Fission Products Experimental Programme: Validation and ... · Nicolas Leclaire, Tatiana Ivanova, Eric Létang, Emmanuel Girault, Jean-François Thro Abstract ... 133 Cs, nat Nd,

1

Fission Products Experimental Programme: Validation and Computational Analysis

Nicolas Leclaire*1, Tatiana Ivanova1, Eric Létang1, Emmanuel Girault2, Jean-François Thro3

1 Institut de Radioprotection et de Sûreté Nucléaire (IRSN), BP 17 - 92262 Fontenay-aux-Roses Cedex, France

[email protected], [email protected], [email protected] 2 Commissariat à l’Energie Atomique (CEA), centre de Valduc –

21120 Is-sur-Tille, France [email protected]

3 AREVA NC - 2, rue Paul Dautier 78000 Vélizy, France

[email protected]

*Corresponding author, Tel: +33 1.58.35.91.66, Fax: +33 1.46.57.29.98

Number of pages: 11 Number of Figures: 31 Number of Tables: 14

2

Fission Products Experimental Programme: Validation and Computational Analysis

Nicolas Leclaire, Tatiana Ivanova, Eric Létang, Emmanuel Girault, Jean-François Thro

Abstract – From 1998 to 2004 a series of critical experiments referred as the Fission

Products (FP) experimental programme was performed at the Valduc research facility

(CEA, France). The experiments were designed by IRSN, and funded by AREVA NC

and IRSN within the French programme supporting development of a technical basis

for burnup credit validation. The experiments were performed with the following six

key fission products encountered in solution either individually or as mixtures: 103Rh,

133Cs, natNd, 149Sm, 152Sm, and 155Gd. The programme aimed at compensating for the

lack of information on critical experiments involving fission products and at

establishing a basis for fission products credit validation. 145 critical experiments

have been performed, evaluated and analyzed with French CRISTAL criticality safety

package and American SCALE5.1 code system employing different cross-section

libraries. The aim of the paper is to show the experimental data potential to improve

the ability to perform validation of full burnup credit calculation. The paper describes

three phases of the experimental programme, the results of preliminary evaluation,

3

calculation, and sensitivity/uncertainty study of the FP experiments used to validate

APOLLO2-MORET 4 route in CRISTAL criticality package for burnup credit

applications.

4

I. INTRODUCTION

In the 1980s, French nuclear reprocessing plants were designed taking into account the burnup of

fissile materials. As far as burnup credit offers significant advantages for transport and storage, credit

for reactivity change due to major actinides as the least value for 50-cm of the irradiated rod was

adopted for criticality safety analysis. In recent years, need to handle and store higher quantities of

fissile material led nuclear fuel managers to increase benefit of burnup credit by considering both the

burnup profile and estimating a reactivity margin from the fission products in the safety design studies.

To support the safety basis for the fission products credit validation, IRSN, on one side, investigated1

profit associated with burnup credit in the criticality safety evaluation for pressurized-water-reactor UOx

spent nuclear fuel, and, on the other side, studied need of integral critical experiments involving fission

products. As a consequence of that study, the key fission products accounting for approximately half of

the total worth of all the fission products in irradiated fuel were selected2, and experimental programmes

were performed to support validation of both actinide-only (HTCa programme3) and fission product

credit.

This paper describes 145 experiments referred to as the FP experiments, 73 of which were performed

with the following fission products: 103Rh, 133Cs, natNd, 149Sm, 152Sm, and 155Gd. Three phases of the

experimental programme are summarized in Table I: “Physical” (P), “Elementary Dissolution” (ED) and

“Global Dissolution” (GD).

This work contributes to the validation of APOLLO2-MORET 4 route of CRISTAL V1 criticality

package4 for burnup credit calculation.

a “Haut Taux de Combustion” experiments with rods having U and Pu isotopic composition similar to U(4.5%)O2 fuel with burnup of 37.5 GWd/MTU.

5

II. EXPERIMENTAL INSTALLATION

The FP experimental programme was conducted at the Apparatus B in CEA/Valduc research center.

The experimental device, shown in Fig. 1, is commonly used for assembling the configurations with

epithermal and thermal neutron energy spectra. Flexibility of the installation provided easy assembling

of the FPs configurations for each phase of the programme.

II.1. Apparatus B

The Apparatus B presented in Fig. 1 consisted of a parallelepiped-shaped reflector pool, which is

approximately centered in a large room of 12.1 x 8.8 x 10 m3 with concrete walls, floor, and ceiling.

The pool had inner dimensions of 189.7 × 189.7 × 140 cm3 for “Physical” type configurations and

140 × 120 cm2 × 148.8 cm3 for “Elementary Dissolution” and “Global Dissolution” experiments. The

0.3-cm-thick pool walls and 0.6-cm-thick bottom were reinforced with girders. The fuel rods were

installed into a basket, made of AG3Mb, which could contain a maximum of 2500 rods in a 50 x 50

array at 1.3-cm square pitch. The basket was supported by a stainless steel (Z2 CN 18.10) 2.5-cm-thick

pedestal except “Physical” type experiments, for which the support was made of two joined plates with

thicknesses of 1.0 cm and 2.5 cm. The pedestal was elevated above the reflector pool on 17.5, 33.7, and

42.3 cm for “Physical”, “Elementary Dissolution”, and “Global Dissolution” type configurations,

accordingly.

Variation of water or depleted uranyl nitrate (DUN) solution level in the tank accomplished the

subcritical configuration within ≈0.1% from criticality. Then the critical condition was linearly

extrapolated. This sub-critical approach procedure is illustrated in Fig. 2.

b Al alloy

6

A moderating solution gradually flooded the tank containing the fuels pin arrays. A side cylindrical

well, communicating at the bottom with the pool tank, was equipped with a needle, which followed and

measured a free upper level (H in Fig. 2) of the solution. The zero-level measurement was the bottom of

the fuel column. Neutron counting rate (C in Fig. 2) was measured with six BF3 counters. Function 1/C

= f(H) was extrapolated to determine the moderating solution critical level.

Usually, the experiments were designed to provide the moderator height as close as possible to the

fuel stack (90 cm). The reactivity was compensated by adding or removing fuel rods symmetrically in

two or four peripheral rows in the initial square array.

II.2. UO2 and HTC rods

To design and assembly the FPs configurations two types of simulated fuel rods in FP or non-FP

solution were employed, depending on the programme’s phase: UO2 and HTC rods.

The UO2 rods had a typical for pressurized-water reactor (PWR) 235U enrichment of 4.738 wt.%.

The HTC rods were specifically designed for the HTC experimental programme to be similar to what

would be found in a PWR fuel assembly that initially had an enrichment of 4.5 wt% 235U and was

burned to 37.5 MWd/MTU. They were composed of (U-Pu)O2 (1.1 wt.% PuO2) with 1.57 wt.% 235U

enrichment and 240Pu content was 24.333 wt.%. The HTC rods also included 241Am. The principal

characteristics of the fuel rods are given in Table II (Uncertainties are indicated as 1σ).

The UO2 and HTC rods are presented in Fig. 3. They consisted of pellets contained within Zircalloy

4 cladding and stuck together by means of a stainless steel spring. The rods diameter corresponded to

the industrial fuel pin diameter. The fuel stack length adjusted to the dimension of the experimental tank

was equal to 90 cm. The fuel rods were held in place by upper and lower grids placed into rectangular

tank.

7

III. EXPERIMENTAL PROGRAMME

The Fission Products experiments followed the Pré-FPs programme5 that had been carried out on the

same facility before its renovation. The assembled configurations were similar to those for “Physical”

type phase. 149Sm nitrate solution was in the central tank surrounded by a driver array of UO2 rods in

AGS (aluminum alloy) clad. The precursor of the FPs programme was the first attempt to examine the

absorption on 149Sm (top contributor to total worth of all FPs in irradiated fuels) and to have a clear idea

of the experiments feasibility and accuracy associated with the FP solutions. The experience obtained

has shown that such kind of experiments can be conducted to study burnup credit problems.

Thus, series of 145 critical experiments referred to as the FP experiments was performed. It

included the following three phases testing different interaction conditions between the fission products

and the UO2 or the HTC rods (see Table I):

1. “Physical” type experiments dealt with the FPs presented individually or as mixture in low acidic

solutions, without interaction with the fuel rods.

2. “Elementary Dissolution” type experiments dealt with the FPs presented individually or as

mixtures in low acidic or depleted uranyl nitrate (DUN) solutions, interacting with array of the UO2 or

the HTC rods.

3. “Global Dissolution” type experiments dealt with the mixture of FPs in DUN solutions,

interacting with an array of the UO2 or the HTC rods.

For each configuration, at least two experiments were conducted, one with and one without FP.

The FPs concentration was chosen in order to reach a sufficient FP reactivity worth from 1.5% to

6%, depending on the FP. The following restrictions were taken into consideration: solubility limit for

8

133Cs and natNd (130 g/l and 177 g/l, respectively) and available quantity of 152Sm. In addition, the FPs

solutions were not systematically pure. Namely, 152Sm contained a small amount (0.29%) of 149Sm,

155Gd did 1.2% of 157Gd. natNd solution used in the experiments contained 12.18% of 143Nd. The latter

being the main absorber among Nd isotopes is of strong interest.

