Fuel Cycle Analysis Methods for Advanced Reactor Concepts Yunlin Xu T.K. Kim D. Tinkler T.J. Downar

Purdue University

Sept. 12, 2001The 2001 ANS International Topic Meeting on Mathematics and Computation

ContentMotivationDepletion Code systemVerificationApplication on SBWRFurther Improvements

MotivationNERI/DOE projects at PurdueSBWR: evolutionary Generation III+

HCBWR: revolutionary Generation IV

We need a depletion code system for Neutonic designing: Fuel cycle analysis Safety analysis (throughout core life)

SBWR Reactor VesselTotal Height 24.6 mInternal Diameter6.0 mFuel Length 2.74 mChimney Height 9 m

SBWR Containment (GE)Gravity Driven Coolant System (GDCS)Automatic Depressurization System (ADS)Passive Containment Cooling System (PCCS)Suppression Pool

HCBWR--principleHCBWRFBRLWR

HCBWR- strategy

HCBWR- Purdue/BNL designTight lattice hard spectrum long cycle length

Thorium as fertile negative void coefficient all through the cycle

Basic Depletion Code system

HELIOSHELIOS is a comercial (Studsvik Scandpower) lattice physics code for solving Boltzmann equation with fine energy group, heterogeneous, two-Dimensional models of the fuel lattice

HELIOS uses consistent fuel assembly homogenization and energy group collapsing methods to produce few group cross sections at all fuel assembly conditions throughout the burnup cycle.

GENPXS and PMAXSGENPX read the outputs of HELIOS and generate PMAXS files

PMAXS tabulates the XSs of the base state and the derivatives or difference of XS of the branches and related information

Base state and BranchesBase stateBranches

PARCSPurdue Advanced Reactor Core Simulator

A Multidimensional Multigroup Reactor Kinetics Code Based on the Nonlinear Nodal Method

Under NRC Contract

T. J. Downaretc

PARCS ValidationBoiling Water Reactor OECD Peach Bottom Turbine Trip BenchmarkOECD Ringhalls Stability Benchmark (Ongoing) Pressurized Water Reactor:Reactivity Initiated Transients (CEA, etc.)OECD TMI Main Steam Line Break (PARCS coupled to RELAP5 and TRAC-M)

Coupling of Code System

Coupling of Code System

Algorithm for Depletion code system

PARCS Cross SectionThe Cross Section representation used in PARCS

Where r: XS at reference state ppm: soluble boron concentration (ppm) Tf: fuel temperature (k) Tm: moderator temperature (k) D: moderator density (g/cc)

Burnup and History Calculation in Depletor Burnup Distribution.B(i): burnup increment of ith region Bc: Core average burnup increment G(i): the heavy metal loading in ith region Gc: total heavy metal loading in the core P(i): Power in ith region Pc: Total power in core.History( moderator density)

Multidimension linear interpolation

Reference XS and Derivatives

Reference XS and Derivatives

VerificationMaximum Difference 210-5Comparison with HELIOSProblem 1: Single Assembly with reflective B.C.

kic

1.04604385231.0460310967-1.275559645

1.02252717921.02252800220.082303735

1.0197711921.01977565860.446653017

1.01886549081.01887719531.170448625

1.01938517071.01940242281.725211517

1.02005340991.02007025151.684155377

1.02060559921.02062258421.69850575

1.02120715931.02122985012.269074492

1.02202068641.02203105961.037314145

1.02310151451.02312070741.9192897

1.02453450121.02454698021.247904248

1.0257356011.02575206211.646117543

1.02618095581.02620489142.39356171

1.02567803121.02571673733.870605357

1.02385912931.02390863574.950645804

1.02084864881.02091807486.942603266

1.01910550551.01916613356.06280017

1.01870666441.01876345125.678682177

1.01948647941.0195385875.210757378

1.02111688431.02115820234.131798373

1.02326887861.02329882242.994382378

1.02548529741.02550338011.808261759

inifinite

critical

Difference

Burnup(GWD/T)

Kinf

Difference(pcm)

