EXTENSION OF THE TRANSURANUS BURN-UP MODEL FOR GD-DOPED UO2 FUEL IN WWER REACTORS

A. SCHUBERT1, CS. GYŐRI1, J. VAN DE LAAR1, P. VAN UFFELEN1,

S. BZNUNI2, T. SAFARYAN2

1European Commission, Joint Research Centre Institute for Transuranium Elements

P.O. Box 2340, D-76125 Karlsruhe, Germany

2Nuclear and Radiation Safety Centre of Armenian Nuclear Reg. Authority 4 Tigran Mets str.,Yerevan, 0010, Armenia

ABSTRACT Extensions of the TRANSURANUS burn-up model are reported for simulating Gd-doped UO2 fuel used in WWER reactors. To this end, neutron-transport calculations have been performed with the MONTEBURNS code for both UO2 and UO2-Gd2O3 fuel irradiated in a WWER 440 fuel assembly. After an earlier adaptation of the radial form factor for absorption of resonance neutrons in 238U and 240Pu, the one group effective cross sections for neutron absorption in the isotopes 155Gd and 157Gd have been refined. The impact of applying an additional form factor for neutron absorption on the Gd isotopes has been tested, too. A preliminary verification is based on a) a detailed comparison with the local concentrations of the Gd isotopes and the power form factor calculated by MONTEBURNS and b) central temperatures measured in commercial fuel during its irradiation in the OECD Halden reactor.

1. Introduction TRANSURANUS [1] is a computer code for the thermal and mechanical analysis of cylindrical fuel rods in nuclear reactors. As part of the code, the TUBRNP model [2] calculates the local concentrations of U, Pu and Nd 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. In view of the primary importance of the relative radial power profile for the thermal and mechanical analysis of nuclear fuel, priority is given to relative rather than to absolute concentrations. The latest status of the TUBRNP model is described in [3] and [4]. The latter describes the extension of the range of application for Gd-doped UO2 fuel used in the Heavy Water Reactor (HWR) at Halden, and for UO2 fuel used in Russian-type WWER reactors, making use of neutron transport calculations with the HELIOS and MONTEBURNS codes, respectively. The present paper pursues our work by refining the TUBRNP model for Gd-doped fuel used in WWER reactors. To this end, Gd-doped fuel rods in a WWER-440 assembly were simulated by neutron transport calculations and isotope depletion calculations for two different initial fuel compositions and two different neutron spectra. The calculated local concentrations of 155Gd and 157Gd were used to expand the formulation in TUBRNP.

2. Data for model development – neutron transport analyses In order to optimize the TUBRNP model for WWER fuel, three-dimensional Monte Carlo neutron transport calculations were carried out in combination with isotope depletion calculations in the MONTEBURNS code [5]. A symmetric model was set up comprising three Gd-doped WWER-440 fuel assemblies (Figure 1). Two assemblies were modeled with an averaged Gd concentration for all fuel rods while the third one (Figure 1, top) takes into account the detailed configuration of the fuel rods inside the assembly. For the latter case, two configurations (FA 1 and FA 2) were simulated, corresponding to WWER-440 assembly layouts designed for the Dukovany NPP (Figure 2, taken from [6]) with two different initial compositions. For evaluating the radial profiles across a Gd-doped fuel pellet, one rod next to the inner corner of the Gd-assembly (Figure 1, Gd-R) was simulated with 30 radial nodes of equal volume. Regarding the hardness of the neutron spectrum, two bounding irradiation conditions ('hard' and 'soft') were considered (Table 1). In this way four datasets were compiled for radial distributions of the isotopes 155Gd and 157Gd in UO2 fuel irradiated in a WWER-440 reactor. For each of these 4 simulations, 15 iteration steps were performed with an irradiation time interval of 20 days each. This approach leads to an average relative error of 0.08% for the calculated Keff at the end of each iteration. The ENDF-B-VI cross section library [7] was used for all simulations.