The preparation of FPs solutions was a subject matter for the experimental programme. The

desirable accuracy of the solutions’ characteristics was obtained thanks to the method employed by

chemists.

III.1. “Physical” type experiments

The first step of the FPs programme was 45 “Physical” type experiments with slightly acidic

solutions (0.014 to 2 N) of FPs in Zircaloy central tank. This tank of 6.2×6.2-cm2 internal dimension

and 0.15-cm thickness was located in the center of UO2 rods array. The system was moderated and

reflected by water.

This series comprised 32 experiments with the following FPs presented at different concentrations in

solution both separately and in the mixture: 103Rh, 133Cs, natNd, 149Sm, 152Sm, and 155Gd. The

experiments without FP (13) and with boron solution (1) were also performed. Figures 4 and 5

demonstrate the picture and scheme of a “Physical” type configuration.

III.2. “Elementary Dissolution” type experiments

The second phase, “Elementary Dissolution”, included 86 configurations performed with one FP or

mixed FPs in slightly acidic solutions (around 1 N), in a central tank with internal dimension 14.2 × 14.2

cm2 made of Zircaloy and containing an array of 11 × 11 UO2 or HTC rods at 1.271-cm square pitch.

9

This tank is located in the center of a driver array of UO2 rods at 1.3-cm square pitch, moderated and

reflected by water.

Vertical slice through the “Elementary Dissolution” type configuration is presented in Fig. 6.

This series of experiments can be categorized into two groups:

� 68 experiments with UO2 (54) or HTC (14) rods in the central tank in water solution with (35) or

without (33) the fission products,

� 18 experiments with UO2 (10) or HTC (8) rods in the central tank in DUN solution with (7) or

without (11) the fission products.

III.3. “Global Dissolution” type experiments

The third phase performed within the framework of the programme was a series of 14 experiments

referred to as “Global Dissolution” type. They were conducted to address needs for validation of

resonance self-shielding calculation for uranium, plutonium, and americium.

The configurations were assembled from a tank with the UO2 or HTC rods array. The main part of

the tank was a parallelepiped box made of stainless steel with internal dimensions of

70.40 x 70.40 x 114.8 cm3, wall thickness of 0.6 cm, and base thickness of 2.0 cm. The rods were

secured by upper and lower horizontal grids fastened to the tank walls. Two identical 0.4-cm thick grids

with dimensions 70.2 x 70.2 cm2 were placed face to face at distance of 96.8 cm to fix rods vertically in

array. Vertical slice through the “Global Dissolution” type configuration is presented in Fig. 7.

The experiments of this phase may be categorized as follows:

� 7 configurations with a 23 × 23 or 26 × 26 array of UO2 fuel rods at 1.3-cm square pitch,

moderated and reflected by DUN solutions with concentrations of 300 gU/l and 100 gU/l;

10

� 7 configurations with a 44 × 44 array of HTC fuel rods at 1.6-cm square pitch, moderated by

DUN (300 gU/l and 92 gU/l), poisoned or not by FPs, and reflected by water.

Reproducibility of “Global Dissolution” type experiments was examined by performing several

experiments with solutions of each uranium concentration (92 gU/l and 300 gU/l).

IV. EVALUATION OF EXPERIMENTAL DATA

The Pré-FPs programme6, the precursor of the described FP experimental programme, was evaluated

on the basis of the experimental data issued with tolerances (especially for the rods, clads, etc). In 1994,

during re-cladding of the UO2 rods, measurements were performed to obtain more precise information

about the fuel pellets and the clad. As a consequence, the uncertainties associated with their dimensions

were also defined more precisely. The new data of the dimensions’ measurements were then used for

evaluation of the FP experiments.

Sensitivity studies were performed to assess the impact of various experimental uncertainties upon

the configuration reactivity in accordance with recommendation of the ICSBEP uncertainty guide5. The

3D APOLLO2-MORET 4 Monte Carlo computations were used to determine the sensitivity of the

results to variation of geometrical and material data. The sensitivity study was also performed with two-

dimensional cylindrical geometries using the APOLLO2 discrete ordinate code. The reactivity changes

produced by the above tools were adopted as the associated components of the keff uncertainty.

A specific treatment was applied to impurities in the fissile material and the FPs. Namely, for the

UO2 fuel, the detected and measured impurities were modeled while other impurities were omitted

adding the uncertainties. The impurities in composition of the HTC fuel and the fission products have

negligible impact to the overall uncertainty.

11

The principal components of the keff errors are shown in Table III for the three types of experiments

along with the overall uncertainty, calculated as the square root from sum of squares of its individual

components.

It can be seen that the rods density, pellet diameters, oxide impurities in the UO2 rods, and the rod

positioning have a paramount effect on the overall uncertainty while the specific uncertainties associated

with the FPs solutions are very small.

The measurements of the rods performed during their re-cladding and accurate method of the

solution FPs preparation lead to small overall uncertainties: less than 0.1% for the first two phases

(“Physical” and “Elementary Dissolution” types) and about 0.15% for phase 3 (“Global Dissolution”

type). The level of rigor associated with these experiments shows that they have a potential to

contribute to fission product credit validation, adding to the small number of experiments applicable to

this purpose.

V. ANALYSIS OF THE EXPERIMENTS

The benchmark-models of all the critical configurations have been used to validate APOLLO2-

MORET 4 calculational route, which is utilized in France for criticality calculations within CRISTAL

criticality package.

The APOLLO2 – MORET 4 validation procedure7 is conducted through a comparison of the

computed keff results for a designed system with the experimental data. The area of applicability of the

experimental data is defined on the basis of comparison of such systems characteristics as: fuel material,

fuel form, neutron energy spectra, reflection and moderation conditions, heterogeneity, interaction,

spectral characteristics similar to those presented in the ICSBEP Handbook, etc. For the design systems

that fall inside the area of applicability of the experiments, the expected computational bias is

12

established through an expert judgment of the computation-to-experiment difference for all of the

selected critical configurations. No bias is assumed if the calculated values do not exceed experimental

results for more than three combined standard deviations, which are computed as follows:

2

benchmark

2

ncalculatioσσσ += , where

ncalculatioσ is a statistical uncertainty associated with Monte Carlo method,

and benchmarkσ is an error associated with the uncertainties encountered in the experimental data and

derivation of the benchmark model.

Before performing such an analysis for the FP configurations, the APOLLO2-MORET 4 results

were compared with those obtained by TRIPOLI-4.38 reference route, which uses continuous energy

cross sections based on the same evaluated nuclear data library. If observed, the discrepancy between

the two results allows separating the modeling error originating from approximations adopted in the

APOLLO2 multi-group code and the uncertainty due to cross-section data.

The calculations of the FP experiments have been performed to complete the APOLLO2-MORET 4

validation database. The SCALE5.19 codes system widely used for criticality safety study has been also

employed to take advantage of variety of the codes for the FP experiments analysis. The details of

eigenvalue calculations are presented in the following sections. All the computational results for three

phases are gathered in Tables IX-XIV.

13

V.1. Computations with the CRISTAL Package

The French CRISTAL package allows performing criticality calculations in two ways: standard

APOLLO2-MORET 4 route with multi-group cross sections and TRIPOLI-4 Monte Carlo reference

route with its specific point-wise neutron data library.

The “standard” calculation is run in two steps using the following codes:

� APOLLO2 is a one-dimensional lattice code used for preparation of multi-group cross sections

in equivalent cell approximation.

� MORET 4 is the 3D Monte Carlo code for neutron transport calculation. It uses macroscopic

homogenized, self-shielded cross sections generated by the APOLLO2 code. Typically, each

calculation employed 1000 neutrons per generation and is run to achieve a precision of 0.0003 (about

3000 generations).

The following 172-group cross-section libraries were used by the APOLLO2 code:

� CEA93 V6 is the standard route library based on the JEF2.2 evaluation. All isotopes are

developed in P1 Legendre polynomials, except moderating elements (such as H2O) and heavy nuclides

(U, Pu) developed at the 5th and 9th order, respectively.

� CEA2003 library is based on JEFF3.1 evaluation. All isotopes are developed in P5 Legendre

polynomials.

� ENDF/B-VI cross-sections library is derived from ENDF/B-VI.4 evaluation. All isotopes are

developed in P5 Legendre polynomials.

The model used for the APOLLO2 calculations is a cell equivalent to a fissile rod in the array

configuration. It is simulated by coaxial infinite cylinders representing the fuel rod, surrounded by those

14

modeling cladding and water in the cell. Output of the APOLLO2 code is macroscopic cross sections

homogenized in the cell. Thus, the model for 3D neutron transport calculation with the MORET 4 is a

set of homogenized zones corresponding to different cells. Fig. 8 shows a view of the model as

generated by MORET 4 graphical user interface.

The reference TRIPOLI-4 route is a continuous energy Monte Carlo code. It employs continuous

energy cross sections derived from JEF2.2 or ENDF/B-VI.4 evaluated nuclear data files. For the

reference calculation the models are prepared without simplifications. An example of X-Z cut of the

TRIPOLI-4 model is presented in Fig. 9.