Fig.E2 Difference between inifinite/critical spectrum XS

Bc

680.69677.5356346121-3.1543653879

356.66339.5485446797-17.1114553203

278.77299.484960134220.7149601342

278.95287.07051953448.1205195344

295.88296.02361455170.1436145517

306.53306.88835283260.3583528326

315.58315.3158394936-0.2641605064

323.96324.29899537350.3389953735

335.94335.4601381976-0.4798618024

352.12350.5901193584-1.5298806416

373.42369.8703208857-3.5496791143

395.09385.4680161953-9.6219838047

405.25389.749133138-15.500866862

398.57380.7978918836-17.7721081164

381.38351.7526013212-29.6273986788

326.8303.846469737-22.953530263

303.23274.1389353122-29.0910646878

288.67263.2759731108-25.3940268892

291.78267.467316488-24.312683512

307.67281.6819894675-25.9880105325

325.9300.8267367486-25.0732632514

346.91318.6332905752-28.2767094248

MASTER

PARCS

Difference

Burnup(GWD/T)

Critical Boron Concentration(ppm)

Difference(ppm)

Fig.E2 PARCS/MASTER comparison for P212

kc

1.0460421.0460310967-1.090331245

1.0235971.0225280022-106.899780207

1.0182211.0197756586155.465855474

1.0181111.018877195376.619526807

1.0191131.019402422828.942281807

1.0197091.020070251536.125149125

1.0201581.020622584246.458423071

1.020621.021229850160.985007761

1.02141.022031059663.105955845

1.0224951.023120707462.570739514

1.0239861.024546980256.098021335

1.0254891.025752062126.306213103

1.0261481.02620489145.689136962

1.0255791.025716737313.773727848

1.0243661.0239086357-45.736427733

1.0205991.020918074831.907480827

1.019061.019166133510.613352715

1.0182771.018763451248.645123867

1.0187481.01953858779.058698859

1.0204961.021158202366.220229995

1.0221481.0232988224115.082242839

1.0246791.025503380182.438005239

MASTER

PARCS

Difference

Burnup(GWD/T)

Kinf

Difference(pcm)

Fig.E2 PARCS/MASTER comparison for P212 with 1 ppm

Bi

679.92677.4027168024-2.5172831976

356.61339.4566892651-17.1533107349

279.47299.302003560719.8320035607

279.13286.90444352017.7744435201

296.42295.7017007173-0.7182992827

307.1306.4942344612-0.6057655388

316.04314.904044506-1.135955494

324.62323.7961499654-0.8238500346

336.32334.9633719269-1.3566280731

353.01350.0334443144-2.9765556856

375.14369.2936428138-5.8463571862

396.02384.7018594522-11.3181405478

405.75388.7607624326-16.9892375674

400.54379.597392474-20.942607526

383.06350.4267310076-32.6332689924

328.07302.2984152442-25.7715847558

304.28272.6595289289-31.6204710711

288.91261.7619140089-27.1480859911

292.97265.9539324481-27.0160675519

309.09280.1837587233-28.9062412767

326.82299.2802229729-27.5397770271

349.38316.9951071599-32.3848928401

MASTER

PARCS

Difference

Burnup(GWD/T)

Critical Boron Concentration(ppm)

Difference(ppm)

Fig.E2 PARCS/MASTER comparison for P112

ki

1.0460871.0460438523-4.3147716

1.0236581.0225271792-113.082083942

1.0183021.019771192146.919202457

1.0180991.018865490876.649078182

1.0190651.019385170732.01707029

1.0196481.020053409940.540993748

1.0201761.020605599242.959917321

1.0206981.021207159350.915933269

1.0214281.022020686459.2686417

1.0225321.023101514556.951449814

1.0240631.024534501247.150117087

1.0254891.02573560124.66009556

1.0260921.02618095588.895575252

1.025621.02567803125.803122491

1.0243751.0238591293-51.587073537

1.0205551.020848648829.364877561

1.0190311.01910550557.450552545

1.018261.018706664444.66644169

1.0188391.019486479464.747941481

1.0205681.021116884354.888431622

1.0222411.0232688786102.787860461

1.0247381.025485297474.72974348

MASTER

PARCS

Difference

Burnup(GWD/T)

Kinf

Difference(pcm)

Fig.E2 PARCS/MASTER comparison for P112 with 1 ppm

kb501

1.0116421.01165155470.955466541

0.9898840.98988890230.4902294843

0.9874040.9874017257-0.2274325578

0.9866890.98669300180.4001750201

0.988030.9880257966-0.4203412126

0.9891330.9891266407-0.6359323346

0.9907460.9907390203-0.697965468

0.9931130.993102068-1.0931994139

0.9871480.9871479478-0.0052230845

0.9838910.9838836078-0.7392229876

0.9862530.98626254510.9545108245

0.9563350.95633803190.3031866223

0.8530260.85303018670.4186727287

HELIOS

PARCS

Difference

Burnup(GWD/T)

