Applying Advanced Neutron Transport Calculations

Proceedings of Top Fuel 2009 Paris, France, September 6-10, 2009 Paper 2173

Applying Advanced Neutron Transport Calculations for Improving Fuel Performance Codes

P. Botazzolia*, L. Luzzia, A. Schubertb, P. Van Uffelenb, W. Haeckc Politecnico di Milano, Department of Energy, Nuclear Engineering Division (CeSNEF) via Ponzio 34/3, I-20133 Milano, Italy b European Commission, Joint Research Centre, Institute for Transuranium Elements Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany c Institute de Radioprotection et de Sûreté Nucléaire avenue de la Division Leclerc 31, F-92260 Fontenay-aux-Roses, France *Corresponding author. Tel: +39 02 2399 6333, Email: [email protected]

a

Abstract – We present refinements of the Helium production model implemented in the TRANSURANUS fuel performance code. Helium is produced in oxide fuels by three main paths: (i) alpha decay of the actinides; (ii) (n,α) reactions; and (iii) ternary fission. In this work, the contributions due to ternary fission and the 16O(n,α)13C reaction as well as some refinements in the 241Am burn-up chain have been included in TRANSURANUS. The 16O(n,α)13C cross section has been evaluated in PWR conditions by means of the MCNP Monte Carlo code for different fuel compositions. The Monte Carlo depletion code VESTA has been used for the validation of the Helium production model. For specific PWR conditions the comparison of TRANSURANUS predictions with those of VESTA is satisfactory, and the applied cross section library is the main source of uncertainty.

I. INTRODUCTION

contribution of the Helium released plays a fundamental role in the gap pressure and subsequently in the mechanical behaviour of the fuel rod6-8, in particular during the storage of the high burn-up spent fuel.

TRANSURANUS1 is a computer code simulating the thermo-mechanical behaviour of a single fuel rod in nuclear reactors. As part of the code, the TUBRNP model2 calculates the local concentration of the actinides (U, Pu, Am, Cm), the main fission products (Xe, Kr, Cs and Nd) and 4He produced during the irradiation as a function of the radial position across a fuel pellet (radial profiles). These local quantities are required for the determination of the local power density, the local burn-up, and the source term of fission products and other inert gases. In previous works3,4 the Monte Carlo depletion code ALEPH5 has been used to validate the models for the actinides and fission products concentrations in UO2 fuels. A similar approach has been adopted in the present work for validating the Helium production.

The paper is organized as follows. In Section II the proposed model and the evaluation of the required parameters for different fuel compositions under PWR conditions are presented. In Section III the Monte Carlo depletion code VESTA9 has been used for the validation of the model by selecting two PWR fuel types (UO2 and MOX) and compositions. Firstly, the proposed model has been verified by considering the model parameters evaluated by VESTA. Secondly, a sensitivity analysis has been performed for MOX fuel in order to evaluate the impact of the model parameter uncertainties on the Helium production, and then the results obtained by the updated version of the TRANSURANUS code have been compared with the VESTA code. Finally, a preliminary evaluation of the impact that the released Helium has on the fuel rod pressure has been carried out by conservatively considering a 50% release of Helium7,8. In the last section the main conclusions are summarized.

The present paper focuses on modelling of the Helium production in PWR oxide fuels (MOX and UO2). A reliable prediction of the Helium production and release in LWR oxide fuels is of great interest in view of increasing burnup, linear heat generation rates and Plutonium content. The

213


0.6

II.A. Model Description

0.5

Cross section [barn]

II. HELIUM PRODUCTION MODEL

Helium is produced in oxide fuels by three main paths: (i) alpha decay of the actinides (the main contribution is due to 242Cm, 238Pu and 244Cm); (ii) (n,α) reactions (the main contribution is due to 16O(n,α)13C); and (iii) ternary fission. In the present work, the contributions due to ternary fission and the (n,α) reaction on 16O as well as some refinements in the 241Am burn-up chain have been included in TUBRNP.