V.2. Computations with SCALE 5.1 Code System

The detailed input files were created for calculations with SCALE 5.1 Version codes system using

both ENDF/B-V or ENDF/B-VI.7 238-group cross sections. Fig. 9, generated using SCALE5.1, shows

a model for “Elementary dissolution” experiments. The CSAS25 control module utilized BONAMI and

CENTRM for cross-section processing and then called KENO-V.a for the Monte Carlo calculations.

The unit cell cylindrical model that comprised fuel pellet, cladding and water was used to create a

problem-specific shielded cross-section set for each calculation.

V.3. Computational Results

The keff results are depicted in Figures 10 to 19, where the statistical uncertainty of Monte Carlo

computations is given as 3σ. All the computation results are shown also numerically in Tables IX to

XIV.

Comparison of the APOLLO2-MORET 4 and TRIPOLI-4 results obtained with group- and point-

wise JEF2.2 cross-sections libraries shows that the discrepancies associated with self-shielded cross-

15

section processing are quite small (0.2% in average). A slight overestimation of the APOLLO2-

MORET 4 results compared to the experiments is also highlighted.

Study of performance of different cross-sections libraries (see Fig. 10-12, 16, and 17) and both codes

and libraries (see Fig. 13-15, 18, 19) revealed the following conclusions.

� Use of the ENDF/B-VI evaluation with the CRISTAL standard (APOLLO2-MORET 4) and

reference (TRIPOLI-4) routes leads to under-predicting keff for “Physical” and “Elementary

Dissolution” type experiments with UO2 and HTC (internal array) rods placed at 1.3-cm square pitch

lattices.

� However, for the “Global Dissolution” configurations with the HTC rods placed at 1.6-cm pitch

in DUN solution with concentration of 300gU/l, the results show a good agreement regardless of the

library used. For the systems with higher moderator-to-fission ratio, the absence of the typically

observed difference can be explained by shift of the neutron spectrum to softer energy range where

probability to avoid resonances capture increases.

� Use of JEFF3.1 evaluation with APOLLO2-MORET 4 leads to statistically slightly higher

multiplication factor than those based on JEF2.2 evaluation. The new evaluation of 238U cross sections

adopted in JEFF3.1 library may cause such a tendency.

� The SCALE5.1 results obtained with ENDF/B-VI.7 and ENDF/B-V based cross sections are

coherent with TRIPOLI-4 results employing ENDF/B-VI.4 library (the results are not available in this

paper). All the mentioned libraries calculate from 1.1 to 0.6% low for the experiments with 1.3-cm-

pitch lattice. This tendency has been already observed10 for ENDF/B-V results. The resonance data

adopted in the libraries can have a significant effect on results for the under moderated systems like

the FP configurations with a tight pitch.

16

� The calculations of 103Rh solutions with different codes and cross sections under-predict the keff

significantly for all the “Elementary Dissolution” assemblies while the results for the “Physical” type

configurations obey the common tendency observed for all the FPs experiments. The computations

with different codes and both point- and group-wise libraries prove that this problem is not caused by

the cross-sections processing. Since the neutron spectra in “Physical” and “Elementary dissolution”

type experiments are similar, a similar calculation-to-experiment difference is expected for the

configuration of both series, which is not the case. Sensitivity study shows that 10% change in 103Rh

concentration could explain the above discrepancy. Concretion of 103Rh on the fuel rods and tank

surface may lead to such a decrease of the solution concentration. This assumption makes sense given

that chemical features of rare-earth elements stipulate such 103Rh behavior. The investigations are in

progress to reveal an origin of the results deviation for the experiments with 103Rh.

VI. SENSITIVITY ANALYSIS

The FPs programme was carried out with the aim to address evaluation of reactivity margins

associated with the fission products. Since this can be assessed only if the eigenvalue of the experiments

are sensitive enough to the FPs nuclear data, the FPs reactivity worth along with the keff sensitivity to the

FPs atomic density have been investigated.

VI.1. Fission Products Reactivity Worth

The fission products worth was calculated as the difference between results for configuration

containing the FP and without it. The results of the computations with the KENO V.a (SCALE5.1) code

and the APOLLO2-MORET 4 route are presented in Table IV. The FP worth provided by the two

calculational routes demonstrates a quite good agreement despite different cross-sections libraries are

used in the above tools.

17

To examine response of absorption on fission products to their concentration, calculations were

performed with variation of FPs atomic density keeping it constant for remaining nuclides. The

computational results for two experiments (2883 Elementary Dissolution (ED) and 2834 Physical (P)

type) with 103Rh are presented in Fig. 20 along with eigenvalue sensitivity to 103Rh atomic density. The

above values were computed with APOLLO2-MORET 4 route. Sensitivity coefficients were received

with correlated sampling method by 1% variation of FPs atomic densities, remaining constant densities

for other nuclides. Fig. 20 exhibits that the saturation is obtained when the sensitivity coefficient

approaches zero, i.e. when 103Rh concentration is up to 100 g/l. Thus, the range of FPs concentrations

examined in the solutions (for example, about 20, 40, and 50 g/l for 103Rh) is chosen far enough from the

saturation limit.

The worth of FPs in the mixtures was analyzed and presented in Tables V-VII for three

configurations related to each sub-programme. Statistical dispersion for both KENO V.a and

APOLLO2-MORET 4 results is about 40 pcm. The second column in the tables shows worth of every

FP in order of their consecutive addition to the solution of the FP mixture. While the last columns

represent the worth of equivalent quantity of the FP being independent in the solution. Since in the

“Elementary” and “Global dissolution” type configurations, contribution of capture on the FPs to the

total neutron balance (captured by 238U) is smaller than in “Physical” type experiments, the

“independent” FP worth and those in the mixture do not differ much (see Tables VI and VII). The

difference is observed for the “Physical” type configurations (see Table V) because the FPs affect

distinctly the total capture process in the system.

VI.2. Fission Product Absorption Rate The normalized cumulated absorption rate is plotted versus energy in Fig. 21 for the six FPs tested in

the “Elementary Dissolution” type experimental programme. The so-called normalized cumulated

18

absorption rate1 is used to determine and to observe dependency of absorption rate upon energy. It can

be seen that 149Sm, 155Gd and 143Nd absorb neutrons mainly in the thermal energy range; 103Rh, 152Sm,

and 133Cs do at higher energy.

VI.3. Sensitivity Coefficients

The SCALE5.1 code system and the APOLLO2-MORET 4 route used for computation of sensitivity

coefficients allow comparing perturbation and correlated sampling method, respectively.

TSUNAMI-3D code implemented in the SCALE5.1 code system calculates the sensitivity

coefficients using adjoint based 1st order linear perturbation theory11 as follows:

δσ

σ

k

δks ⋅= , where σ is the nuclear data parameter of interest. In this work, sensitivity coefficients

were calculated as the percent change in the system keff for one percent total cross section change in

every of 238 energy groups and isotope of interest. The energy-dependent sensitivity profiles were

studied and compared for different types of experiments (see Figures 24-29). Integrated sensitivities

have been calculated as sum of the 238-group coefficients. Following the recommendations given in the

TSUNAMI-3D manual, the obtained results have been compared with the sensitivity coefficients from

direct perturbation of atomic density using KENO V.a Monte Carlo code with ENDF/B-VI.7 based 238-

group cross sections.

The APOLLO2-MORET 4 route was also used for sensitivity analysis. Monte Carlo perturbation in

MORET 4 is based on the correlated sampling method12 that allows calculating simultaneously keff value

and an effect of small perturbation of initial data on the eigenvalue. The atomic densities were perturbed

in this study.

19

Then integrated sensitivities obtained by different ways have been compared. Fig. 22 depicts the

results of SCALE5.1 computations with ENDF/B-VI.7 library for major actinides, hydrogen, and 133Cs.

The sensitivities for fission products are small relatively to those for major actinides. This may require

special approach to quantify the bias and its uncertainty associated with the fission products credit.

Table VIII and Fig. 23 illustrates that three different calculations produce quite good agreement for

all major actinides and fission products in the configurations of three types.

The neutron-energy dependent sensitivity profiles for all the tested FPs are compared for “Physical”

and “Elementary Dissolution” experiments. The profiles comparison is given in Fig. 24 to 29. The

eigenvalues for the configurations are sensitive to the FP and major actinides total cross sections in

thermal and resonance energy range.

VI.4. Use of experimental data in estimation bias associated with the fission products

As shown in previous section, eigenvalue sensitivities to fission products cross-section data are little

relative to other materials such as fuel and moderator (see Fig. 22). This requires special technique that

would magnify the effect of the fission products for evaluation of specific bias in keff associated with

their nuclear data.

As it was mentioned, the FP experimental programme was planned and performed in such a way to

have pairs of the configurations with and without fission product. Both experiments had similar arrays

and same fuel rods, but different heights of moderating solution (because the FP negative reactivity was

compensated by increase of the solution height).

For every pair, the experimental reactivity (change in keff between the two systems) is equal to zero

within the experimental uncertainty, i.e. 00001.== −FPnon

benchmark

FP

benchmarkkk . It makes possible to estimate

computational bias associated with fission products cross-section data as follows: FPnon

calc

FP

calc

FP

kkk−∆−∆=∆ . Such

20

differences were calculated with the APOLLO2-MORET 4 route and 172-group JEF2.2 cross sections.