Kinf

Difference(pcm)

Fig.E2 PARCS/HELIOS comparison for P112 with 501ppm

sm

1000043290000000000000

47964500000000004796000000000000-0.9381938726

17369300000000000173700000000000000.4030099083

24399200000000000244000000000000000.3278796026

2750270000000000027500000000000000-0.9817217946

28379900000000000283800000000000000.0352362059

2898280000000000028980000000000000-0.9660902328

2946440000000000029460000000000000-1.493327541

2985110000000000029850000000000000-0.3684956333

3016500000000000030160000000000000-1.6575501409

30425500000000000304300000000000001.4790225304

30647200000000000306500000000000000.9136234305

3084020000000000030840000000000000-0.0648504225

31009200000000000310100000000000000.257987952

31257000000000000312600000000000000.9597850082

3156300000000000031560000000000000-0.9504799924

3157400000000000031570000000000000-1.2668651422

3139410000000000031390000000000000-1.3059778748

3104440000000000031040000000000000-1.4173248637

30546500000000000305500000000000001.1457941172

2992350000000000029920000000000000-1.1696492723

29197800000000000292000000000000000.7534814267

2839220000000000028390000000000000-0.7748607012

27529400000000000275300000000000000.2179488111

2663470000000000026630000000000000-1.7646153326

25736700000000000257400000000000001.2822156687

2486290000000000024860000000000000-1.1663965185

2403290000000000024030000000000000-1.2066791773

2325310000000000023250000000000000-1.3331555793

2252010000000000022520000000000000-0.0444047762

21827700000000000218300000000000001.053706987

2117120000000000021170000000000000-0.5668077388

20547500000000000205500000000000001.2166930283

19956300000000000199600000000000001.8540511017

HELIOS

PARCS

Difference

Burnup(GWD/T)

Nsm

Relative Difference(1E-4)

012 PARCS/HELIOS DEPLETION COMPARISION

xe

1000024920000000000000

27004100000000002700000000000000-1.5182879637

270364000000000027040000000000001.3315382225

271067000000000027110000000000001.2174111935

271876000000000027190000000000000.8827553738

27252900000000002725000000000000-1.0641069391

272856000000000027290000000000001.6125721993

272900000000000027290000000000000

27270300000000002727000000000000-0.1100097909

272268000000000027230000000000001.1753125597

27160700000000002716000000000000-0.2577253164

270765000000000027080000000000001.2926338338

26983200000000002698000000000000-1.1859230929

268876000000000026890000000000000.8926047695

267669000000000026770000000000001.1581468157

26552900000000002655000000000000-1.0921594251

262362000000000026240000000000001.4483804819

25862400000000002586000000000000-0.9279881218

25434100000000002543000000000000-1.6120090744

24954600000000002495000000000000-1.8433475191

244280000000000024430000000000000.8187326019

238589000000000023860000000000000.4610438872

23252300000000002325000000000000-0.9891494605

22614100000000002261000000000000-1.813028155

21952400000000002195000000000000-1.0932745395

212779000000000021280000000000000.9869395006

20603500000000002060000000000000-1.6987405053

19940400000000001994000000000000-0.2005977814

192953000000000019300000000000002.4358263411

18671100000000001867000000000000-0.5891457922

180688000000000018070000000000000.664128221

174889000000000017490000000000000.6289703755

16932500000000001693000000000000-1.4764506127

16401200000000001640000000000000-0.7316537814

HELIOS

PARCS

Difference

Burnup(GWD/T)

Nxe

Relative Difference(1E-4)

