Assessment of the MCNP-ACAB code system for burnup credit analyses

Transcription

1 Assessment of the MCNP-ACAB code system for burnup credit analyses N. García-Herranz, O. Cabellos, J. Sanz UPM - UNED International Workshop on Advances in Applications of Burnup Credit for Spent Fuel Storae, Transport, Reprocessin, and Disposition October 2009, Córdoba, Spain

2 Outline 1 Introduction 2 MCNP-ACAB code system 3 Propaation of uncertainties in Monte Carlo burn-up calculations Sources of uncertainties in a depletion calculation Uncertainty propaation by a brute force random samplin method Uncertainty propaation by a sensitivity method Uncertainty propaation by a hybrid Monte Carlo method 4 Validation 5 Conclusions and onoin work

3 Introduction Burn-up credit analyses are based on depletion calculations that provide an accurate prediction of spent fuel isotopic contents, followed by criticality calculations to assess k eff Different systems couplin a neutron transport code with an isotopic inventory code are bein applied: MONTEBURNS SCALE 5 MCNP ORIGEN NEWT KENO ORIGEN-S In order to have confidence in the results need of evaluatin uncertainties in isotopics for spent fuel and assess their potential impact on reactivity uncertainties in the basic data assumptions made in the calculation models

4 Introduction Many efforts in last years focused on investiatin the impact of the lare variety of reactor operatin conditions (fuel T, moderator/density T, burn-up profile, ) Our oal: to present the capabilities of the MCNP-ACAB system, which combines MCNP and the inventory code ACAB, as a suitable tool for burn-up credit calculations By means of ACAB capabilities, the system allows computin: Isotopic inventory dealin with all nuclear processes that can occur in a hih-burnup fuel reime MCNP ACAB Isotopic-related quantities useful for safety and waste manaement assesment (decay heat, neutron emission, radiotoxicity,...) Uncertainties in the prediction of the isotopic inventory as well as in the different inventory-related response functions

5 MCNP-ACAB code system ACAB Computational alorithm based on that ORIGEN Capability of treatin the possible decay transitions from round, first and second isomeric states The most updated nuclear data libraries can be easily processed: Nuclear reaction cross-section data : EAF2007, JEFF-3.1.1, Nuclear decay data : EAF2007, Fission product yields : JEFF-3.1.1, Uncertainty libraries : EAF2007/UN, Uncertainty propaation by two methodoloies: sensitivity and Monte Carlo Code widely validated aainst benchmarks, experiments and other depletion codes

6 MCNP-ACAB code system Methodoloy of couplin XS Library Temp. dependent ENDF/B-VII,... Others XS (T=300K): EAF2007,... XS Uncertainty: EAF2007,... Fission Yields: JEFF3.1.1,... DECAY EAF2007, JEFF3.1.1,... Libs. Decay heat, Waste Index,... MCNP (neutron transport calculation) φ(e) MCNP σ 1 N MCNP collapsin & linkae module Power t φ < γ > ACAB σ 1 N ACAB ACAB (isotopic inventory prediction) N i Decay heat Neutron emission...

7 Propaation of uncertainties in Monte Carlo burn-up calculations Sources of uncertainties in a depletion calculation dn dt = [ ] [ eff λ N σ ] ΦN A N = + N ( eff ) λ, σ, Φ = N ( λ, σ, φ ( ), Φ) = N E Uncertainties in decay constants Uncertainties in one-roup effective xs eff σ = σ φ φ uncertainties in the evaluated nuclear xs data σ uncertainties in the flux spectrum obtained from the transport calculation φ (E) λ eff σ Uncertainties in the interated neutron flux Φ

8 Propaation of uncertainties in Monte Carlo burn-up calculations Sources of uncertainties in a depletion calculation The influence of all these sources should be investiated in order to understand and quantify the uncertainties associated with computer code predictions for spent fuel isotopics So far, we have only investiated the influence of uncertainties in activation cross sections and statistical errors in the neutron flux spectrum No uncertainties in decay constants, fission yields, No uncertainties in the interated neutron flux Uncertainties in the transport input data lead to smaller errors in the flux spectrum than the statistical fluctuations N ( eff ) λ, σ, Φ = N ( λ, σ, φ ( ), Φ) = N E Useful for burnup credit: e.. the actual environment conditions durin fuel irradiation will produce spectral shifts whose effects in the inventory could be evaluated in a similar way