Fig. 30 shows them for “Physical” type configurations. It can be seen that the computational biases vary

between 0 and 0.3%, depending on the testing FP.

The experimental uncertainty associated with difference between the FP and non-FP configurations

includes such components, as the FP solutions concentration and density, and critical height of

moderator, which in sum do not exceed 0.02% (see Table III).

The eigenvalue sensitivities were calculated by TSUNAMI-3D for each pair of experiments. Then

differences of the sensitivities at the two states for some pairs of the experiments were calculated. As an

example, sensitivities differences profiles for “Physical” dissolution configurations with and without

133Cs are depicted in Fig. 31. For the change in keff between the two cases, the 235U fission and 238U

capture sensitivities are noticeably smaller than that for 133Cs capture, while keff sensitivities to 235U

fission and 238U capture shown in Fig. 22 and Table VIII are approximately an order of magnitude

greater than that of 133Cs capture.

For the “Elementary dissolution” type configurations the 235U sensitivities for keff differences are

higher and have the same order of magnitude as the FP sensitivities. This might be caused by greater

differences between the FP and non-FP solution critical heights than those for “Physical type”

experiments. Since the FP sensitivities can no longer be magnified experimentally by, for example,

variation of the fuel rods number on the core periphery instead of the critical height of moderated

solution, the calculational way to do this will be investigated.

Preliminary analysis of the calculated bias, experimental uncertainty, and sensitivities for difference

between the experiments with and without testing fission products has shown potential to magnify the

effect of the tested materials. Work is planned to estimate bias due to fission products cross-section data

for a burnup test application system employing the above values for Sensitivity/Uncertainty analysis

21

based on Generalized Linear Least Square Methodology13. This may allow fully taking advantage of the

valuable information provided by the FP experimental programme.

CONCLUSION

145 critical experiments, presented in the paper, were conducted at the Valduc research facility to

support fission products credit validation. The following six key fission products were studied within

three phases of the programme: 103Rh, 133Cs, natNd, 149Sm, 152Sm, and 155Gd.

The benchmark models of the experimental configurations were created. The uncertainties of

experimental data were assessed using guidance of the ICSBEP. Since the experiments were performed

with high level of rigor - the accurate data for the fission products solutions were provided by

experimentalists, along with the new measurements, performed during UO2 rods re-cladding - the

resulting experimental keff uncertainties do not exceed 0.15%. That allows using FP configurations as

criticality benchmarks, adding to the previously small number of experiments applicable to assess FP

credit.

All the configurations were modeled using the French CRISTAL V1.1 package and American

SCALE5.1 code system developed for criticality calculation. The performance of the two codes

employing several cross-sections libraries was compared. The results of both standard and reference

routes show a good agreement and tend to slightly over predict (except for 103Rh) the keff when using the

CRISTAL V1.1 package with JEF2.2 based nuclear data. While SCALE5.1 with both ENDF/B-V and

ENDF/B-VI.7 based cross sections tends to under predict keff. The origin of these tendencies can be

mainly attributed to 235U and 238U cross section data10 in the employed libraries.

Study of keff sensitivity to atomic density (total cross section) for major actinides and the FPs was

performed. Use of different codes for calculation of the sensitivity coefficients allowed testing their

22

capability and has shown a good agreement for the values obtained with correlated sampling method

(MORET 4), the 1st order direct perturbation theory (TSUNAMI-3D), and a direct perturbation for the

majority of the cases.

The sensitivity analysis exhibited that the sensitivity coefficients for the FPs are quite small

compared to those for major actinides. This will most likely create necessity to use

Sensitivity/Uncertainty analysis not for keff but for keff-difference to magnify the effect of the fission

products and to predict bias and the bias uncertainty associated with their cross-section data. Work is

planned to validate fission product credit calculation against the results of the presented experimental

programme.

23

REFERENCES 1.J. Anno et al., “Planned Experimental Programme Qualifying the Safety Margins given by 6

Selected Fission Products in Spent Fuels”, Proc. Criticality Safety Challenges in the Next Decade,

Chelan, 1997, 271 (1997).

2.J. Raby, C. Lavarenne, A. Barreau, Ph. Bioux, M. Doucet, E. Guillou, G. Léka, C. Riffard, B.

Roque, H. Toubon, “Current studies related to the use of Burnup Credit in France”, Proc. ICNC2003,

Tokaï, 2003.

3.F. Fernex, E. Girault, S. Evo; E. Letang, “High burnup experimental programme”, Proc. ANS 2006

summer meeting, Reno, 2006.

4.J.M. Gomit, P. Cousinou, Cheikh Diop, G. Fernandez de Grado, F. Gantenbein, J.P. Grouiller, A.

Marc, D. Mijuin and H. Toubon, “CRISTAL V1: criticality package for burnup credit calculations”,

Proc. ICNC2003, Tokaï, 2003.

5.International Handbook of Evaluated Criticality Benchmark Experiments

NEA Nuclear Science Committee, NEA/NSC/DOC (95)03 – September 2007 Edition

6.J. Anno et al., “LEU-COMP-THERM-050. 149Sm solution tank in the middle of water-moderated

4.738-wt.%-enriched uranium dioxide rods arrays”, ICSBEP Handbook, Sept. 2005.

7.N. Leclaire, I. Duhamel, E. Gagner, Y. K. Lee, C. Venard, “Experimental Validation of the French

CRISTAL V1 package”, Proc. NCSD2005, Knoxville, 2005.

8.Y.K. Lee, E. Gagnier, L. Aguiar, N. Vedrenne, “Validation of the 3D Transport Monte Carlo Code

TRIPOLI-4.3 for Moderated and Unmoderated Metallic Fissile Configurations with JEF2.2 and

ENDF/B-VI.4 Cross Section Evaluations”, Proc. ICNC2003, Tokaï, 2003.

9.SCALE: A Modular Code System for Performing Standardized Computer Analyses for Licensing

Evaluations, NUREG/CR-0200, Rev. 7 (ORNL/ NUREG/CSD-2/R7), Vols. I, II, and III (May 2004)

24

(Draft). Available from Radiation Safety Information Computational Center at Oak Ridge National

Laboratory as CCC-725.

10. S. M. Bowman, W. C. Jordan, J. F. Mincey, C. V. Parks, L. M. Petrie, ORNL, “Experience With

the SCALE Criticality Safety Cross-Section Libraries”, NUREG/CR-6686, ORNL/TM-1999/322,

October 2000.

11. B. T. Rearden, "Perturbation Theory Eigenvalue Sensitivity Analysis with Monte Carlo

Techniques," Nucl. Sci. Eng. 146, 367-382 (2004).

12. J. Anno, O. Jaquet, J. Miss, Validation of MORET 4 Perturbation against “Physical” Type

Fission Products Experiments, Proc. ICNC2003, Tokaï, 2003.

13. B. L. Broadhead, "Application of Generalized Linear Least-Squares Methodology to Criticality

Safety Computations," ANS 1997 Winter Meeting and Embedded Topical Mtgs., Albuquerque, NM,

November 16-20, 1997.

VII. ACKNOWLEDGMENTS The authors wish to thank AREVA NC, who supports the Fission Product experimental programme

and allowed publication of the results.

25

FOOTNOTES IN THE TEXT a“Haut Taux de Combustion” experiments with rods having U and Pu isotopic composition similar to

U(4.5%)O2 fuel with burnup of 37.5 GWd/MTU. b Al alloy

26

Fig. 1. Apparatus B.

27

C = C0/(1-keff)

When H HC 1/C 0

H0

1/Ckeff = F(H)

H

HC

For each water height H, the neutron counting rate depends on the Keff = f(H). When the Keff increases and tends to 1, 1/C decreases and tends to 0. Thus, the intersection with the tangent abscissa axis to the curve 1/C = F(H) at the last measurement point determines the critical height Hc.

Water height measurement system

Pilot lattice Uo2 Rod

Pilot lattice fissile zone upper limit

Zr tankcontaining the FP solutionand the intern array

or HTCUO2

Pilot lattice fissile zone lower limit

Support

Water input and output

Neutron counters

Counting rate, C

Brace with input and output of the FP solution, or acid solutionor DUN solution

Clamp FP sol.or DUN or HNO3levelmeter

FP solution upper level

Fig. 2. Sub-critical approach technique.

28

90.

0 cm

9.1

cm

Spring Steel39 spires0.13 cm diameter

Pellet 0.794 cm diameter

Clad Zr40.95 cm outside diameter0.064 cm thick

Bottom plug Zr4

0.0 cm

102 cm

0.95 cm

1.8

cm

1.1

cm

Top plug Zr4

1.468

0.949

Zircaloy-4 plug

Spring

4,738 % 235U

Zircaloy 4 clad Φext = 0.949Φint = 0.836

Zircaloy 4 Plug

Dimensions in centimeters

9.049

102.082

89.765

1.8

= 0.789φ

UO2 rods

(a) (b) Fig.3. HTC (a) and UO2 (b) rods.

