 1.646 20.142 2 4.935 1.101 71.938 15.023 10.19 1.745 20.647 4 4.935 1.142 71.504 15.162 10.39 1.803 20.984 3 4.935 1.17 71.24 15.253 10.49 1.846 21.216 6 4.935 1.288 70.487 15.512 10.71 2.005 22.030 5 4.935 1.371 69.794 15.755 10.96 2.12 22.669 7 4.935 1.477 69.385 15.833 11.11 2.223 23.179


146

Fig. 4a, 4b, 4c, 4d. Correlation graphs for Pu from PWR from Yankee Rowe core VII

Table 6. Correlation coefficients, slope, intercept for various Pu isotopes for different reactors

Isotope Slope, intercept, coefficients Indian PHWR

Natural U PWR (BR3 Reactor)

Mixed U and Pu (MOX) Yankee Rowe core VII

Enriched 235U (4.935%) Slope –0.966 –1.119 –1.100 Intercept 97.533 96.981 94.718

239Pu

Correlation coefficient 0.9984 0.9971 0.9985 Slope 0.741 4.251 0.380 Intercept 4.082 0.741 7.117

240Pu

Correlation coefficient 0.9977 0.9978 0.9965 Slope 0.136 0.131 0.1866 Intercept 2.171 –2.309 2.108

242Pu

Correlation coefficient 0.9630 0.9816 0.9999 Slope 0.011 0.012 0.056 Intercept 0.158 –0.144 0.727

238Pu

Correlation coefficient 0.9798 0.9544 0.9580

Conclusions

A non-destructive method based on isotopic correlation technique (ICT) has been developed for the estimation of isotopic composition of plutonium obtained from thermal reactors. Correlations between %Eff 240Pu and various plutonium isotopes formed in thermal reactors were derived and verified

experimentally. Neutron coincidence counter was employed for the determination of %Eff 240Pu content of plutonium samples. The observed graphs between various plutonium isotopes and %Eff 240Pu were highly linear as predicted theoretically. The ICT holds good for enriched uranium and MOX (mixed uranium-plutonium oxide) fuelled thermal reactors also, only the values of the coefficients (slope, intercept) vary. The present ICT


147

method offers a non-destructive, rapid alternative and can be applied at various stages of nuclear fuel cycle. The method is applicable to large size samples and finished products of known Pu amount. In MOX fuel production for it can be applied to verify and confirm the fissile content (239Pu+241Pu) specifications. The correlations were found linear upto burnup levels of 43950 MWd/t.

*

Authors are thankful to H. S. KAMATH, Director, Nuclear Fuels Group for his continuous support, to Dr. V. VENUGOPAL, Director, Radiochemistry and Isotope Group for his keen interest and active support during the course of this work. Special thanks are due to Dr. V. K. BHARGAVA for his valuable discussions and guidance.

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3. R. BERG, Verification of Reprocessing Plant Input and Output Analysis, Proc. Symp. on Nuclear Safeguards Technology, IAEA-SM-231/16, 1978.

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5. M. BENEDICT, T. H. PIGFORD, H. W. LEVI, Nuclear Chemical Engineering, 2 nd ed., McGraw-Hill Book Co., NewYork, 1981.

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8. R. GUNNINK, Nucl. Mater. Managem., 9(2) (1980) 83. 9. J. C. LEE, SIN TAO HSUE, Nucl. Technol., 76 (1987) 203. 10. K. LASSMANN, C. T. WALKER, J. VAN DE LAAR, J. Nucl. Mater.,

255 (1998) 222. 11. K. LASSMANN, J. Nucl. Mater., 188 (1992) 295. 12. K. LASSMANN, C. O. CARROLL, J. VAN DE LAAR, C. T. WARKER,

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1977. 20. C. V. STRAIN, NRL Memorandum Report, 2127, May 1970. 21. K. BÖHNEL, KFK 2203, 1975 and AWRE Translation No. 70

(54/4252), 1978. 22. M. S. KRICK, M. L. EVANS, N. ENSSLIN, C. HATCHER,

H. O. MENLOVE, J. L. SAPIR, J. E. SWANSEN, Proc. of IAEA Symp. on Nuclear Safeguards Technology, IAEA-SM-231/50, 1978.

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(2000) 39. 32. J. E. SWANSEN, P. R. COLLINSWORTH, M. S. KRICK, Nucl. Instr.

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Symp. on Nuclear Safeguard Technology, IAEA-SM-231/129, 1978.

