Jaakko Leppänen Technical Research Centre of Finland VTT PROCESSES / Nuclear Energy

1. EMERALD1: A Systematic Study of Cross Section Library Based Discrepancies in LWR Criticality Calculations Jaakko Leppänen Technical Research Centre of Finland VTT PROCESSES / Nuclear Energy

2. Outline • Background • Calculations, tools and methods • Example results

3. Background • The MCNP Monte Carlo transport calculation code is routinely used at VTT for various reactor physics calculations. • A few years ago, some validation calculations on newly acquired cross section libraries showed relatively large cross section library based differences in criticality calculations. • It was decided to look into these differences more thoroughly, in order to find out what kind of uncertainties can be expected in common LWR calculations. • The main conclusions of a literature survey and preliminary comparison calculations were that the differences can be: 1) large, 2) systematic. • The study was continued and the differences investigated in a systematic manner.

4. Calculations • Instead of using realistic geometry models, an infinite LWR pin-cell lattice was chosen as the starting point for various reasons: • The simplicity allows straightforward and systematic study of the most significant sources of discrepancies. • The system parameters can be varied easily and the impacts on the results assessed. • Most of the comparison calculations encountered in the literature used realistic models – there was no need to duplicate the results. • Since the differences seemed to be strongly dependent on flux spectrum, fuel-to-moderator ratio was chosen as the main free parameter in the system. • Various modifications of the basic lattice were also studied (finite lattice with leakage, burnable and control absorber pins, high-burnup fuel, etc...).

5. Calculation tools • The comparison calculations were carried out using MCNP version 4C. • Burnup calculations were carried out using Monteburns 1.0 (MCNP-ORIGEN coupling). • The cross section data libraries were generated using the NJOY-99 nuclear data processing system from five evaluated nuclear data files: • ENDF/B-VI.8 (USA 2001) • JEFF-3.0 (NEA Databank 2002) • JENDL-3.3 (Japan 2002) • JEF-2.2 (NEA Databank 1993) • JENDL-3.2 (Japan 1994)

6. Calculation methods • In addition to a direct comparison of multiplication factors, an analytic method based on the detailed neutron balance of the system was used (next slide). • Only the most significant isotopes in the fuel were included in the study: • U-235, U-238 and O-16 in the regular lattice. • Gd isotopes in the modified lattice with burnable absorber pins. • Boron, Ag, In and Cd isotopes in the modified lattice with control rods. • U-236, the most significant plutonium and minor actinide isotopes and fission products in the regular lattices with high- and low-burnup fuel. • Various sensitivity studies were also performed on the results (fuel enrichment, fuel and moderator temperature, chemical shim, level of heterogeneity, unresolved resonance probability treatment).

7. The multiplication factor can be written as a function of simple source and sink terms. Each term consists of group-wisereaction rates that can be easilycalculated using MCNP. The impact of small differences in thegroup-wise reaction rates can beassessed by linearising k. Four energy groups were used in the calculations (thermal, resonance, unresolved/slowing-down, fast fission). Various significant contributions were separated from the overall differences. The total differences were predicted correctly by summing up the individual terms. Calculation methods

8. Example results Figure 1: Total reactivity differences between the libraries. Comparison to ENDF/B-VI.8.

9. Example results Figure 2: The most significantly contributing terms. Results of JEF-2.2 compared to ENDF/B-VI.8.

10. Example results, summary • The essential results can be summarised as follows: • There are significant cross section library based discrepancies in LWR criticality calculations. • These discrepancies are systematic and strongly dependent on the level of neutron moderation. • The most significant contributors are the fission and the radiative capture rates of U-235 and U-238, especially in the resonance region. • The compatibility between two libraries depends mostly on how well the individual discrepancies cancel each other out. • The differences are not particularly dependent on small deviations in system parameters (except fuel enrichment). • These discrepancies should be taken into account in all calculations as an additional source of uncertainty.

11. Thank you for your attention !