29

Dimensions in cm Drawing not to scale

96.5

9517.524

130.4

“Zero”Level

1.2

0.4

Water

Central Tank (Zircaloy)Internal Dimensions 6.2 x 6.2 x 92.7 cmThickness 0.15 cm AG3M Plate

AG3M grid Solution (FP, Boron or HNO3)H = 91 cm

1.2

0.4

8.3

3.5

1.2

Fig. 4. Scheme of “Physical” type experimental configuration (vertical cut).

30

Fig. 5. “Physical” type experimental installation.

31

2.5

Dimensions in cm Drawing not to scale

160.1

“Zero” level

Water

Upper GridHolediam. 0.98

Square Pitch 1.3

Lower Grid Holediam. 0.98

Square Pitch 1.3

(Acidicor DUN solution)

with or without FPs

Thick. 0.16

36.2

89.765 95.0

44.7

14.35

80.0

93.80 98.8104.6

CriticalHeight

Fig. 6. Scheme of “Elementary Dissolution” type experimental configuration (vertical cut).

32

2.0

DUNcriticalHeight

170

“Zero” level

Water

Upper GridHolediam. 0.98Square Pitch 1.6

Lower GridHolediam. 0.98Square Pitch 1.6

(DUN)with or

without FPs

Thick. 0.60

Thick. 0.50140.044.0

112.890.0

96.895.0

70.4

Fig. 7. Scheme of “Global Dissolution” type experimental configuration (vertical cut).

33

Fig. 8. Half of the homogenized model (Vertical cut) for computation with the MORET 4 code.

34

Fig. 9. Heterogeneous model (Vertical cut) for computation with TRIPOLI-4 and SCALE 5.1.

35

0.988

0.99

0.992

0.994

0.996

0.998

1

1.002

1.004

1.006

1.008

1.01

1.012

103Rh

103Rh

103Rh

103Rh

133Cs

133Cs

133Cs

133Cs

133Cs

133Cs

133Cs

133Cs

133Cs

133Cs

Ndnat*

Ndnat*

152Sm

152Sm

152Sm

152Sm

152Sm

155Gd

155Gd

155Gd

155Gd

155Gd

Mixt.

Mixt.

Mixt.

149Sm

149Sm

keff

APOLLO2-MORET 4 - JEF2.2

APOLLO2-MORET 4 - ENDF/B-VI.4

APOLLO2-MORET 4 - JEFF3.1

Fig. 10. keff for “Physical” type experiments. Library effect.

36

0.988

0.99

0.992

0.994

0.996

0.998

1

1.002

1.004

1.006

1.008

1.01

1.012

133Cs

133Cs

133Cs

133Cs

133Cs

103Rh

103Rh

103Rh

103Rh

103Rh

143Nd

143Nd

149Sm

149Sm

149Sm

149Sm

149Sm

152Sm

152Sm

155Gd

155Gd

155Gd

Mixt1

Mixt1

Mixt2

Mixt2

Mixt3

Mixt3

Boron

Boron

keff

APOLLO2-MORET 4 - JEF2.2APOLLO2-MORET 4 - ENDF/B-VI.4APOLLO2-MORET 4 - JEFF3.1

Fig. 11. keff for “Elementary Dissolution” type experiments (UO2 rods in central tank). Library effect.

37

0.988

0.99

0.992

0.994

0.996

0.998

1

1.002

1.004

1.006

1.008

1.01

1.012103Rh

103Rh

155Gd

155Gd

149Sm

149Sm

Mixt4

Keff

APOLLO2-MORET 4 - JEF2.2APOLLO2-MORET 4 - ENDF/B-VI.4APOLLO2-MORET 4 -JEFF3.1

Fig. 12. keff for “Elementary Dissolution” type experiments (HTC rods in central tank). Library effect.

38

0.988

0.99

0.992

0.994

0.996

0.998

1

1.002

1.004

1.006

1.008

1.01

1.012

103Rh

103Rh

103Rh

103Rh

133Cs

133Cs

133Cs

133Cs

133Cs

133Cs

133Cs

133Cs

133Cs

133Cs

Ndnat*

Ndnat*

152Sm

152Sm

152Sm

152Sm

152Sm

155Gd

155Gd

155Gd

155Gd

155Gd

Mixt.

Mixt.

Mixt.

149Sm

149Sm

keff

APOLLO2-MORET 4 - JEF2.2TRIPOLI4 - JEF2.2SCALE5.1 - ENDF/B-VI.r7SCALE5.1 - ENDF/B-V

Fig. 13. keff for “Physical” type experiments. Code and library effect.

* 142Nd was not available for the APOLLO2 computations. TRIPOLI-4 results have shown that its impact can be neglected.

39

0.988

0.99

0.992

0.994

0.996

0.998

1

1.002

1.004

1.006

1.008

1.01

1.012

133Cs

133Cs

133Cs

103Rh

103Rh

143Nd

149Sm

149Sm

149Sm

152Sm

155Gd

Mixt1

Mixt2

Mixt3

Boron

keff


Fig. 14. keff for “Elementary Dissolution” experiments (UO2 rods in central tank). Codes and library

effect.

40

0.988

0.99

0.992

0.994

0.996

0.998

1

1.002

1.004

1.006

1.008

1.01

1.012

103Rh

103Rh

155Gd

155Gd

149Sm

149Sm

Mixt4

keff


Fig. 15. keff for “Elementary Dissolution” type experiments (HTC rods in central tank). Codes and library

effect.

41

0.988

0.99

0.992

0.994

0.996

0.998

1

1.002

1.004

1.006

1.008

1.01

1.012

2967 2968 2969 2970 2971 2972 2973

Experiment Number

keff

APOLLO2-MORET 4 - JEF2.2



300 g/l 100 g/l

Fig. 16. keff for “Global Dissolution” (UO2 rods in DUN solution). Library effect.

42

0.988

0.99

0.992

0.994

0.996

0.998

1

1.002

1.004

1.006

1.008

1.01

1.012

2974 2975 2976 2977 2978 2979 2980

Experiment Number

keff

APOLLO2-MORET 4 -JEF2.2



300 g/l 92 g/l

Fig. 17. keff for “Global Dissolution” experiments (HTC rods in a DUN +FPs solution). Library effect.

43

0.988

0.99

0.992

0.994

0.996

0.998

1

1.002

1.004

1.006

1.008

1.01

1.012

2967 2968 2969 2970 2971 2972 2973

Experiment Number

keff

APOLLO2-MORET 4 - JEF2.2TRIPOLI4 -JEF2.2SCALE5.1 - ENDF/B-VI.r7SCALE5.1 - ENDF/B-V

300 g/l 100 g/l

Fig. 18. keff for “Global Dissolution” type experiments (UO2 rods in DUN solution). Code and library effect

44

0.988

0.99

0.992

0.994

0.996

0.998

1

1.002

1.004

1.006

1.008

1.01

1.012

2974 2975 2976 2977 2978 2979 2980

Experiment Number

keff

APOLLO2-MORET 4 -JEF2.2

TRIPOLI4 - JEF2.2

SCALE5.1 - ENDF/B-VI.r7

SCALE5.1 - ENDF/B-V

300 g/l 92 g/l

Fig. 19. keff for “Global Dissolution” experiments (HTC rods in DUN + FPs solution). Code and library

effect.

45

1

6

11

16

21

26

0 50 100 150 200 250 300 350 400 450 500

Concentration (g/l)

10

3R

h w

ort

h (

%)

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

Sensitivity (%/%)

Worth - P type (2834)

Worth - ED type (2925)

Sensitivity - P type (2834)

Sensitivity - ED type (2925)

Fig. 20. 103Rh worth and eigenvalue sensitivity to 103Rh atomic density vs FP concentration.

46

0.E+00

1.E-01

2.E-01

3.E-01

4.E-01

5.E-01

6.E-01

7.E-01

8.E-01

9.E-01

1.E+00

1.E-09 1.E-08 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02

Energy, MeV

No

rmal

ized

cu

mu

late

d a

bso

rpti

on

rat

e

103Rh

133Cs

143Nd

152Sm

149Sm

155Gd

Fig. 21. Fission Products Cumulated Absorption Rate in a mixture.

47

Fig. 22. Integrated sensitivity coefficients for major actinides, hydrogen, 103Rh and 133Cs.

-0.150

-0.100

-0.050

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.350

133Cs

103Rh

235U

1H

238U

133Cs

103Rh

235U

1H

238U

133Cs

235U

1H

238U

239Pu

240Pu

∆∆ ∆∆Keff (%)

TSUNAMI-3D integral sensitivity (ENDF/B-VI evaluation)SCALE5.1 (ENDF/B-VI evaluation) direct perturbation

P type ED type GD type

48

-0.050

-0.045

-0.040

-0.035

-0.030

-0.025

-0.020

-0.015

-0.010

-0.005

0.000

Rh103

Rh103

Cs133

Cs133

Cs133

Cs133

Ndnat

Sm152

Sm152

Gd155

Gd155

Mixture

Sm149

Sm149

Cs133

Rh103

Rh103

Rh103

Ndnat

Sm149

Sm149

Sm152

Gd155

Gd155

Mixture 1

Mixture 1

Gd155

Rh103

Sm149

Sm149

Mixture - Global Disso

Fission Product

Sensitivity (%/%)

APOLLO2-MORET 4

TSUNAMI-3D (SCALE5.1)

SCALE5.1 - direct perturbation

PHYSICAL

ELEMENTARY DDISSOLUTION

Fig. 23. Fission products: integrated sensitivities for three types of experiments.