9 Propaation of uncertainties in Monte Carlo burn-up calculations Brute force random samplin method Same sequence followed in the coupled calculation scheme to infer an error propaation procedure throuhout the time Simultaneous random samplin of the PDF of all the input parameters MCNP calculations φ Μ depletion M, with flux from MCNP M depletion E [ N ] M OUTPUT Sample of M vectors [N] of isotopic concentrations For each isotope, N i : PDF N i φ 1 E depletion 1, with flux from MCNP 1 [ N ] 1 depletion Burnup steps (S) INPUT PDF [ N ] 0 σ i

10 Propaation of uncertainties in Monte Carlo burn-up calculations Sensitivity/ Uncertainty Analysis (S/U) N i ( σ eff Procedure based on a first order Taylor series approach ) = N i ( ˆ σ eff ) + R N i σ j= 1 j ˆ eff σ ( eff eff σ ˆ σ ) +... j j Sensitivity coefficient ρ ij ε j error in the 1-G effective xs σ eff j j = σ φ ε j G G ( ) ( σ σ σ φ φ ) T T j ˆ j + j ˆ = φ ε σ + σ j ε φ = φ = 1 = 1 j errors due to uncertainties in the multiroup xs errors due to uncertainties in the multiroup flux spectrum [ ] COV [ ] σ j COV φ to be processed from the uncertainty libraries to be obtained from a sinle MCNP calculation

11 Propaation of uncertainties in Monte Carlo burn-up calculations Sensitivity/ Uncertainty N ( σ ) N ( σ ) S ε Analysis (S/U) eff ˆ eff var N S T T [ ] S S T [ ] T COV ˆ COV ˆ + ˆ [ COV ] ˆ eff 0 φ φ σ σ S j σ σ 0 0 j 0 φ j Propaates the multiroup xs uncertainties when there is no statistical flux errors Propaates statistical flux errors when there is no multiroup xs covariances σ 0 σ 0 φ 1 φ 2 σ 0 Best-estimated calculation σ 0 = (σ 10,, σ j0,, σ R0 ) MCNP [ N ] 0 [ N ] 1 E dn dσ 1 MCNP E [ N ] 2 dn dσ 2 Burnup OUTPUT Sensitivity matrix alon burnup depletion with flux from MCNP representative of step 1 depletion with flux from MCNP representative of step 2

12 Propaation of uncertainties in Monte Carlo burn-up calculations Hybrid Monte Carlo method Based on a random samplin a PDF is assined to each involved variable Propaatin uncertainties in XS Propaatin flux errors The PDF is assumed to be lonormal The flux fits a normal distribution σ j lo σ j 0 N(0, j ) φ N ( ˆ φ, sˆ ( ˆ φ ) We use simultaneous random samplin of all the PDFs involved in the problem to predict the concentration of each nuclide

13 Propaation of uncertainties in Monte Carlo burn-up calculations Hybrid Monte Carlo method [ N ] 0 [ N ] 1 σ 0 σ 0 ACAB step 1 ACAB step 2 Best-estimated calculation σ 0 = (σ 10,, σ j0,, σ m0 ) φ 1 MCNP φ 2 MCNP Burnup N(σ 0 )=(N 1,, N i,,n n ) Uncertainty calculations history 1 E history 1 E Burnup OUTPUT Sample of M vectors [N] of isotopic concentrations For each isotope, N i : PDF.. history M.. history M N i N i PDF σ 1 σ 1 <N i > N i (σ 0 ) N i σ m σ m

14 Validation PWR Pin Cell Benchmark Objective Validate MCNP-ACAB for hih-burnup applications Int. Conf. On Mathematics and Computation, M&C2005 CASMO-4 MCODE MONTE- BURNS MCNP-ACAB Studsvik MIT LANL UPM Transport Code Deterministic MCNP-4C MCNP-4C MCNP-4C Depletion Code - ORIGEN2.1 ORIGEN2.2 ACAB Couplin alorithm middletimestep predictorcorrector predictorcorrector middletimestep XS Libraries in transport calculations ENDF/B-6 JEF-2.2 ENDF/B-5 ENDF/B-6 + other evaluated libraries ENDF/B-5 ENDF/B-6 JENDL3.2 Libraries in burnup and decay calculations PWRUE.LIB DECAY.LIB

15 Validation BWR Atrium-10XP assembly Objective Comparison MCNP-ACAB vs MONTEBURNS to predict the isotopics alon burnup Int. Conress on Nuclear Fuel, TOPFUEL materials 60 burnup steps (up to 60 GWd/tU) histories Results Very similar isotopics for most of nuclides. Differences in some minor actinides due to isomeric transition treatment

