A burn-up module for application in fuel performance codes ......The extension of the model to Lead Cooled Fast Reactors (e.g., Alfred, Myrrha) of interest for Gen-IV and for INSPYRE

A. Cechet, S. Altieri, T. Barani, L. Cognini, S. Lorenzi, D. Pizzocri, L. LuzziPolitecnico di Milano, Department of Energy, Nuclear Reactors Group

PAUL SCHERRER INSTITUTE – 05.11.2019NuFuel – MMSNF Workshop

A burnup model for application in fuel performance codes: methodology, assessment and verification for MOX fuel in

thermal and fast neutron spectra

• Why burnup module?

• Statement of the problem

• Methodology

• Assessment and Verification

• Conclusions and future developments

2

OUTLINE

3

Helium behaviorFundamental to assess the fuel performance • Gaseous Swelling• Gas Release

Actinides evolutionImpact on the evolution of- power distribution in the fuel pin- thermal and mechanical properties - isotope redistribution

WHY BURNUP MODULE?

• Evaluation of the local concentrationof relevantisotopes

• Evaluation of the helium source to be included in the fission gas model

State-of-the-art depletion software(SCALE, MONTEBURNS, SERPENT)• Complete• Cross-sections libraries specific to the

fuel material/reactor type combination• Long computational time

Novel approach:• Exploit the high-fidelity results from depletion codes• Short computational time• Adaptability to any fuel-reactor combination

STATEMENT OF THE PROBLEM

0D stand-alone meso-scale code developed at PolimiGoal: model fuel behavior at grain scale • Designed for coupling with Fuel Performance Code• Burnup module to assess the evolution of actinides

Fuel Performance Codes• Short computational time• Depletion calculation

oversimplified

4

https://gitlab.com/poliminrg/sciantix

METHODOLOGY

ONLINE

OFFLINE

SERPENTSIMULATION

SCIANTIXSIMULATION

5

METHODOLOGY

ONLINE

OFFLINE

SERPENTSIMULATION

Average cross sections�𝜎𝜎(𝑖𝑖, 𝑏𝑏𝑏𝑏, 𝑒𝑒0)

0 5 10 15

5% 5.17 5.02 5.04 5.08 ...

6% 4.87 4.73 4.74 4.76 ...

7% 4.63 4.52 4.51 4.53 ...

8% 4.45 4.34 4.33 4.34 ...

Lookup Tables

SCIANTIXSIMULATION

Relevantsimulationcase

6

METHODOLOGY

ONLINE

OFFLINE

SERPENTSIMULATION


0 5 10 15

5% 5.17 5.02 5.04 5.08 ...

6% 4.87 4.73 4.74 4.76 ...

7% 4.63 4.52 4.51 4.53 ...

8% 4.45 4.34 4.33 4.34 ...

Lookup Tables

Bateman Equations

SCIANTIXSIMULATION



Interpolator

7

METHODOLOGY

ONLINE

OFFLINE

SERPENTSIMULATION


0 5 10 15

5% 5.17 5.02 5.04 5.08 ...

6% 4.87 4.73 4.74 4.76 ...

7% 4.63 4.52 4.51 4.53 ...

8% 4.45 4.34 4.33 4.34 ...

Lookup Tables

Bateman Equations

SCIANTIXSIMULATION



Comparison

Interpolator

8

METHODOLOGY

Nuclides evolution

The nuclides concentration evolution

with burnup, to be used as high-

fidelity results for the sake of

verification (23 nuclides)

cUranium


0 5 10 15

5% 5.17 5.02 5.04 5.08 ...

6% 4.87 4.73 4.74 4.76 ...

7% 4.63 4.52 4.51 4.53 ...

8% 4.45 4.34 4.33 4.34 ...

Lookup Tables


cPlutonium

cNeptunium

cAmericium

cCurium

234 • 235 • 236 • 237 • 238

237 • 238 • 239

238 • 239 • 240 • 241 • 242 • 243

241 • 242 • 242m • 243 • 244

242 • 243 • 244 • 245

SERPENTSIMULATION

OFFLINE

9Helium

c

METHODOLOGY

Cross Sections

Average microscopic cross sections,

selected for specific reactions, specific

isotopes representing the training data for

the burnup model

Reactions: fission, capture,

(n,2n),(n,3n),(n,α)

SERPENTSIMULATION


0 5 10 15

5% 5.17 5.02 5.04 5.08 ...

6% 4.87 4.73 4.74 4.76 ...

7% 4.63 4.52 4.51 4.53 ...

8% 4.45 4.34 4.33 4.34 ...

Lookup Tables


cCross section Lookup Table to be

implemented in the model

OFFLINE

10

METHODOLOGY

0 5 10 15

5% 5.17 5.02 5.04 5.08 ...

6% 4.87 4.73 4.74 4.76 ...

7% 4.63 4.52 4.51 4.53 ...

8% 4.45 4.34 4.33 4.34 ...