0.4 0.3 0.2 0.1 0 0

The local Helium build-up in an oxide fuel is described by the following ordinary differential equation:

dN He − 4 = + N Cm − 242 ⋅ λCm − 242 + N Cm − 244 ⋅ λCm − 244 + dt q ′′′ + N Pu − 238 ⋅ λ Pu − 238 + ⋅ y TF + E fiss

ENDF/B VII.0 JEFF 3.1 ≡ ENDF/B VI.8 JENDL 3.3

2

4

6 Energy [MeV] 16

8

10

13

Fig. 1. Comparison between O(n,α) C cross sections from different libraries. In addition to ENDF/B VII.0 and JEFF 3.1, the JENDL 3.314 library is also shown.

In order to choose the correct one-group effective cross section for the model, the energy distribution of the neutrons in the fuel (neutron spectrum) has to be computed. To this end, the neutron transport problem has been solved by means of the MCNP Monte Carlo code15 adopting the JEFF 3.1 cross section library. In particular, to simulate the conditions of a typical PWR, an infinite series of cells containing water and a pin with a fuel diameter of 8.2 mm, a Zircaloy cladding outer diameter of 9.4 mm and a pin pitch of 12.55 mm has been computed. UO2 fuels with an enrichment from 2% to 5% and different MOX compositions with Plutonium content from 3% to 8% have been considered. The computed spectra have been averaged adopting the 16O(n,α)13C cross section of both the JEFF 3.1 and the more recent ENDF/B VII.0 libraries, in order to find the required effective cross sections. Between the two libraries, a discrepancy of about 40% has been found for all the fuel compositions. The results are reported in Fig. 2 and Fig. 3, and a trend can be seen as function of the 235U enrichment and Plutonium content. Because of the high uncertainty related to the cross section library, and because a different geometry can lead to a difference of few percent, an average value of 3.2·10-3 barn for MOX fuel and an average value of 2.5·10-3 barn for UO2 fuel have been considered. They arise from integrating the spectra with the ENDF/B VII.0 16O(n,α)13C cross section.

(1)

+ σ α ,O −16 ⋅ Φ ⋅ N O −16 where N represents the atom concentrations (at/cm3), λ the decay constants (h-1), q''' the local power density (MW/cm3), Efiss the average energy per fission (MWh), yTF the ternary fission yield, σα,O-16 the one-group 16O(n,α)13C effective cross section (cm2) and Φ the total neutron flux (n/cm2h). II.B. Evaluation of the Model Parameters A correct evaluation of the 242Cm, 244Cm and 238Pu concentrations, the ternary fission yield, the one-group effective 16O(n,α)13C cross section and the neutron flux are necessary for a correct prediction of the Helium build-up. A precise modelling of the ternary fission yield should consider the neutron spectrum and the fissile isotope concentrations. Nevertheless, the value of 0.22% proposed in Ref. 8 has been applied, because (i) the values for different fissile isotopes and different incident neutron energies are all in the range 0.15÷0.25 %10,11, and (ii) this contribution has a low influence on the total amount of Helium produced (as will be shown in Section III.D).

A second issue in the 16O(n,α)13C contribution concerns the concentration of 16O as a function of time, which should be considered for the solution of Eq. (1). Because this concentration is not computed by TUBRNP, the initial concentration is always considered. In order to confirm the negligibility of the oxygen consumption, the following set of ordinary differential equations has been solved:

The 16O(n,α)13C reaction is a threshold process, as can be seen in Fig. 1, where the corresponding cross sections from different libraries are shown. While a difference of approximately 30% can be noticed between the cross sections in the JEFF 3.112 and the ENDF/B VII.013 nuclear data libraries, the more recent ENDF/B VII.0 library is preferred8.

214


3.8E-03

1

3.2E-03 JEFF 3.1 ENDF/B VII.0

Error [%]


10

0.1

2.6E-03 0.01

2.0E-03

0.001 1

2

3

4

5

6

1

Enrichment [at%]

100

1000

Time [year]

Fig. 2. Computed 16O(n,α)13C cross sections as a function of the 235U enrichment (UO2 fuel).

Fig. 4. Error of the approximate solution (neglecting the oxygen consumption) with respect to the exact solution (Eq. (3)) as a function of time under constant conditions.