012 PARCS/HELIOS DEPLETION COMPARISION

K

1.046041.025101

1.022521.022532

1.019771.019779

1.018861.018881

1.019391.019143

1.020051.019406

1.020611.01974

1.021211.020073

1.022021.020349

1.023111.020626

1.024551.020929

1.025751.021233

1.026191.021633

1.025691.022034

1.023871.022578

1.020871.023123

1.019131.023835

1.018721.024549

1.01951.025151

1.021131.025754

1.023281.02598

1.025491.026207

1.02731.025963

1.028091.025719

1.027051.024817

1.023111.023911

1.015411.022422

1.003881.02092

0.989241.020049

0.9725631.019168

0.9548341.018967

0.9367731.018765

0.9188191.019146

0.9012381.019539

1.020335

1.021159

1.022207

1.023299

1.024375

1.025503

1.026375

1.027304

1.027685

1.028118

1.027597

1.02711

1.025186

1.02326

1.019489

1.015674

1.010014

1.004276

0.997057

0.98974

0.981483

0.973121

0.964299

0.955369

0.946333

0.937191

0.928165

0.919036

0.910151

0.901167

HELIOS

PARCS

Burnup(GWD/T)

Kinf

PARCS/HELIOS comparison

Sheet1

P002K1ppm

MASTERPARCSDiff (PCM)dif(C-I)

SpectrumSpectrumSpectrumKinfKinfNxeNsmNxeNsmNxeNsm

DayBurnupCritical *)Infinite **)CriticalInfiniteCriticalInfiniteHELIOSPARCSDKPARCSPARCSHELIOSHeliosHELIOSHeliosDnxeDnsm

0.000.001.046041.046091.046031.04604-1.1-4.3-1.30.001.046041.046040.3852.492E+154.329E+151.000E-201.000E-201.000E+041.000E+0401.025101

5.730.151.023601.023661.022531.02253-106.9-113.10.10.151.022521.0225311.1002.700E+154.796E+152.700E-094.796E-092.700E+154.796E+15-1.5183-0.93820.151.022532

19.110.501.018221.018301.019781.01977155.5146.90.40.501.019771.0197750.5002.704E+151.737E+162.704E-091.737E-082.704E+151.737E+161.33150.40300.51.019779

38.211.001.018111.018101.018881.0188776.676.61.21.001.018861.0188690.9002.711E+152.440E+162.711E-092.440E-082.711E+152.440E+161.21740.327911.018881

76.432.001.019111.019071.019401.0193928.932.01.72.001.019391.019389-0.1002.719E+152.750E+162.719E-092.750E-082.719E+152.750E+160.8828-0.98171.51.019143

114.643.001.019711.019651.020071.0200536.140.51.73.001.020051.0200570.7002.725E+152.838E+162.725E-092.838E-082.725E+152.838E+16-1.06410.035221.019406

152.864.001.020161.020181.020621.0206146.543.01.74.001.020611.020609-0.1002.729E+152.898E+162.729E-092.898E-082.729E+152.898E+161.6126-0.96612.51.01974

191.095.001.020621.020701.021231.0212161.050.92.35.001.021211.021210.0002.729E+152.946E+162.729E-092.946E-082.729E+152.946E+160.0000-1.493331.020073

229.256.001.021401.021431.022031.0220263.159.31.06.001.022021.022015-0.5002.727E+152.985E+162.727E-092.985E-082.727E+152.985E+16-0.1100-0.36853.51.020349

267.517.001.022501.022531.023121.0231062.657.01.97.001.023111.023104-0.6002.723E+153.016E+162.723E-093.017E-082.723E+153.017E+161.1753-1.657641.020626

305.678.001.023991.024061.024551.0245356.147.21.28.001.024551.024537-1.3002.716E+153.043E+162.716E-093.043E-082.716E+153.043E+16-0.25771.47904.51.020929

343.919.001.025491.025491.025751.0257426.324.71.69.001.025751.025738-1.2002.708E+153.065E+162.708E-093.065E-082.708E+153.065E+161.29260.913651.021233

382.0910.001.026151.026091.026201.026185.78.92.410.001.026191.026183-0.7002.698E+153.084E+162.698E-093.084E-082.698E+153.084E+16-1.1859-0.06495.51.021633

420.3311.001.025581.025621.025721.0256813.85.83.911.001.025691.02568-1.0002.689E+153.101E+162.689E-093.101E-082.689E+153.101E+160.89260.258061.022034

458.5512.501.024371.024381.023911.02386-45.7-51.65.012.501.023871.023861-0.9002.677E+153.126E+162.677E-093.126E-082.677E+153.126E+161.15810.95986.51.022578

573.1715.001.020601.020561.020921.0208531.929.46.915.001.020871.020851-1.9002.655E+153.156E+162.655E-093.156E-082.655E+153.156E+16-1.0922-0.950571.023123