Lookup Tables

Bateman Equations

SCIANTIXSIMULATION


Interpolator

ONLINE11

The cross section values are collected in lookup tables in function of the enrichment, the burnup, the target isotope, and the nuclear reaction

const double xsec_capt_table_MOX_PWR[23][6][31]={/*U234*/{/*5.0 %*/ {17.6318, 16.9942, 16.4351, 16.2394, ...},/*6.0 %*/ {17.1904, 16.4657, 16.0427, 15.7761, ...},/*7.0 %*/ {16.6601, 16.0613, 15.6437, 15.3129, ...},/*8.0 %*/ {16.2361, 15.6615, 15.3301, 14.9894, ...},/*9.0 %*/ {15.9639, 15.4080, 15.0226, 14.6763, ...},/*10.0 %*/ {15.6461, 15.1485, 14.6701, 14.3972, ...}},/*U235*/{/*5.0 %*/ {5.1726, 5.0292, 5.0496, 5.0846, ...},/*6.0 %*/ {4.8709, 4.7389, 4.7426, 4.7675, ...},/*7.0 %*/ {4.6361, 4.5222, 4.5161, 4.5301, ...},/*8.0 %*/ {4.4525, 4.3446, 4.3381, 4.3418, ...},/*9.0 %*/ {4.3004, 4.1999, 4.1847, 4.1907, ...},/*10.0 %*/ {4.1693, 4.0760, 4.0667, 4.0626, ...}},/*U236*/{/*5.0 %*/ {8.7434, 8.4190, 8.1292, 7.9253, ...},/*6.0 %*/ {8.6177, 8.2958, 8.0090, 7.7583, ...},/*7.0 %*/ {8.4673, 8.1268, 7.9003, 7.6827, ...},/*8.0 %*/ {8.3140, 8.0433, 7.7865, 7.5616, ...},/*9.0 %*/ {8.2575, 7.9342, 7.6674, 7.3965, ...},/*10.0 %*/ {8.1114, 7.8409, 7.5072, 7.3169, ...}},...

METHODOLOGY

Interpolator tool allows for the calculation of the set of cross sections needed for an online simulation by interpolating the Lookup Table.

const double xsec_capt_table_MOX_PWR[23][6][31]={/*U234*/{/*5.0 %*/ {17.6318, 16.9942, 16.4351, 16.2394, ...},/*6.0 %*/ {17.1904, 16.4657, 16.0427, 15.7761, ...},/*7.0 %*/ {16.6601, 16.0613, 15.6437, 15.3129, ...},/*8.0 %*/ {16.2361, 15.6615, 15.3301, 14.9894, ...},/*9.0 %*/ {15.9639, 15.4080, 15.0226, 14.6763, ...},/*10.0 %*/ {15.6461, 15.1485, 14.6701, 14.3972, ...}},

ONLINELever rule performed on the areas

0 5 10 15

5% 5.17 5.02 5.04 5.08 ...

6% 4.87 4.73 4.74 4.76 ...

7% 4.63 4.52 4.51 4.53 ...

8% 4.45 4.34 4.33 4.34 ...

Lookup Tables

Bateman Equations

SCIANTIXSIMULATION

Interpolator

e0 = 5.3%

bu0 = 12 GWd/tU

e2 = 6%

bu2 = 15 GWd/tU

e1 = 5%

bu1 = 10 GWd/tU


12

METHODOLOGY

ONLINE

0 5 10 15

5% 5.17 5.02 5.04 5.08 ...

6% 4.87 4.73 4.74 4.76 ...

7% 4.63 4.52 4.51 4.53 ...

8% 4.45 4.34 4.33 4.34 ...

Lookup Tables

Bateman Equations

SCIANTIXSIMULATION

Interpolator


13

𝑑𝑑𝑁𝑁1𝑑𝑑𝑑𝑑

= �𝑖𝑖

𝜆𝜆𝑖𝑖𝑁𝑁𝑖𝑖 −�𝑖𝑖

𝜆𝜆𝑖𝑖𝑁𝑁1 −�𝑖𝑖

𝜎𝜎𝑖𝑖𝜙𝜙𝑁𝑁1 + �𝑖𝑖

𝜎𝜎𝑖𝑖𝜙𝜙𝑁𝑁𝑖𝑖

Α𝑐𝑐 1 = 𝑐𝑐[0]

𝐹𝐹𝐹𝐹 = �𝐼𝐼

𝑁𝑁𝐼𝐼[0]𝜎𝜎𝑓𝑓𝑖𝑖

𝜙𝜙 =𝐹𝐹𝐹𝐹 ∗ 𝜈𝜈𝐹𝐹𝐹𝐹

Bateman’s equations

Flux calculation

Effective fission probability

Time: implicit Euler scheme

A matrix: LU factorization(Numerical Methods, Prentice Hall, 1974)

Solver

ASSESSMENT AND VERIFICATION

Computational time for SCIANTIX comparable to the state-of-the-art FPC

This is a fundamental requirement for the effective coupling of the burnup model in fuel performance codes

14

SERPENT SCIANTIX TRANSURANUSIntel®Xeon® E5-2680 Intel®Celeron® n4100 Intel®Celeron® n4100