4.7E-03


10

expressed by Eq. (3) is shown as a function of time. For the time scale of interest (less than 10 years) the discrepancy between the two approaches is negligible.

4.2E-03

Concerning the contribution due to the α decay of the actinides, a correct evaluation of 242Cm, 244Cm and 238Pu concentrations requires a complete evaluation of the burnup chains. For this purpose, the following branching ratios have been included in the TUBRNP burn-up chain:

○ JEFF3.1

3.7E-03

□ ENDF\B VII.0

3.2E-03

2.7E-03 2.5

4.5

6.5

8.5

•

The branching ratio for the reaction (20%16).

•

The branching ratio for the 242Am decay due to electron capture (17.3%17), leading to 242Pu.

Plutonium content [at%]

Fig. 3. Computed 16O(n,α)13C cross sections as a function of the Plutonium content (MOX fuel).

241

Am(n,γ)242mAm

If these branching ratios are neglected, the concentrations of 242Cm and of the produced Helium will be overestimated (see Section III.C).

 dN O −16 = −σ abs,O −16 ⋅ N O −16 ⋅ Φ  dt  dN He − 4  = σ α ,O −16 ⋅ N O −16 ⋅ Φ  dt

(2)

III. RESULTS AND DISCUSSION III.A. The VESTA Code

where σabs,O-16 is the O one-group total absorption effective cross section (cm2). 16

The Monte Carlo depletion code VESTA9 has been used for the validation of the Helium production model. The generic VESTA Monte Carlo depletion interface developed at IRSN (Institute de Radioprotection et de Sûreté Nucléaire) allows us to couple different Monte Carlo codes with a depletion module. It currently allows combining the ORIGEN 2.2 isotope depletion code18 with any version of MCNP15 or MCNPX19 for reaction rate calculation. By means of the multi-group binning approach5 implemented into VESTA, the speed and accuracy of any burn-up and activation calculation have been drastically improved.

Assuming constant neutron flux and constant cross sections, the set of Eq. (2) can be solved analytically:

N He − 4 (t ) = N O −16 (0) ⋅

(

σ α ,O −16 −σ ⋅ 1− e σ abs,O −16

abs ,O −16

⋅Φ ⋅t

)

(3)

For estimating the impact of using a constant oxygen concentration, a conservative value of 5·10-3 barns for both cross sections has been implemented in Eq. (3). Furthermore, a constant flux of 5·1014 n/(cm2s) has been considered. In Fig. 4 the error between the solution obtained neglecting the oxygen consumption and that one

215

5.5E+14

40

VESTA Case 1 TU formula - original

30

Flux [n/(cm2·s)]

Linear Heat Generation Rate [kW/m]


20

TU formula - more nuclides

4.5E+14

TU formula - best fit

3.5E+14

10

0 0

1500

3000 Time [day]

4500

6000

III.B. The Simulated Power History

dn fiss

Typical PWR conditions (geometry and materials) have been considered for the VESTA code simulations and two fuel compositions have been selected: UO2 with an initial enrichment of 3.5% and MOX with an initial Pu content of 5.6%. In Fig. 5 the simulated power history is shown, reaching a burn-up of about 100 MWd/kgHM. For both initial compositions four simulations have been run with different libraries, namely: (i) JEFF 3.1 cross section library plus the ORIGEN fission yield database (case 1); (ii) JEFF 3.1 for both the cross sections and the fission yields (case 2); (iii) ENDF/B VII.0 cross section library plus the ORIGEN fission yield database (case 3); and (iv) ENDF/B VII.0 for both the cross sections and the fission yields (case 4).

dt

•

concentrations of the main isotopes as a function of time;

•

one-group cross sections of the most relevant reactions as a function of time.