649.6017.501.019061.019031.019171.0191110.67.56.117.501.019131.019107-2.3002.624E+153.157E+162.624E-093.157E-082.624E+153.157E+161.4484-1.26697.51.023835

764.0620.001.018281.018261.018761.0187148.644.75.720.001.018721.018708-1.2002.586E+153.139E+162.586E-093.139E-082.586E+153.139E+16-0.9280-1.306081.024549

840.7222.501.018751.018841.019541.0194979.164.75.222.501.019501.019487-1.3002.543E+153.104E+162.543E-093.104E-082.543E+153.104E+16-1.6120-1.41738.51.025151

955.3425.001.020501.020571.021161.0211266.254.94.125.001.021131.021117-1.3002.495E+153.055E+162.495E-093.055E-082.495E+153.055E+16-1.84331.145891.025754

1031.7827.501.022151.022241.023301.02327115.1102.83.027.501.023281.023269-1.1002.443E+152.992E+162.443E-092.992E-082.443E+152.992E+160.8187-1.16969.51.02598

1146.5030.001.024681.024741.025501.0254982.474.71.830.001.025491.025485-0.5002.386E+152.920E+162.386E-092.920E-082.386E+152.920E+160.46100.7535101.026207

32.5032.501.027301.02729-0.8032.325E+152.839E+162.325E-092.839E-082.325E+152.839E+16-0.9891-0.774910.51.025963

35.0035.001.028091.028100.5812.261E+152.753E+162.261E-092.753E-082.261E+152.753E+16-1.81300.2179111.025719

37.5037.501.027051.02705-0.1222.195E+152.663E+162.195E-092.663E-082.195E+152.663E+16-1.0933-1.764611.751.024817

40.0040.001.023111.023110.3212.128E+152.574E+162.128E-092.574E-082.128E+152.574E+160.98691.282212.51.023911

42.5042.501.015411.015410.2842.060E+152.486E+162.060E-092.486E-082.060E+152.486E+16-1.6987-1.166413.751.022422

45.0045.001.003881.003890.7081.994E+152.403E+161.994E-092.403E-081.994E+152.403E+16-0.2006-1.2067151.02092

47.5047.500.989240.989240.0801.930E+152.325E+161.930E-092.325E-081.930E+152.325E+162.4358-1.333216.251.020049

50.0050.000.972560.972570.9381.867E+152.252E+161.867E-092.252E-081.867E+152.252E+16-0.5891-0.044417.51.019168

52.5052.500.954830.95483-0.0131.807E+152.183E+161.807E-092.183E-081.807E+152.183E+160.66411.053718.751.018967

55.0055.000.936770.93677-0.4091.749E+152.117E+161.749E-092.117E-081.749E+152.117E+160.6290-0.5668201.018765

57.5057.500.918820.918820.4661.693E+152.055E+161.693E-092.055E-081.693E+152.055E+16-1.47651.216721.251.019146

60.0060.000.901240.901240.0081.640E+151.996E+161.640E-091.996E-081.640E+151.996E+16-0.73171.854122.51.019539

23.751.020335

MASTERPARCSDiff (PCM)P002K501ppm251.021159

SpectrumSpectrumSpectrumKinfKinf26.251.022207

DayBurnupCritical **)Infinite **)CriticalInfiniteCriticalInfiniteHELIOSPARCS27.51.023299

0.000.00680.7679.9677.53563677.40272-3.2-2.50.001.011641.011650.95528.751.024375

5.730.15356.7356.6339.54854339.45669-17.1-17.20.150.989880.989890.490301.025503

19.110.50278.8279.5299.48496299.3020020.719.80.500.987400.98740-0.22731.251.026375

38.211.00279.0279.1287.07052286.904448.17.81.000.986690.986690.40032.51.027304

76.432.00295.9296.4296.02361295.701700.1-0.73.000.988030.98803-0.42033.751.027685

114.643.00306.5307.1306.88835306.494230.4-0.65.000.989130.98913-0.636351.028118

152.864.00315.6316.0315.31584314.90404-0.3-1.17.000.990750.99074-0.69836.251.027597

191.095.00324.0324.6324.29900323.796150.3-0.810.000.993110.99310-1.09337.51.02711