3. The TUBRNP model In the TUBRNP model the calculation of the radial power profiles is split into (a) the approximation of the neutron flux on the basis of thermal diffusion theory [2] and (b) the computation of the local concentrations of the relevant actinide isotopes with simplified depletion equations

− − −⎡ ⎤= −σ + σ ∗⎣ ⎦, , 1 1 1( ) ( ) ( ) ( ) ( ) ( )m a m m m c m m mdN r N r f r N r f r A dbu r (1)

where Nm(r) is the local concentration of the isotope m, ,a mσ and ,c mσ are the one-group effective cross-sections for total neutron absorption and neutron capture, respectively, dbu(r) is the local burn-up increment, and A is a conversion constant. The latest version of TUBRNP covers the isotopes 235U, 236U, 238U, 237Np, and 238-242Pu; a complete list of implemented equations can be found in ref. [3]. The form factor fm(r)

⎡ ⎤= + − −⎣ ⎦3

1 2( ) 1 exp ( )pm of r p p R r (2)

is applied for 238U and 240Pu and accounts for the radial dependence of absorption of resonance neutrons (where Ro is the fuel outer radius) . The parameters p1, p2, p3 were first evaluated for 238U by a careful comparison to experimental data of intermediate burn-up UO2 fuel [2] and afterwards estimated for 240Pu on the basis of resonance integrals and thermal capture cross sections [3]. A specific set of parameters has been recommended for WWER reactors [4]. A first version of TUBRNP for calculating the radial power profiles in Gd-doped UO2 fuel was developed in the late 90’s [8]. The present version is a straight-forward extension that applies the absorption term of eq. (1) for the depletion of 155Gd and 157Gd:

= −σ ∗,( ) ( ) ( ) ( )m a m m mdN r N r f r A dbu r (3)

The local burn-up increment dbu(r) is calculated using the diffusion approach of Lassmann et al. [2] where the macroscopic cross sections must include the local neutron absorption in 155Gd and 157Gd. It is well known that the application of diffusion theory has limits in presence of extreme neutron absorption (at the very beginning of the irradiation). As will be shown later, this approach is however justified because fuel temperatures in Gd-doped fuel at start-up are very low. The initial version of TUBRNP for Gd [8] made use of data from [9] for a first evaluation of the total and thermal effective neutron absorption cross sections of 155Gd and 157Gd. Its implementation in the TRANSURANUS fuel performance code however led to an under-estimation of fuel temperatures in the first phase of the irradiation prior to Gd "burn-out", i.e. below ~10 MWd/kgHM. These differences could be eliminated by applying directly radial power profiles from neutron transport calculations [10]. Following the standard isotope depletion approach for both isotopes 155Gd and 157Gd (eq. (3)) we re-visited the total effective neutron absorption cross sections applied in the TUBRNP model, ,155aσ and ,157aσ , and assumed a common factor [4]:

σ σ

= =σ σ

, , 155 , , 157

, 155 , 157 a th a th

a aR (4)

In view of the specific objectives of TUBRNP this approximation is justified thanks to the similar energy dependences of the total absorption cross sections of 155Gd and 157Gd. In this work the form factors f155(r) and f157(r) (for 155Gd and 157Gd, respectively) have been introduced in order to simulate the large local gradient in the concentrations that is gradually moving from the periphery to the centre of the fuel pellet. They have been approximated by an empirical function:

( )

( )( )

= ++ −

= + − +

=

( ) 11 exp ( )

with ( ) 50

155 ; 157

mm

m

m m o m

Cf rh r

h r A bu r R B bum

(5)

Here bu is the slice average burn-up, and R0 is the outer fuel radius (in mm), respectively, and A155, A157, B155, B157, C155, C157 are model parameters. Using the results of MONTEBURNS for the four available irradiation configurations (FA1 and FA2, combined with 'hard and 'soft' neutron spectrum, cf. Table 1) in a burn-up range up to ~ 3.5 MWd/kgHM, the Levenberg-Marquardt method [11] was applied in order to minimize the differences between the quantities calculated by HELIOS and TUBRNP: In this way, a total of nine parameters were optimized ( , 155a Gdσ , , 157a Gdσ , R, A155, A157, B155, B157, C155, C157 ). The optimized parameters are compiled in Table 2. Figure 3 and Figure 4 show satisfactory agreement of the local Gd concentrations calculated by MONTEBURNS and TUBRNP, and illustrate the impact of the present model extension. A comparison with the different MONTEBURNS simulations confirms that in the present approach it is sufficient to derive one set of model parameters for the four considered irradiation configurations. The differences between the TUBRNP calculations for FA1 and FA2 are hence negligible. A separate analysis of different burn-up intervals confirmed that a burn-up dependence of the effective cross sections does not improve the agreement between MONTEBURNS and TUBRNP models. For Gd-doped fuel irradiated in the Halden HWR (used for a earlier evaluation [4]), expression (5) has been fitted, too. While the radial nodalization of the available HELIOS simulations does not provide sufficient data points for optimizing nine parameters, both C155 and C157 have been fixed. Nevertheless in this case the application of the form factors f155(r) and f157(r) does not lead to an improved agreement with the neutron transport calculations performed by HELIOS (Figure 5). The effective cross sections derived for the current model differ only slightly from those evaluated in [4], and the parameters Am, Bm and Cm (Table 2) lead to form factors very close to 1.