1500

3000 Time [day]

4500

6000

= Φ ⋅ ∑ N i ⋅ σ i fiss → Φ = i

dn fiss dt

∑N

i

⋅ σ i fiss

(4)

i

In a time step ∆t, the fluence is approximated by:

∆n fiss

∫ Φ ⋅ dt ≅ Φ ⋅ ∆t = ∑ N i

i

⋅σ i

fiss

∝

ρ ⋅ ∆bu E fiss

∑N

i

⋅ σ i fiss

(5)

i

where nfiss represents the number of fissions (fissions/cm3), Φ the total neutron flux (n/cm2s), Ni the concentration of the i-th nuclide (at/cm3), σifiss the one-group fission cross section of the i-th nuclide (cm2), bu the burn-up (MWd/tHM), ρ the density (g/cm3) and Efiss the energy released per fission (MeV). For more details, see Ref. 2. The TRANSURANUS formula has been independently evaluated considering the fission cross sections and the isotope concentrations computed by VESTA. The results are shown in Fig. 6 for the MOX case 1. This graph is qualitatively representative of all simulated cases. The green line represents the neutron flux computed by the VESTA code, while the red squares are the results obtained using the TRANSURANUS formula: an overestimation can be seen that increases as a function of time. The increasing overestimation can be explained by the fact that the TRANSURANUS formula considers only the main fissile and fissionable isotopes. By including the minor actinide isotopes in the denominator of Eq. (5) (at high burn-up the most important are 245Cm and 242mAm due to their high fission cross sections), this overestimation disappears (purple circles). In order to explain the remaining overestimation, the energy released per fission has been modified in order to fit the VESTA results (black triangles).

The evaluated quantities are: neutron flux as a function of time;

0

Fig. 6. Comparison between the flux computed by VESTA and the results obtained by means of the TRANSURANUS (TU) formula.

Fig. 5. Simulated power history.

•

2.5E+14

These quantities have been compared with the results obtained by means of the TRANSURANUS code (version v1m4j08). III.C. Model Verification Before making a blind comparison of results in terms of isotope concentrations, the models implemented in TRANSURANUS have been verified. As a first step, the neutron flux computed by VESTA has been compared with the model implemented in the TRANSURANUS code. This model approximates the fluence by considering the following concept:

As a second step, in order to check the TRANSURANUS burn-up chains, the case-specific fission and capture cross

216


2.0E-04

VESTA Case 1 TU best fit TU best fit, without B.R.

7.5E-06

VESTA Case 1 TU best fit TU best fit, without B.R.

Concentration[at/(cm·barn)]

Concentration[at/(cm·barn)]

1.0E-05

5.0E-06

2.5E-06

0.0E+00

1.5E-04 Pu-242 1.0E-04 Pu-238 5.0E-05

0.0E+00 0

1500

3000 Time [day]

4500

6000

0

1500

3000 Time [day]

4500

6000

Fig. 7. Comparison between the 242Cm concentration computed by TRANSURANUS (TU best fit version) and by VESTA (MOX case 1).

Fig. 8. Comparison between the 238Pu and 242Pu concentrations computed by TRANSURANUS (TU best fit version) and by VESTA (MOX case 1).

sections computed by VESTA have been fitted as a function of the burn-up and implemented in a test version of the TRANSURANUS code (referred to as TU best fit in the graphs). Furthermore, the flux computation that fitted better to the VESTA results (black triangles in Fig. 6) has been implemented in this version of the code. The comparison of the main isotope concentrations computed by VESTA and the results obtained by means of TRANSURANUS is satisfactory for all the cases. In Fig. 7 and Fig. 8 a comparison of the results neglecting or considering the branching ratios (see Section II.B) is shown for the MOX case 1. A good agreement can be noticed when the branching ratios (B.R.) are considered, while

neglecting them leads to an overestimation of 242Cm, 238Pu and to a slight underestimation of 242Pu. This can be explained by the fact that if we include the branching ratio for the reaction 241Am(n,γ)242mAm, less 242Am is produced. Since 242Am β decays to 242Cm, less 242Cm is produced, as well as 238Pu (that results from the α decay of 242Cm). Concerning the branching ratio for the 242Am decay by electron capture (leading to 242Pu), this path further decreases the production of 242Cm and enhances the 242Pu build-up. If 242 Cm, 244Cm and 238Pu are not well predicted, Helium production cannot be correctly evaluated − see Eq. (1). The same conclusions can be drawn also for the other cases.