-0.060

-0.050

-0.040

-0.030

-0.020

-0.010

0.000

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

Energy, eV

Sensitivity per unit of lethargy (%/%

)

1

10

100

1000

10000

Cross section, barn

Sensitivity for P type (2834)Sensitivity for ED type (2925) Total cross section

Fig. 24. 103Rh: Total cross section and sensitivity profiles for physical and elementary dissolution type experiments.

49

-0.05

-0.045

-0.04

-0.035

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

Energy, eV

Sensitivity per unit of lethargy (%/%)

1

10

100

1000

10000

Cross section, barn

Sensitivity for P type (2809)Sensitivity for ED type (2875)Total cross section

Fig. 25. 133Cs: total cross section and sensitivity profiles for physical and elementary dissolution type experiments.

50

-0.018

-0.016

-0.014

-0.012

-0.01

-0.008

-0.006

-0.004

-0.002

0

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

Energy, eV


)

1

10

100

1000

10000

100000

1000000

10000000

Cross section, barn

Sensitivity for P type (2828)

Sensitivity for ED type (2926)

Total cross section

Fig. 26. 155Gd: Total cross section and sensitivity profiles for physical and elementary dissolution type

experiments.

51

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

1.E

-05

1.E

-04

1.E

-03

1.E

-02

1.E

-01

1.E

+00

1.E

+01

1.E

+02

1.E

+03

1.E

+04

1.E

+05

1.E

+06

Energy, eV


)

0.1

1

10

100

1000

10000

100000

Cross section, barn



Total cross section

Fig. 27. 152Sm: total cross section and sensitivity profiles for physical and elementary dissolution type

experiments.

52

-0.04

-0.035

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

Energy, eV

Sensitivity per unit of lethargy (%/%)

1

10

100

1000

10000

100000

1000000

10000000

Cross section, barn



Total cross section

Fig. 28. 149Sm: total cross section and sensitivity profiles for physical and elementary dissolution type

experiments.

53

-0.005

-0.0045

-0.004

-0.0035

-0.003

-0.0025

-0.002

-0.0015

-0.001

-0.0005

0

1.E

-05

1.E

-04

1.E

-03

1.E

-02

1.E

-01

1.E

+00

1.E

+01

1.E

+02

1.E

+03

1.E

+04

1.E

+05

1.E

+06

1.E

+07

1.E

+08

Energy, eV

Sensitivity per unit of leth

arg

y (%/%

)

0.1

1

10

100

1000

10000

Cro

ss section, barn



Total cross section

Fig. 29. 143Nd: total cross section and sensitivity profiles for physical and elementary dissolution type

experiments.

54

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

2805

2807

2809

2811

2813

2815

2817

2819

2821

2823

2825

2827

2829

2831

2833

2835

2837

2839

2841

2843

2845

2847

2849

Experiment Number

k eff

FP-k

eff

No

FP (

%)

103Rh 133Cs 149Sm 152Sm 155Gd Nd

Fig. 30. Fission Products bias for “Physical” type experiments (results of APOLLO2-MORET 4 computation with JEF2.2 based library)

55

Fig. 31. keff difference sensitivity for “Physical” type configurations with (#2809) and without

(#2803) 133Cs

56

TABLE I Fission Products Experimental Programme Configurations

Type PHYSICAL ELEMENTARY DISSOLUTION GLOBAL DISSOLUTION

Date (Nov 1998 - June 1999)

(Sept. 2000 – Nov. 2001)

(Sept. 2000 – March 2002)

(Nov-Dec. 2003 and April 2004)

Driver array in water 1.3-cm square pitch array of U(4.738 % 235U)O2 rods 23 × 21 to 27 × 27

Central tank 6.2 × 6.2 cm2 14.35 × 14.35 cm2

with 1.271-cm square pitch array of U(4.738 % 235U)O2 or HTC rods

N/A UO2 HTC UO2 HTC

UO2 rods in 1.3-cm

square pitch array

26 x 26 or 23 x 23

HTC rods in 1.6-cm

square pitch array

44 × 44 Fuel rods → Solution ↓ Number of experiments

Water + HNO3 13 26 7 8 3

Water + Boron 1

FP solution Water + HNO3 Depleted Uranyl Nitrate (DUN)

Non FP 2 2 7 3 149

Sm 2 5 2 1 103Rh 4 5 2 133Cs 10 5 natNd 2 2 152Sm 5 2 155Gd 5 3 2

Mixture 3 6 1 2 4

Sub-total 45 54 14 10 8 7 7

Total 45 68 18 14 General Total 145

57

TABLE II

Characteristics of HTC and UO2 rods.

Characteristic Value Uncertainty (1σ)

HTC rods Density (g/cm3) 10.333 0.445

Stoichiometry O/(U+Pu) (atomic ratio)

1.9971 0.005

Pu/(U+Pu) (wt. %) 1.104 0.060 Outer clad diameter (cm) 0.94958 0.00058 Fuel pellet diameter (cm) 0.7940 0.0058

Isotope Weight % Uncertainty 234U 0.013 < 5.10-4 235U 1.570 < 5.10-4 236U 0.001 < 5.10-4 238U 98.416 < 5.10-4 238Pu 1.304 < 5.10-4 239Pu 59.227 < 5.10-4 240Pu 24.333 < 5.10-4 241Pu 10.076 < 5.10-4 242Pu 5.056 < 5.10-4

241Am 1.432 < 5.10-4 UO2 rods

Density (g/cm3) 10.38 0.22 Stoichiometry O/U

(atomic ratio) 2.000 0.001

Outer clad diameter (cm) 0.94924 0.00044 Fuel pellet diameter (cm) 0.78919 0.00176

Isotope Weight % Uncertainty 234U 0.0302 0.0005 235U 4.7376 0.0020 236U 0.1362 0.0005 238U 95.0959 0.0010

58

TABLE III

Major Contributors and Overall Maximum Experimental Uncertainty for “Physical” type, “Elementary Dissolution” type and “Global Dissolution” type Experiments

Programme type PHYSICAL ELEMENTARY DISSOLUTION

GLOBAL DISSOLUTION

Component of uncertainty ↓ 1σ Uncertainty (%)

UO2 and HTC rods

Isotopic content 0.010 0.033 0.005 Rods density 0.025 0.025 0.025 Oxide impurities 0.031 0.035 0.058 Pellet diameter 0.025 0.025 0.005 Inner clad diameter 0.011 0.023 0.007 Outer clad diameter 0.025 0.025 0.132

Physical data

Temperature 0.012 0.012 0.003 Rods positioning (pitch + grid hole diameter)

0.034 0.020 0.006

Critical height 0.016 0.020 0.008

Fission Products

Concentration 0.001 0.006 0.010 Density 0.001 0.001 0.001 Total 0.067 0.075 0.147

59

TABLE IV

FPs Reactivity Worth

FP worth (pcm) Exp N° (Programme

Type) FPs

C(FP) g/l APOLLO2-

MORET 4 KENO V.a/ SCALE5.1

2835 (P) 103Rh 20 1737 1766 2811 (P) 133Cs 130 2169 1980 2817 (P) 133Cs 77 1387 1278 2823 (P) 152Sm 50 4510 4332

2826 (ED) 152Sm 20 3361 3112 2828 (P) 155Gd 0.2 2705 2752 2844 (P) Mixture N/A 2899 2923 2847 (P) 149Sm 0.2 3592 3496

2883 (ED) 103Rh 50 6241 6177 2925 (ED) 103Rh 20 3626 3677 2880 (ED) natNd 90 1568 1677 2897 (ED) 149Sm 0.4 6594 6470 2901 (ED) 152Sm 15 3522 3376 2929 (ED) 155Gd 0.15 3368 3286 2943 (ED) Mixture N/A 3541 3593 2912 (ED) 155Gd 0.4 3436 3430 2910 (ED) 103Rh 30 3206 3171 2915 (ED) 149Sm 0.2 3514 3539 2917 (ED) Mixture N/A 3436 3444 2964 (ED) 149Sm 0.2 2337 2228 2965 (ED) Mixture N/A 2831 2777 2977 (GD) Mixture N/A 4516 4281

* The FP concentrations have been rounded (protected data)

60

TABLE V

FP Worth in “Physical” type Experiment #2844

FP FP worth in

mixture (pcm) “Independent” FP worth (pcm)

103Rh 783 783 133Cs 617 623 155Gd 469 671 149Sm 658 993 152Sm 122 192 143Nd 150 338

Total (All)) 2799 3600

61

TABLE VI

FP worth in “Elementary Dissolution” type Experiment #2943

FP FP worth in

mixture (pcm) “Independent” FP worth (pcm)

133Cs 638 638 103Rh 808 791 natNd 196 211 155Gd 657 687 149Sm 708 732 152Sm 543 593