4. Verification

Radial power profiles

The verification of TUBRNP on experimental data for Gd-doped fuel is complicated owing to the lack of microscopic measurements, e.g. radial profiles of the Gd isotopes. Publicly available data from post-irradiation examinations (PIE) of Gd-doped fuel, as compiled in the IFPE database [12], do not contain this type of measurements. Therefore as first step of verification a comparison is made to the radial power profiles simulated by the neutron transport calculations. Figure 6 and Figure 7 show radial power profiles calculated by both codes. The curves at very low burn-up reflect the intrinsic limitation of the diffusion theory applied in TUBRNP to strong absorbing media – in contrast to the transport theory applied in MONTEBURNS or HELIOS. The agreement between the simpler TUBRNP model and the neutron transport calculations is improving with the process of "burning out" the neutron-absorbing Gd isotopes.

Figure 6 confirms that the differences between the two WWER-440 configurations (FA1 and FA2), as well as between the two sets of spectrum conditions ('hard' and 'soft') have only an negligible impact on the radial power profiles simulated by MONTEBURNS. Both figures also confirm the "flattening" of the power profiles with decreasing Gd concentration and increasing burn-up. It is interesting to note that the previous version of TUBRNP already achieved fair agreement of the radial power profiles, i.e. the differences in the Gd isotope concentrations (Figure 3 and Figure 4) have only limited impact on the relative radial power distributions.

Fuel centre temperatures

As indirect verification on available experimental data, the central temperatures obtained on-line in the experimental reactor of the OECD Halden Reactor Project were used [4]. This is relevant because of the importance of temperature predictions on the fuel behavior. Figure 8 shows the comparison of the measured and calculated temperatures for one instrumented fuel rod with high initial Gd content (8 wt.%). As expected from the shape of the radial power profiles, there is no difference to the situation evaluated in [4]. After refinement of the effective cross sections the agreement is getting into the band of 100 K difference (Figure 8) and the remaining small systematic under-prediction of the measured fuel temperatures at very low burn-up can be attributed to the physical limitation of the diffusion approach under the condition of a very strong radial distortion of the neutron flux. However, in this irradiation phase the fuel centre temperatures are sufficiently low so that their safety-related impact is negligible compared to the standard UO2 fuel rods. It is important to note that the experimental verification for Gd-doped UO2 fuel is still limited to irradiation conditions of the Halden HWR. Nevertheless, the application of the present model to the different irradiation conditions in a WWER-440 fuel assembly indicates that – also for Gd-doped fuel irradiated in WWER or LWR – variations of the neutron spectrum from rod to rod have only a low impact on the relative radial power profiles.

5. Summary and conclusions For Gd-doped fuel used in WWER reactors we have for the first time performed a combination of neutron transport and isotope depletion calculations, using the MONTEBURNS code [5] with a radial nodalization across the fuel rod. Simulations have been made for two different initial fuel compositions and two different neutron spectra. Applying an extended formulation for the depletion of 155Gd and 157Gd in TUBRNP incl. two additional radial form factors, one set of parameters has been found that leads to a very satisfactory agreement between the local Gd concentrations simulated by both codes. Further verification on power distributions across the fuel rod has confirmed that the extended TUBRNP can be fairly applied to simulate radial power profiles for Gd-doped UO2 fuel in WWER-440 reactors. For irradiation conditions in the OECD Halden reactor, an application of the extended TUBRNP model confirmed the situation evaluated in [4], i.e. a net improvement of the fuel temperature predictions thanks to the refinements of effective cross sections in the TUBRNP model based on the HELIOS calculations during the first 10 MWd/kgHM, when the neutron absorbing Gd isotopes are being burned out. Similar measurements of fuel temperatures would be needed for WWER irradiation conditions. In future microscopic experiments, priority should be given to local concentrations of Pu and Gd isotopes in Gd-doped UO2 fuel irradiated in LWR and WWER that should be measured for at least 2-3 different values of initial Gd-content. Reliable data can be obtained by a

combination of complementary experimental techniques, as EPMA, e.g. [13,14], and Secondary Ionization Mass Spectrometry (SIMS), e.g.[15]. While experimental data would be the optimum source of information, it is obvious that the corresponding measurements are technically challenging and very time consuming. Hence additional neutron-physical calculations will be required. They should be performed with a similar nodalization as the MONTEBURNS simulations in the present work and should cover typical Gd-doped fuel configurations as used in PWR's and BWR's.