1.2E-05

1.0E-04

VESTA Case 1 - MOX

8.0E-06

TU best fit (Case 1) - MOX

8.0E-05

Concentration [at/(cm·barn)]

MOX

4.0E-06 TU best fit (Case 1), without T.F. - MOX

0.0E+00 0

6.0E-05

250

500

750

1000 TU best fit (Case 1), without B.R. - MOX

UO2 VESTA Case 2 - UO2

4.0E-05

TU best fit (Case 2) - UO2

2.0E-05 VESTA Case 4 - UO2

TU best fit (Case 4), without T.F. - UO2

0.0E+00 0

1000

2000

3000

4000

5000

6000

Time [day]

Fig. 9. Helium production computed by TRANSURANUS (TU best fit version) and by VESTA. Red symbols and lines correspond to the UO2 cases, while black symbols and lines correspond to the MOX simulations.

217


Fig. 9 shows the comparison of produced Helium for the MOX case 1 (JEFF 3.1+ORIGEN) and UO2 cases 2 (JEFF 3.1) and 4 (ENDF/B VII.0). Case 3 is very similar to case 4 and therefore not shown. The symbols mark the VESTA results, while the TRANSURANUS results are indicated by lines. Concerning the MOX case 1 and the UO2 case 4 good agreement can be found when neglecting the ternary fission (T.F.), while for the UO2 case 2 the agreement is good if the ternary fission contribution is considered. This is explained by the fact that the ORIGEN 2.2 fission yield database as well as the ENDF/B VII.0 library does not include the ternary fission yield, which is taken into account by JEFF 3.1. Furthermore, the effect of the branching ratios is shown for the MOX case: an overestimation occurs when they are neglected, due to the already explained overestimation of 242 Cm and 238Pu. This overestimation is more significant for MOX, where the α-decay contribution is more important (due to the initial content of Plutonium that produces more Cm isotopes by neutron capture).

parameters. In Table I the orthogonal array applied for the present case is shown. Nine simulations have been performed instead of 34 (=81) that would be necessary for a full factorial method. The three levels have been assigned as follows: •

For the neutron flux, the original TRANSURANUS formula (level 1 – red squares in Fig. 6), the formula including more nuclides (level 2 – purple circles in Fig. 6) and the 'TU formula - best-fit' (level 3 – black triangles in Fig. 6) have been considered.

•

For the 16O(n,α)13C cross section, values of 3·10-3 (level 1), 4·10-3 (level 2) and 4.5·10-3 (level 3) barn have been tested; level 1 and level 3 correspond to the minimum and the maximum values found by means of MCNP with different MOX compositions and cross section libraries (see Fig. 3).

•

For the ternary fission yield, the values of 0.18%, 0.2% and 0.22% have been chosen as level 1, 2 and 3, respectively.

•

Finally, for the capture and fission cross sections required by TRANSURANUS, the following levels have been set: the cross sections obtained with the VESTA cases 2 and 4 have been averaged as a function of the burn-up and implemented in TRANSURANUS (they correspond to the level 3 and 1, respectively), while the original dataset of TRANSURANUS has been used as level 2.

Two conclusions can be drawn: •

The set of equations implemented in the TRANSURANUS code correctly predicts the isotope concentrations, hence the considered isotopes are sufficient.

•

When considering Neutron Transport codes: (i) the adopted cross section libraries play a fundamental role, as can be clearly noticed from the UO2 cases 2 and 4 shown in Fig. 9; (ii) fission yield databases do not always include the ternary fission yields (in these cases the Helium production is under-predicted).

TABLE I Simulations setting in accordance with the Taguchi method

III.D. Sensitivity Analysis Run

As a further step for the assessment of the Helium production model, a sensitivity analysis has been performed for the considered MOX fuel by means of the Taguchi method (for further details about the method, see Refs. 20 and 21). In particular, the influence of four different input parameters on the calculated production of Helium has been analyzed: (i) the neutron flux; (ii) the 16O(n,α)13C cross section; (iii) the ternary fission yield; and (iv) the capture and fission cross sections from different libraries.