Total (All) 3550 3652

62

TABLE VII

FP worth in “Global Dissolution” type Experiment #2977

FP FP worth in

mixture (pcm)

“Independent” FP worth

(pcm) 103Rh 140 140 133Cs 1118 1175 155Gd 1020 1058 149Sm 1251 1318 152Sm 60 61 natNd 617 694

Total (All) 4206 4446

63

TABLE VIII

keff Sensitivity for Nuclide Atomic Density or Total Cross Section (TSUNAMI-3D) (%/%)

Exp. N° (Programm

e Type) Isotope

APOLLO2-MORET 4 correlated sampling

(uncertainty)

SCALE5.1 direct

perturbation (uncertainty)

TSUNAMI-3D

(uncertainty)

2811 (P) 133Cs -0.0144 (1) -0.0151 (2) -0.0139 (6) 2834 (P) 103Rh -0.01800 (5) -0.0183 (2) -0.0186 (7)

2875 (ED) 133Cs -0.01992 (3) -0.0199 (2) -0.0209 (3) 2925 (ED) 103Rh -0.02817 (4) -0.0265 (2) -0.0295 (3) 2917 (ED) 133Cs -0.0040 (1) -0.0033 (2) -0.0039 (8) 2834 (P) 235U 0.1536 (3) 0.1551 (2) 0.1555 (5)

2925 (ED) 235U 0.1616 (1) 0.1549 (2) 0.1541 (7) 2977 (GD) 235U 0.1679 (1) 0.1658 (2) 0.1664 (3) 2834 (P) 1H - 0.2895 (2) 0.2911 (3)

2925 (ED) 1H - 0.3143 (2) 0.3227 (3) 2977 (GD) 1H - 0.1253 (2) 0.1297 (1) 2834 (P) 238U -0.0736 (3) -0.0691 (2) -0.0677 (6)

2925 (ED) 238U -0.0808 (2) -0.0773 (2) -0.0666 (3) 2977 (GD) 238U -0.1198 (4) -0.1165 (2) -0.1099 (9) 2977 (GD) 239Pu 0.1266 (4) 0.1227 (2) 0.1229 (2) 2977 (GD) 240Pu -0.0432 (1) -0.0442 (2) -0.0453 (3)

64

TABLE IX

keff Results and FP Reactivity Worth for “Physical” Type Experiments (σcalc = 0.00030)

APOLLO2-MORET 4 TRIPOLI-4.3 SCALE5.1 Case

Exp. N°

C(FP)* g/l Solution JEF2.2 JEF3.1 ENDF/B-VI.4

FP worth (pcm) JEF2.2 ENDF/B-VI.7

1 2833 40 103Rh 1.00300 1.00526 0.99855 3124 1.00000 0.99268

2 2834 40 103Rh 1.00363 1.00567 0.99966 2798 1.00109 0.99152 3 2835 20 103Rh 1.00331 1.00439 0.99867 1793 0.99887 0.99175

5 2837 20 103Rh 1.00266 1.00478 0.99762 1953 0.99919 0.99141

6 2805 130 133Cs 1.00176 1.00236 0.99800 2147 0.99907 0.99171

7 2806 130 133Cs 1.00029 1.00262 0.99812 2294 0.99895 0.99160

8 2811 130 133Cs 1.00104 1.00278 0.99770 2169 0.99990 0.99118

9 2807 80 133Cs 1.00091 1.00276 0.99775 1501 0.99914 0.99099

10 2808 80 133Cs 1.00079 1.00274 0.99794 1490 0.99777 0.99129

11 2809 80 133Cs 1.00206 1.00343 0.99723 1448 0.99910 0.99118

12 2810 80 133Cs 1.00183 1.00287 0.99857 1438 0.99918 0.99160 13 2812 80 133Cs 1.00255 1.00395 0.99781 1314 0.99929 0.99148

14 2817 80 133Cs 1.00150 1.00325 0.99856 1359 0.99945 0.99113

15 2818 80 133Cs 1.00154 1.00277 0.99766 1523 0.99894 0.99206

16 2821 120 natNd 1.00402 1.00529 1.00078 1470 0.99948 0.99209

17 2822 120 natNd 1.00404 1.00553 1.00088 1877 0.99907 0.99152

18 2823 50 152Sm 1.00109 1.00237 0.99780 4474 0.99987 0.99151

19 2824 50 152Sm 1.00073 1.00203 0.99722 4555 0.99843 0.99175

20 2825 50 152Sm 1.00154 1.00273 0.99736 4654 0.99901 0.99145

21 2826 20 152Sm 1.00161 1.00319 0.99793 3361 1.00042 0.99235 22 2827 20 152Sm 1.00196 1.00224 0.99830 3358 0.99932 0.99264

23 2828 0.2 155Gd 1.00259 1.00415 0.99883 2705 1.00118 0.99115

24 2829 0.2 155Gd 1.00256 1.00346 0.99862 2747 0.99899 0.99118

25 2830 0.2 155Gd 1.00167 1.00321 0.99817 2880 0.99967 0.99108

26 2831 0.1 155Gd 1.00287 1.00369 0.99825 1932 0.99800 0.99190

27 2832 0.1 155Gd 1.00331 1.00426 0.99871 1737 0.99851 0.99176

28 2844 Mixt. 1.00294 1.00366 0.99981 2899 1.00000 0.99190

29 2845 Mixt. 1.00296 1.00391 0.99870 - 0.99894 0.99169

30 2846

103Rh 7 133Cs 30

155Gd 0.05 152Sm 1.5

149Sm 0.04 natNd 25

Mixt. 1.00254 1.00395 0.99901 - 0.99963 0.99137

31 2847 0.2 149Sm 1.00198 1.00317 0.99865 3592 0.99834 0.99198

32 2848 0.1 149Sm 1.00247 1.00370 0.99847 2246 0.99903 0.99132

34 2820 0.9 natB 1.00332 1.00544 0.99953 1.00009 0.99045

35 2803 HNO3 1.00215 1.00391 0.99842 0.99819 0.99031

36 2804 HNO3 1.00108 1.00270 0.99758 0.99709 0.99031

* The real concentrations are close to the given values

65

TABLE IX (cont’d)

keff Results and FP Reactivity Worth for “Physical” Type Experiments (σcalc = 0.00030)

APOLLO2-MORET 4 TRIPOLI-4.3 SCALE 5.1 Case Exp. N° Solution

JEF2.2 JEF3.1 ENDF/B-

VI.4 JEF2.2 ENDF/B-VI.7

37 2813 HNO3 1.00280 1.00509 0.99910 0.99910 0.99072

38 2814 HNO3 1.00303 1.00446 0.99901 0.99964 0.99146

39 2815 HNO3 1.00241 1.00401 0.99942 0.99998 0.99202

40 2816 HNO3 1.00242 1.00472 0.99887 0.99888 0.99151

41 2838 HNO3 1.00320 1.00448 0.99914 0.99862 0.99148

42 2839 HNO3 1.00300 1.00413 0.99815 0.99903 0.99064

43 2840 HNO3 1.00341 1.00447 0.99860 0.99930 0.99130

44 2841 HNO3 1.00303 1.00418 0.99895 0.99981 0.99138

45 2842 HNO3 1.00283 1.00392 0.99831 0.99861 0.99151

46 2843 HNO3 1.00264 1.00426 0.99909 0.99970 0.99159

47 2849 HNO3 1.00295 1.00449 0.99874 0.99936 0.99194

66

TABLE X

keff Results and FP Reactivity Worth for “Elementary Dissolution” Type Experiments – UO2 Rods in Central Tank (σcalc = 0.00030)


Experiment N°

Concentration* (g/l)