16 Validation HTR Plutonium Cell Burnup Benchmark Objective Validation of several code systems to be used for the analysis of HTR up to unusually hih burn-up of 800 MWd/kHM Case C1 with 1.5 Pu per fuel element Annals of Nuclear Enery, 35, 2008 Main requested calculations Multiplication factor Isotopic composition durin the irradiation 1200 full power days Comparisons with NRG calculations NRG-WIMS NRG-OCTOPUS MCNP-ACAB Transport code WIMS8A MCNP-4C3 MCNP-4C3 Depletion code FISPACT ACAB Couplin alorithm Predictor step Middle-time step approach Burn-up steps XS libraries JEFF-2.2 based 172-roup JEFF-2.2 based point enery EAF4 UN library JEFF-3.1 / EAF2005 / JEFF-2.2 fission yields EAF2005 UN library

17 Validation HTR Plutonium Cell Burnup Benchmark Results with no uncertainties 1,2 Case C1-2nd eneration plutonium 1,1 1 0,9 0,8 k-infinity 0,7 0,6 0,5 0,4 0,3 NRG-FISPACT NRG-WIMS8A kinf-mcnp-acab 0,2 0, Burnup (MWd/kHM)

18 Validation HTR Plutonium Cell Burnup Benchmark Results with no uncertainties Table 1. Nuclide densities of some Pu isotopes as function of burn-up, takin NRG-WIMS as reference solution. For the other solutions the relative difference respect to WIMS is iven Isotopes Burn-up NRG-WIMS NRG-OCTOPUS MCNP-ACAB (MWd/kHM) (10 24 at /cm 3 ) (%) (%) Pu E E E E Pu E E E E Pu E E E E

19 Validation HTR Plutonium Cell Burnup Benchmark Results with uncertainties: Impact of xs uncertainties Table 2. Calculated uncertainties in the some Pu concentrations due to cross section uncertainties as function of burn-up Isotopes Burn-up NRG-OCTOPUS MCNP-ACAB (MWd/kHM) (%) (%) Pu Pu Pu

20 Validation HTR Plutonium Cell Burnup Benchmark Results with uncertainties: Impact of xs uncertainties and flux errors Different number of histories in MCNP calculations have been considered in order to have different qualities of the transport calculations, that is, flux spectrum relative errors of different order of manitude Table 3. Different MCNP calculations to compute the neutron flux spectrum Number of histories Relative error (%) in k-eff Order of manitude of the relative errors (%) in the flux tallies 5k (50 cycles with 100 histories/cycle) k (50 cycles with 1k histories/cycle) k (50 cycles with 10k histories/cycle)

21 Validation HTR Plutonium Cell Burnup Benchmark Results with uncertainties: Impact of xs uncertainties and flux errors Table 4. Relative error (%) of the final concentration computed by the Monte Carlo technique. Only due to XS errors Only due to flux errors Total errors Isotope Neutron histories Neutron histories Neutron histories 500k 50k 5k 500k 50k 5k 500k 50k 5k Pu Pu Pu Pu Pu Pu Table 5. Relative errors (%) of the final isotopic concentration computed by sensitivity. Isotope Only due to XS errors Only due to flux errors Total errors Neutron histories Neutron histories Neutron histories 500k 50k 5k 500k 50k 5k 500k 50k 5k Pu Pu Pu Pu Pu Pu

22 Conclusions An automated tool called MCNP-ACAB that links MCNP with our inventory code ACAB is presented It has been successfully applied to different benchmarks to predict the isotopic inventory in hih-burnup calculations It enables to estimate the impact of neutron cross section uncertainties as well as neutron flux statistical errors on the inventory in transport-burn-up combined problems, by usin either a sensitivity/uncertainty or a Monte Carlo propaation technique. Uncertainties in the predicted decay heat, neutron emission, can be obtained in a similar way Both uncertainty methodoloies are acceptable to deal with the benchmark problem. Even at very hih burn-ups, such as 800 MWd/kHM, non-linear effects are not important and the sensitivity method is useful to infer isotopic uncertainties Provided that the flux statistical deviations in the MC transport calculation do not exceed a iven value, the effect of the flux errors in the calculated isotopic inventory are neliible compared to the effect of the lare xs uncertainties available at present in the data files

23 Onoin work Validation of MCNP-ACAB for burnup credit analysis will be performed to quantify biases and uncertainties between analytic predictions and measured isotopics In order to estimate uncertainties, the methodoloies already implemented could be useful to achieve a better understandin of the influence of some assumptions made in the depletion calculations For example, it could be useful to evaluate the effects of the spectral shift due to 2D/3D environmental conditions durin fuel irradiation The influence of the other sources of uncertainties should also be evaluated and further developments in this area will be needed. This is the case of the effect of the normalization factor (i.e. effect of the power when held constant with time)

24 Thank you for your attention