1 2 3 4 5 6 7 8 9

Flux model 1 1 1 2 2 2 3 3 3

σα,O-16 1 2 3 1 2 3 1 2 3

Levels Ternary fission yield 1 2 3 2 3 1 3 1 2

Cross sections library/dataset 1 2 3 3 1 2 2 3 1

Fig. 10 shows the influence that the different parameters have on the Helium production at a burn-up of 60 MWd/kgHM (red lines) and at the end of the simulated power history (about 100 MWd/kgHM – black lines). Results are normalized to the average value of the nine simulations. It is possible to notice that the most relevant parameter is the 16O(n,α)13C cross section: it has an influence of about ±5% at 60 MWd/kgHM. It is slightly lower at the

For evaluating the impact of the input parameters, the Taguchi method uses a special set of orthogonal arrays. These arrays stipulate the way of conducting the minimal number of simulations, which could give the full information of all the factors affecting the output parameter (in our case the Helium produced). In particular, three representative values (levels) have been adopted for the four selected input

218


Ternary fission yield

Normalized He production [// ]

1.05

Cross sections library

1

1.0E-05


σα,O-16

Flux model

1.15 1.1

0.95

1.05

0.9

1

0.85

0.95

TRANSURANUS - UO2 VESTA Case 2 - UO2 VESTA Case 3 - UO2 TRANSURANUS - MOX VESTA Case 2 - MOX VESTA Case 3 - MOX

8.0E-06 6.0E-06 4.0E-06 2.0E-06 0.0E+00

0.8

0

0.9 0

1

2

3

4

1

2

3 8 1 Levels

2

3 12

1

2

3 16

5

10 15 20 Burn-up [MWd/kgHM]

25

30

Fig. 11. Comparison between the produced He computed by TRANSURANUS and by VESTA up to 30 MWd/kgHM.

Fig. 10. Influence of the parameters on the Helium produced at 60 MWd/kgHM (red lines and right axis) and at the end of life (black lines and left axis).

Based on this sensitivity analysis, the following values/modifications have been implemented in the release of the TRANSURANUS code (see Section II.B):

end of the irradiation when the contribution from the α decay is important (it increases exponentially as a function of the burn-up). The cross section library gives an uncertainty of about ±2÷3%: it increases as a function of the burn-up because the importance of the α decay contribution increases with burn-up. The choices of the flux model and of the ternary fission yield influence the Helium production by about ±1%. The influence of the different parameters on the Helium production at burn-up of 5 and 10 MWd/kgHM (not shown) has also been analyzed, finding that the most influencing parameters are the 16O(n,α)13C cross section and the ternary fission yield (they have an influence of ±10÷12% and about ±3%, respectively), whereas the choices of the flux model and of the cross section library influence the Helium production by about ±1%. At such low burn-up the contribution due to the α decay is negligible, hence the flux model and the cross section libraries have no influence, and the effects of the 16O(n,α)13C cross section and of the ternary fission yield dominate.

•

Ternary fission yield: 0.22%.

•

16

•

O(n,α)13C cross section: 3.2·10-3 barn (MOX); 2.5·10-3 barn (UO2). For completeness, the concentrations of 238Pu, Am, 243Am, 244Cm and 245Cm have been included in the formula for the flux computation.

241

III.E. Helium Production − Comparison between TRANSURANUS and VESTA Results The MOX and UO2 cases have been simulated by means of the updated version of the code and the results in terms of Helium production are shown in Fig. 11 (up to 30 MWd/kgHM) and Fig. 12 (complete simulation up to 100 MWd/kgHM). All results lie between the two extreme cases computed by VESTA (cases 2 and 3). This is in accordance with the fact that: (i) the 16O(n,α)13C cross section implemented in TRANSURANUS has been evaluated on the basis of the ENDF/B VII.0 library (the same used for the case 3), which is about 40% lower than that one of JEFF 3.1 (used in the case 2); (ii) the case 3 does not consider the ternary fission contribution. For UO2, the contribution due to the α decay tends to be slightly overestimated at high burn-up (due to a difference in the cross sections) and the Helium computed by TRANSURANUS reaches the value computed with the VESTA case 2 at the end of life.