Solution JEF2.2 JEFF3.1 ENDF/B-VI.4

FP worth (pcm) JEF2.2 ENDF/B-VI.7

1 2875 110 133Cs 1.00397 1.00515 0.99990 2823 1.00033 0.99291 2 2876 110 133Cs 1.00354 1.00443 1.00063 2777 1.00137 0.99277 3 2877 110 133Cs 1.00265 1.00480 0.99986 2901 1.00078 0.99279 4 2878 110 133Cs 1.00291 1.00377 0.99945 2876 1.00069 0.99284 5 2879 110 133Cs 1.00307 1.00483 0.99944 2876 0.99999 0.99264 6 2883 50 103Rh 0.99912 1.00205 0.99399 6241 0.99619 0.98928 7 2884 50 103Rh 0.99935 1.00131 0.99482 6322 0.99762 0.98862 8 2923 20 103Rh 0.99952 1.00109 0.99478 3399 0.99723 0.98922 9 2924 20 103Rh 0.99886 1.00185 0.99426 3554 0.99792 0.98907 10 2925 20 103Rh 0.99933 1.00100 0.99416 3626 0.99664 0.98919 11 2880 90 natNd 1.00398 1.00464 0.99945 1568 1.00057 0.99227 12 2881 90 natNd 1.00416 1.00479 1.00030 1599 0.99800 0.99248 13 2897 0.4 149Sm 1.00426 1.00237 1.00054 6594 1.00080 0.99393 14 2898 0.4 149Sm 1.00417 1.00220 1.00003 6502 1.00091 0.99309 15 2928 0.15 149Sm 1.00188 1.00335 0.99812 3484 1.00037 0.99149 16 2929 0.15 149Sm 1.00379 1.00275 0.99920 3368 1.00124 0.99324 17 2931 0.15 149Sm 1.00237 1.00207 0.99851 3370 1.00005 0.99205 18 2901 15 152Sm 1.00309 1.00386 0.99881 3522 1.00139 0.99254 19 2902 15 152Sm 1.00323 1.00383 0.99895 3494 1.00184 0.99312 20 2900 0.8 155Gd 1.00588 1.00620 1.00195 6933 1.00342 0.99475 21 2926 0.4 155Gd 1.00388 1.00467 1.00008 3762 1.00042 0.99262 22 2927 0.4 155Gd 1.00374 1.00417 0.99826 3805 0.99693 0.99286 23 2943 Mixt1 1.00294 1.00380 0.99868 3541 1.00148 0.99141 24 2944 Mixt1 1.00320 1.00420 0.99943 3652 0.99985 0.99280 25 2939 Mixt2 1.00548 1.00574 1.00226 7893 1.00291 0.99487 26 2940 Mixt2 1.00515 1.00515 1.00218 7894 1.00749 0.99462 27 2937 Mixt3 1.00706 1.00581 1.00269 7951 1.00389 0.99573 28 2938 Mixt3 1.00688 1.00604 1.00242 8003 1.00363 0.99291 31 2872 HNO3 1.00193 1.00199 0.99618 0.99952 0.98563 32 2873 HNO3 1.00216 1.00271 0.99624 0.99927 0.99016 33 2885 HNO3 1.00228 1.00376 0.99649 0.99859 0.99017 34 2886 HNO3 1.00127 1.00209 0.99556 0.99936 0.98899 35 2887 HNO3 1.00134 1.00238 0.99588 0.99954 0.98950 36 2888 HNO3 1.00165 1.00189 0.99594 0.99874 0.98968 37 2889 HNO3 1.00104 1.00265 0.99570 0.99951 0.98933 38 2890 HNO3 1.00131 1.00172 0.99574 0.99901 0.98924 39 2891 HNO3 1.00119 1.00261 0.99613 0.99809 0.98952 40 2892 HNO3 1.00084 1.00274 0.99637 0.99803 0.98952 41 2893 HNO3 1.00154 1.00222 0.99566 0.99951 0.98872 42 2894 HNO3 1.00033 1.00120 0.99547 0.99855 0.99155 43 2895 HNO3 1.00027 1.00234 0.99612 0.99867 0.98766 44 2903 HNO3 1.00142 1.00229 0.99618 0.99949 0.98945 45 2904 HNO3 1.00065 1.00116 0.99534 0.99879 0.98656 46 2905 HNO3 1.00104 1.00202 0.99647 0.99878 0.98793 47 2932 HNO3 1.00062 1.00249 0.99601 0.99946 0.98933

67


TABLE X (cont’d)

keff Results and FP Reactivity Worth for “Elementary Dissolution” Type Experiments – UO2 Rods in Central Tank (σcalc = 0.00030)


Experiment N°

Solution JEF2.2 JEFF3.1 ENDF/B-VI.4 JEF2.2 ENDF/B-VI.7

48 2933 HNO3 1.00131 1.00216 0.99658 0.99819 0.98964 49 2934 HNO3 1.00101 1.00256 0.99694 0.99787 0.98990 50 2936 HNO3 1.00146 1.00198 0.99677 0.99880 0.98807 51 2941 HNO3 0.99976 1.00064 0.99400 1.00004 0.98597 52 2942 HNO3 1.00027 1.00165 0.99439 0.99829 0.98592 53 2951 HNO3 1.00129 1.00176 0.99593 0.99850 0.98922 54 2952 HNO3 1.00153 1.00255 0.99643 1.00031 0.98980

68

TABLE XI keff Results and FP Reactivity Worth for “Elementary Dissolution” Type Experiments –

HTC Rods in Central tank (σcalc = 0.00030) APOLLO2-MORET 4 TRIPOLI-4.3 SCALE5.1

Case Experiment

N° Concentration*

(g/l) Solution

FP worth (pcm) JEF2.2 JEFF3.1 ENDF/B-VI.4 JEF2.2 ENDF/B-VI.7

55 2910 30 103Rh 3238 0.99936 1.00306 0.99584 0.99931 0.98991

56 2911 30 103Rh 3169 0.99913 1.00112 0.99484 0.99721 0.99001 57 2912 0.4 155Gd 3369 1.00368 1.00443 0.99906 1.00127 0.99379

58 2913 0.4 155Gd 3437 1.00241 1.00379 0.99901 1.00038 0.99326

59 2915 0.2 149Sm 3509 1.00227 1.00299 0.99840 1.00134 0.99265

60 2916 0.2 149Sm 3556 1.00243 1.00245 0.99898 1.00094 0.99290

61 2917 Mixt4 3457 1.00250 1.00342 0.99939 1.00072 0.99377

62 2906 HNO3 1.00128 1.00266 0.99765 0.99995 0.99214

63 2907 HNO3 1.00074 1.00224 0.99650 0.9992 0.99214

64 2908 HNO3 1.00024 1.00278 0.99671 1.00021 0.99077

65 2918 HNO3 1.00082 1.00185 0.99571 1.00018 0.99045

66 2919 HNO3 1.00129 1.00239 0.99602 1.00035 0.99050

67 2920 HNO3 1.00094 1.00147 0.99643 0.99964 0.99042

68 2921 HNO3 1.00136 1.00299 0.99663 0.99974 0.99071


69

TABLE XII

keff Results and FP Reactivity Worth of “Elementary Dissolution” Type Experiments – UO2 Rods in DUN Solution in the Central Tank (σcalc = 0.00030)

APOLLO2-MORET 4 TRIPOLI-

4.3f SCALE5.1

Case Experiment N°Concentration*

(g/l) Solution

FP worth (pcm) JEF2.2 JEFF3.1 ENDF/B-VI.4 JEF2.2 ENDF/B-VI.7

1 2960 396 DUN-1 1.00295 1.00404 0.99839 1.00152 0.99240 2 2961 396 DUN-1 1.00325 1.00359 0.99759 1.00051 0.99269 3 2962 396 DUN-2 1.00186 1.00323 0.99724 1.00097 0.99288 4 2963 396 DUN-2 1.00180 1.00255 0.99782 1.00120 0.99305 5 2964 395/0.2 (Sm) DUN+Sm 2291 1.00304 1.00347 0.99952 1.00126 0.99450 6 2965 Mixt5 2841 1.00240 1.00417 0.99960 1.00226 0.99380

7 2966

DUN 125 103Rh 3 133Cs 15 natNd 15

149Sm 0.05 152Sm 3

155Gd 0.05

Mixt5 2730 1.00349 1.00426 0.99947 1.00146 0.99411


70

TABLE XIII

keff Results and FP Reactivity Worth for “Global Dissolution” Type Experiments –

UO2 Rods in DUN Solution. (σcalc = 0.00030) APOLLO2-MORET 4 TRIPOLI-4.3 SCALE5.1

Case Experiment

N° C(DUN)*

(g/l) Solution

JEF2.2 JEFF3.1 ENDF/B-VI.4 JEF2.2 ENDF/B-VI.7

1 2967 300 DUN 0.99999 1.00103 0.99479 0.99699 0.99010

2 2968 300 DUN 1.00114 1.00215 0.99703 0.99645 0.99023

3 2969 300 DUN 1.00165 1.00179 0.99638 0.99573 0.99070

5 2970 92 DUN 1.00202 1.00206 0.99662 0.99884 0.99090

6 2971 92 DUN 1.00136 1.00275 0.99613 0.99812 0.99080

7 2972 92 DUN 1.00143 1.00264 0.99604 0.99906 0.99169

8 2973 92 DUN 1.00100 1.00187 0.99626 0.99833 0.99051


71

TABLE XIV

keff results and FP reactivity worth for “Global Dissolution” type experiments – HTC rods in a uranyl nitrate solution with or without FP. (σcalc = 0.00030)


Experiment N°

C(DUN)* g/l

Solution FP

worth (pcm) JEF2.2 JEFF3.1

ENDF/B-VI.4

JEF2.2 ENDF/B-VI.7

1 2974 300 DUN - 1.00427 1.00563 1.00168 1.00040 0.99829 2 2975 300 DUN - 1.00399 1.00492 1.00167 1.00128 0.99853 3 2976 300 DUN - 1.00474 1.00532 1.00159 1.00073 0.99861 4 2977 92 Mixt. 4516 1.00438 1.00691 1.00458 1.00172 0.99932 5 2978 92 Mixt. 4273 1.00607 1.00603 1.00504 1.00202 0.99959 6 2979 92 Mixt. 4457 1.00467 1.00609 1.00536 1.00178 0.99890 7 2980 92 Mixt. 4459 1.00469 1.00534 1.00420 1.00215 1.00009


Fission Products Experimental Programme: Validation and ... · Nicolas Leclaire, Tatiana Ivanova, Eric Létang, Emmanuel Girault, Jean-François Thro Abstract ... 133 Cs, nat Nd,

Documents