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148

Annex-I

Formation of 238Pu in thermal reactors

As discussed in the section “Introduction”, in nuclear reactor the 238Pu can be formed as indicated in Eqs (2) and (3). Based on these nuclear reactions, the balance equations for 238Pu formation are as follows:

For first reaction the equations are:

NφσNφσtN

c48

483737

48

dd

−= (a1)

NφσNφσtN

nn37

372828

),2(

37

dd

−= (a2)

For second reaction the equations are:

Nφ σNφσtN

c48

483737

48

dd

−= (a3)

NφσNφσtN

C37

372626

37

dd

−= (a4)

NφσNφσtN

c26

262525

26

dd

−= (a5)

The overall rate of formation of 238Pu is given by:

NφσNφσσNφσNφσσNφσt cnncc

4848

3737

372828)2,(

2626

26252548

2 )2(2 )(d

Nd−−++−+= (a6)

For simplification, neglecting the amount of intermediates viz. 236U and 237Np, Eq. (a6) can be written as:

NφσNφσNφσtN

nnc48

4828282525

482

dd

),2(−+= (a7)

In reactor, the rate of depletion of 235U and 238U could be expressed by the expressions:

NφσtN 25

2525

dd −= (a8.1)

NφσtN 28

2828

d

d −= (a8.2)

From Eqs (a8.1) and (a8.2) the amount at time t, can be obtained by integrating within limit at t = 0, 25N = 25N0 and 28N = 28N0 and at time t, N25 and N28:

φ tσeNN 2502525 −= (a8.3)

φ tσeNN 0

2828 28−= (a8.4)

where superscript ‘0’ refers to initial composition. Substituting the values of 25N and 28N from Eqs (a8.3) and (a8.4) into Eq. (a7) and on rearranging, we get:

φ tσnn

φ tσc eNσeNφσNφσ

tN

02828

)2,(

0252548

48

482825 φ 2

dd −− +=+ (a9)

Recalling that solution of the differential equation of type:

)()( dd xQxy p

xy =+ (a10)

is

CxexQy e xxpxxp +∫⋅=∫ ∫ d)( d )(d )( (a11)

Equation (a9) can be solved to:

( ) Ctφ tσeeNφσeNφσφ tσeN φφ σnn

φφ σc ++= ∫ −− d 2 2 48

02828

)2,(025254848 2825 (a12)

where x = t, y = 48N, p(x) = 2σ48ϕ and

Q(x)= t σnn

t σc eNσeNφ σ ϕ−ϕ−

ϕ+ 2825 02828

)2,(02525


149

which on expansion and integration gives:

( ) ( ) Ceφσσ

Nφσe

ΦσσNφσφ tσeN φ tσσnn,φ tσσc +⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛

−+

−= −−

2

2 2 )(2

2848

02828

)2()2(

2548

02525

4848 28482548 (a13)

The equation can be simplified by substituting

A48 = ( )2548

02525

-2

σσNσ c

and B48 = ( )2848

02828

)2,(

2 σσ

Nσ nn

−

The value of C can be evaluated by substituting the limits, time t = 0, N48 = 0, in Eq. (a12). Then C = A48+B48. The expression for 48N can be obtained as:

t σt σtσ eBAeBeAN ϕ−ϕ−ϕ− ++⋅+⋅= 482825 248484848

48 )( (a14)

Annex-2

Expression for 239Pu percentage in terms of %Eff 240Pu

According to DE REGGE and BODEN the formation of 239Pu in thermal reactor can be expressed by the following equation:

)()(49 49 4928 49

φ tσφ tσ eBeAN −− += (b1)

Substituting ϕt = θ into Eq. (b1), expanding the exponential terms, recalling the Maclaurin series for the exponential function [Eq. (7.2)] and neglecting square and higher powers in the expansion, then:

49N = A49 (1–σ28 θ)+B49 (1–σ49 θ) (b2)

Substituting θ )(

x

xB

XA −= into Eq. (b2), 49N can be expressed as:

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ −−+

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ −−=

x

x

x

xB

XAσBB

XAσAN 49492849 1149 (b3)

which can be rearranged to Eq. (b4) as:

XB

σBσABσABB

σAANxx

xx

x ⎥⎦

⎤⎢⎣

⎡ ++⎥

⎦

⎤⎢⎣

⎡+=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

−⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

−)( 49492849

149149492849 (b4)

Hence, the 49N can be expressed as:

XN 494949 βα += (b5)

where ⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

x

x

x

xB

ABB

AA 4949

284949 11 σσα (b6)

.)( 4949284949

xBBA σσβ +

= (b7)

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Estimation of isotopic composition of plutonium from thermal reactors by neutron coincidence counting through isotopic correlation technique