The most important conclusions of the sensitivity analysis are: (i) the cross section dataset and the TRANSURANUS formula for the flux computation already implemented in the code are sufficient to describe the Helium production − the discrepancy at the end of life (at a very high burn-up of 100 MWd/kgHM) is of minor importance; (ii) a ternary fission yield of 0.22% independent of the fuel composition can be used because its influence on the total Helium is low (a maximum of ±3%, when the burn-up is low and hence the production of Helium is negligible); (iii) the 16O(n,α)13C cross section is the most influencing parameter, and the value arising from the ENDF/B VII.0 library has to be considered the most reliable, based on the most recent measurements.

In summary, the TRANSURANUS fuel performance code satisfactorily agrees with the Monte Carlo depletion code VESTA for the UO2 and MOX cases under consideration.

219


1.0E-04 TRANSURANUS - UO2 VESTA Case 2 - UO2 VESTA Case 3 - UO2


8.0E-05

TRANSURANUS - MOX VESTA Case 2 - MOX

MOX

VESTA Case 3 - MOX

6.0E-05

4.0E-05

2.0E-05

UO2

0.0E+00 0

20

40

60

80

100

120

Burn-up [MWd/kgHM]

Fig. 12. Comparison between the produced He computed by TRANSURANUS and by VESTA.

particular, the 241Am(n,γ)242mAm reaction and the decay due to electron capture have been included.

III.F. Estimation of the Impact of the Helium Release on the Fuel Rod Pressure In the present paper we have not dealt with the issues related to the Helium release. Nonetheless, a preliminary evaluation of its impact on the fuel rod inner pressure has been carried out by considering a 50% Helium release. This value has been deduced from the analyses reported in Refs. 7 and 8. However, the pressure linearly depends on the number of moles and hence the actual pressure increase due to the Helium release can be estimated by multiplying the pressure increase due to the total Helium release by the fractional Helium release (the feedback of the small change of the fuel rod free volume can be neglected). By considering a typical fuel rod with an upper plenum of 25.4 cm, a fuel height of 336 cm and an initial pressure of 2.25 MPa, we have found a pressure increase due to Helium release of about 2 and 4 MPa at the end of the simulated power history (hot conditions – see Fig. 5) for the UO2 and MOX cases, respectively. These values correspond to 12% and 26% of the total fuel rod pressure. In conclusion, due to the high fractional releases of Helium, a pressure increase in the MPa range can be reached even after 40-60 MWd/kgHM.

242

Am

The required model parameters have been evaluated on the basis of information available in literature (ternary fission yield and branching ratios) and on the basis of MCNP simulations (16O(n,α)13C cross section). The models and the evaluated parameters have been validated on the basis of the Monte Carlo depletion code VESTA. A typical power history extended to a burn-up of 100 MWd/kgHM has been simulated for two selected PWR fuel compositions (MOX and UO2). Two main conclusions were drawn: (i) both the ENDF/B VII.0 library and the ORIGEN fission yield database do not consider the ternary fission yield, hence the evaluation of the produced Helium obtained by VESTA with the ENDF\B VII.0 library or with the ORIGEN fission yield database have to be corrected adding the ternary fission contribution; (ii) a relevant difference of the total Helium produced can be noticed according to whether the JEFF 3.1 (even when using the ORIGEN fission yield database) or the ENDF/B VII.0 library is adopted. This is mainly due to the differences in the 16 O(n,α)13C cross sections, emphasizing that this reaction is important. As a first step of the validation of the Helium production model, a satisfactory agreement between the flux computed by the TRANSURANUS formula and the values obtained directly by VESTA has been found. This agreement has been improved by including the concentrations of further fissile and fissionable nuclides, becoming important at high burn-up.

IV. CONCLUSIONS In the present work, the Helium production model of the TRANSURANUS fuel performance code has been extended for PWR conditions, by including the 16O(n,α)13C reaction and the ternary fission contributions and by refining the already implemented burn-up chain. In

220


The following conclusions can be drawn from the comparison of TRANSURANUS and VESTA simulations: •

•

The set of equations implemented in TUBRNP are sufficient to correctly describe the evolution of the nuclides that are relevant for power generation in UO2 and MOX fuels. By considering the set of data already present in the code (capture and fission cross sections), together with the new evaluated ones (ternary fission yield, 16O(n,α)13C cross section, branching ratios of the 241Am(n,γ)242mAm reaction and of the 242 Am decay due to electron capture), the agreement with Helium concentrations simulated by the VESTA code is very satisfactory.