CPU usage 8 cores, 16 threads Single Core Single Core2.7 GHz 1 GHz 1 GHz

Execution Time 15.4 hours 0.3 sec 0.516 sec

15

ASSESSMENT AND VERIFICATION – CASE STUDIES

MOX/PWR MOX/SFR

Initial composition

Pu239 and U238

Enrichment steps

Pu239 from 5% to 10%, in 1% steps

Results at 5% Pu239

Burnup max: 150 𝐺𝐺𝐺𝐺𝐺𝐺𝑡𝑡𝑡𝑡𝑡𝑡

Burnup width 5 𝐺𝐺𝐺𝐺𝐺𝐺𝑡𝑡𝑡𝑡𝑡𝑡

Constant power density of 40 kW/kg

Initial composition

U235, U238

Pu238, Pu239, Pu240, Pu241, Pu242

Enrichment steps

Pu/HM from 20% to 40%, in 2% steps

Results at 20% Pu/HM

Burnup max: 200 𝐺𝐺𝐺𝐺𝐺𝐺𝑡𝑡𝑡𝑡𝑡𝑡

Burnup width 5 𝐺𝐺𝐺𝐺𝐺𝐺𝑡𝑡𝑡𝑡𝑡𝑡

Constant power density of 40 kW/kg

ASSESSMENT AND VERIFICATION - URANIUM

MOX/PWR MOX/SFR

• Good agreement between SCIANTIX and the reference: RMSE confined between 1% and3% for the MOX/PWR case and between 0.6% and 4% for the MOX/SFR case

• Comparable performance with TRANSURANUS (Version 2018)

16

ASSESSMENT AND VERIFICATION - NEPTUNIUM

MOX/PWR MOX/SFR

• 11% RMSE in MOX/PWR case and 40%in MOX/SFR case

17

ASSESSMENT AND VERIFICATION - PLUTONIUM

MOX/PWR MOX/SFR

• Good agreement between SCIANTIX and the reference: RMSE confined between 5% and 34% in MOX/PWR case and between 0.4% and 12% in MOX/SFR case

18

ASSESSMENT AND VERIFICATION - AMERICIUM

MOX/PWR MOX/SFR

• RMSE confined between 24% and 62% in the MOX/PWR case and between 20% and 30% in MOX/SFR case

19

ASSESSMENT AND VERIFICATION - CURIUM

MOX/PWR MOX/SFR

• Poor agreement between SCIANTIX and the reference due to error propagation in the cross sections: RMSE confined between 36% and 110% in the MOX/PWR case and between 24% and 70% in the MOX/SFR case

20

ASSESSMENT AND VERIFICATION - HELIUM

MOX/PWR MOX/SFR

• 21% RMSE in MOX/PWR case and 34% error in MOX/SFR case

21

22

ASSESSMENT AND VERIFICATION – OVERVIEW MOX/SFR

SCIANTIX

TRANSURANUS

Comparable performance with state-of-the-art Fuel Performance Code

Cm 0,2445 0,5035 0,4048 0,6826 1Am 0,2875 0,1929 0,8Pu 0,119 0,037 0,0048 0,0778 0,0056 0,6Np 0,395 0,4U 0,0427 0,0065 0,2He 0,3345 0

235 237 238 239 240 241 242 243 244 245 4

Cm 0,1191 0,3027 0,0428 0,4451 1Am 0,1287 0,1921 0,8Pu 0,0338 0,0097 0,0304 0,0076 0,0297 0,6Np 0,7782 0,4U 0,0257 0,0013 0,2He 0,1734 0

235 237 238 239 240 241 242 243 244 245 4

23

CONCLUSIONS

Computational times suitable for FPCs

Self-consistent model: good prediction of relevant nuclides profilesand Helium compared with SERPENT

The error with respect to the high-fidelity results is bounded in allthe considered burnup range

The methodology developed allows easily adapting the model for anyfuel/reactor combination

Results comparable with state-of-the-art approach (e.g., TUBRNP)

We implemented the burnup model in SCIANTIX

We assessed and verified the new burnup module for a selected set ofactinides

We developed a new methodology for burnup calculations whichcouples the properties of high-fidelity depletion codes and FPCs

The lookup table and SCIANTIX itself are open-source and thereforeavailable to the public

24

FUTURE DEVELOPMENTS

Coupling with Fission Gas Behavior models and Fuel Performance Codes

The extension of the model to Lead Cooled Fast Reactors (e.g., Alfred,Myrrha) of interest for Gen-IV and for INSPYRE H2020 Project to whichPolitecnico di Milano is participating

Complete the assessment of the model with intermediate enrichment stepsand inclusion of Fission Products (e.g., Iodine, Caesium, Molibdenum)

THANK YOU FOR YOUR KIND ATTENTION

This work has been partially supported by the ENEN+ project and from the Euratom research and training programme 2014-2018 through the INSPYRE

project under Grant Agreement No. 754329

Slide Number 1Slide Number 2Slide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Slide Number 25

Documents

A burn-up module for application in fuel performance codes ......The extension of the model to Lead Cooled Fast Reactors (e.g., Alfred, Myrrha) of interest for Gen-IV and for INSPYRE