6. Acknowledgement The authors gratefully acknowledge K. Lassmann for laying the foundations of the TRANSURANUS code and the TUBRNP model.

Figure 1: Model of three WWER-440 fuel assemblies applied in the simulation by MONTEBURNS 2.0. The Gd-doped fuel rod used for evaluating the radial profiles across a fuel pellet is marked in black.

Figure 2: Layout and initial 235U concentrations in the Gd-doped WWER-440 fuel assemblies used in the simulation by MONTEBURNS 2.0 (cf. [6]).

FA1 FA2 (84 rods) 235U/ totU: 4.4 % 5.0 % (30 rods) 235U/ totU: 4.0 % 4.6 % (6 rods with 3.35% Gd2O3) 235U/ totU: 4.0 % 4.6 % (6 rods) 235U/ totU: 3.6 % 4.4 % central tube

3 irradiation steps (60 days)

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Figure 3: Radial dependence of the local concentrations of 155Gd and 157Gd calculated by the

extended Gd version of TUBRNP (lines) and calculated by MONTEBURNS (markers), using 'soft' neutron conditions.

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Figure 4: Radial dependence of the local concentrations of 155Gd and 157Gd calculated by the

extended Gd version of TUBRNP (lines) and calculated by MONTEBURNS (markers), using 'hard' neutron conditions.

0

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TuBrnp (2008)TuBrnp incl.Gd form factor

HELIOS

8 wt.% Gd2O31.69 MWd/kgHM

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8 wt.% Gd2O33.12 MWd/kgHM

Radius (mm)

157 G

d/to

t Gd

Figure 5: Radial dependence of the local concentrations of 155Gd and 157Gd calculated by the

extended Gd version of TUBRNP (lines) and calculated by HELIOS (markers), for an instrumented Gd-doped fuel rod irradiated in the Halden HWR.

3 irradiation steps (60 days) 'soft' neutron spectrum

0

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orm

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Figure 6: Radial power profiles calculated by the extended Gd version of TUBRNP (lines)

and calculated by MONTEBURNS (markers).

1.77 MWd/kgHM

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ower

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Figure 7: Radial power profiles for Gd-doped fuel calculated by the extended Gd version of

TUBRNP (lines) and calculated by HELIOS (markers), for an instrumented Gd-doped fuel rod irradiated in the Halden HWR (initial Gd content: 8 wt.% Gd2O3).

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Figure 8: Fuel centre temperatures in Gd-doped UO2 fuel: Comparison of measurements in the OECD Halden reactor project to calculations by TRANURANUS, applying the extended TUBRNP model for two values of initial Gd2O3 content (2 wt.% and 8 wt.%).

Table 1: Main parameters applied for simulating the WWER-440 fuel rods by

MONTEBURNS

A (hard)

B (soft)

Pellet inner radius (mm) 0.7 0.7

Pellet outer radius (mm) 3.8 3.8

Mean fuel temperature (oC) 1000 283

Mean moderator temperature (oC) 300 283

Moderator density (g/cm3) 0.72 0.75

Boron concentration (g/kg H2O) 7 0

Table 2: Parameters for the effective cross sections and the radial Gd form factor derived for Gd-doped UO2 fuel in WWER-440 and in the Halden HWR

Reactor WWER-440 HWR

Initial Gd-content (wt.%) 3.35 8.0

Pellet inner radius (mm) 0.7 0.9

Pellet outer radius (mm) 3.8 4.095

, 155a Gdσ (b) 1080 2260

, 157a Gdσ (b) 2550 5140

R 41.6 13.3

A155 ( (MWd/kgHM)-1 ) -3.86 4060

A157 ( (MWd/kgHM)-1 ) -4.71 36800

B155 ( (MWd/kgHM)-1 ) 19.3 478

B157 ( (MWd/kgHM)-1 ) 31.3 4280

C155 2.49 2.49

C157 3.02 3.02

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