4.

A. SCHUBERT, P. Van Uffelen, J. van de Laar, C. T. Walker and W. Haeck, "Extension of the TRANSURANUS burn-up model". J Nucl Mater, 376, 1–10 (2008).

5.

W. HAECK. and B. Verboomen, "An Optimum Approach to Monte Carlo Burn-Up". Nucl Sci Eng, 156, 180–196 (2007).

6.

K. KATSUYAMA, T. Mitsugi and T. Asaga, "Evaluation of helium gas release behavior in MOX fuel". Proc. of the 1998 ANS Winter Meeting, 115-116, Washington DC (1998).

7.

IS. KAMIMURA, Y. Kobayashi and T. Nomata, "Helium generation and release in MOX fuels". Proc. of the IAEA International Symposium in MOX fuel cycle technologies for medium and long term deployment, 263-270, Vienna (1999).

8.

E. FEDERICI, A. Courcelle, P. Blanpain and H. Cognon, "Helium production and behaviour in nuclear oxide fuels during irradiation in LWR". Proc. of the 2007 International LWR Fuel Performance Meeting, 664-673, San Francisco, California (2007).

9.

W. HAECK, "VESTA User’s Manual – Version 2.0.0", IRSN Report DSU/SEC/T-2008-33 (2009).

Finally, a rough estimation of the pressure increase due to the Helium release has pointed out the importance of this contribution to the fuel rod pressure at high burn-ups. In summary, the TRANSURANUS fuel performance code is able to satisfactorily predict the production of Helium of PWR MOX and UO2 fuels. However, experimental data are necessary to better assess the prediction capability of TRANSURANUS in terms of Helium production, and a model describing its release has to be developed for a more precise evaluation of the inner fuel rod pressure. ACKNOWLEDGMENTS

10. T. R. ENGLAND and B. F. Rider, "Evaluation and Compilation of Fission Yields", ENDF-349, LA-UR94-3106, Los Alamos (1994).

This work has been financially supported by the Institute for Transuranium Elements (European Commission, Joint Research Centre) and by the Politecnico di Milano (Ph.D. fellowship). The authors are grateful to Dr. Antonio Cammi and Mr. Vito Memoli (Politecnico di Milano) for the useful discussion in setting up the MCNP input files.

11. IAEA, "Compilation and evaluation of fission yield nuclear data", IAEA-TECDOC-1168, Vienna (2000). 12. OECD/NEA, "The JEFF-3.1 Nuclear Data Library – Jeff report 21", Technical Report ISBN 92-64-023143, NEA databank (2006).

REFERENCES 1.

K. LASSMANN, "TRANSURANUS: A fuel rod analysis code ready for use". J Nucl Mater, 188, 295– 302 (1992).

2.

K. LASSMANN, C. O’Carroll, J. van de Laar and C. T. Walker, "The radial distribution of Plutonium in high burn-up UO2 fuels". J Nucl Mater, 208, 223–231 (1994).

3.

W. HAECK, B. Verboomen, A. Schubert and P. Van Uffelen, "Application of EPMA Data for the Development of the Code Systems TRANSURANUS and ALEPH". Microsc Microanal, 13, 173–178 (2007).

13. "Evaluated Nuclear Data file ENDF/B-VII.0". Nucl Data Sheets, 107, 12, 2931–3118 (2006). 14. K. SHIBATA et al., "Japanese Evaluated Nuclear Data Library Version 3 Revision-3: JENDL-3.3". J Nucl Sci Technol, 39, 11, 1125–1136 (2002). 15. J. F. BRIESMEISTER, "MCNP − A General Monte CarloN-Particle Transport Code", Version 4C. LA13709-M. Los Alamos, NM: Los Alamos National Laboratory (2000).

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