229.256.00335.9336.3335.46014334.96337-0.5-1.415.000.987150.98715-0.00538.751.025186

267.517.00352.1353.0350.59012350.03344-1.5-3.020.000.983890.98388-0.739401.02326

305.678.00373.4375.1369.87032369.29364-3.5-5.830.000.986250.986260.95541.251.019489

343.919.00395.1396.0385.46802384.70186-9.6-11.345.000.956340.956340.30342.51.015674

382.0910.00405.3405.8389.74913388.76076-15.5-17.060.000.853030.853030.41943.751.010014

420.3311.00398.6400.5380.79789379.59739-17.8-20.9451.004276

458.5512.50381.4383.1351.75260350.42673-29.6-32.646.250.997057

573.1715.00326.8328.1303.84647302.29842-23.0-25.847.50.98974

649.6017.50303.2304.3274.13894272.65953-29.1-31.648.750.981483

764.0620.00288.7288.9263.27597261.76191-25.4-27.1500.973121

840.7222.50291.8293.0267.46732265.95393-24.3-27.051.250.964299

955.3425.00307.7309.1281.68199280.18376-26.0-28.952.50.955369

1031.7827.50325.9326.8300.82674299.28022-25.1-27.553.750.946333

1146.5030.00346.9349.4318.63329316.99511-28.3-32.4550.937191

56.250.928165

57.50.919036

58.750.910151

600.901167

kic

1.04604385231.0460310967-1.275559645

1.02252717921.02252800220.082303735

1.0197711921.01977565860.446653017

1.01886549081.01887719531.170448625

1.01938517071.01940242281.725211517

1.02005340991.02007025151.684155377

1.02060559921.02062258421.69850575

1.02120715931.02122985012.269074492

1.02202068641.02203105961.037314145

1.02310151451.02312070741.9192897

1.02453450121.02454698021.247904248

1.0257356011.02575206211.646117543

1.02618095581.02620489142.39356171

1.02567803121.02571673733.870605357

1.02385912931.02390863574.950645804

1.02084864881.02091807486.942603266

1.01910550551.01916613356.06280017

1.01870666441.01876345125.678682177

1.01948647941.0195385875.210757378

1.02111688431.02115820234.131798373

1.02326887861.02329882242.994382378

1.02548529741.02550338011.808261759

inifinite

critical

Difference

Burnup(GWD/T)

Kinf

Difference(pcm)

Fig.E2 Difference between inifinite/critical spectrum XS

Bc

680.69677.5356346121-3.1543653879

356.66339.5485446797-17.1114553203

278.77299.484960134220.7149601342

278.95287.07051953448.1205195344

295.88296.02361455170.1436145517

306.53306.88835283260.3583528326

315.58315.3158394936-0.2641605064

323.96324.29899537350.3389953735

335.94335.4601381976-0.4798618024

352.12350.5901193584-1.5298806416

373.42369.8703208857-3.5496791143

395.09385.4680161953-9.6219838047

405.25389.749133138-15.500866862

398.57380.7978918836-17.7721081164

381.38351.7526013212-29.6273986788

326.8303.846469737-22.953530263

303.23274.1389353122-29.0910646878

288.67263.2759731108-25.3940268892

291.78267.467316488-24.312683512

307.67281.6819894675-25.9880105325

325.9300.8267367486-25.0732632514

346.91318.6332905752-28.2767094248

MASTER

PARCS

Difference

Burnup(GWD/T)

Critical Boron Concentration(ppm)

Difference(ppm)

Fig.E2 PARCS/MASTER comparison for P212

kc

1.0460421.0460310967-1.090331245

1.0235971.0225280022-106.899780207

1.0182211.0197756586155.465855474

1.0181111.018877195376.619526807

1.0191131.019402422828.942281807

1.0197091.020070251536.125149125

1.0201581.020622584246.458423071

1.020621.021229850160.985007761

1.02141.022031059663.105955845

1.0224951.023120707462.570739514

1.0239861.024546980256.098021335

1.0254891.025752062126.306213103

1.0261481.02620489145.689136962

1.0255791.025716737313.773727848

1.0243661.0239086357-45.736427733

1.0205991.020918074831.907480827

1.019061.019166133510.613352715

1.0182771.018763451248.645123867

1.0187481.01953858779.058698859

1.0204961.021158202366.220229995

1.0221481.0232988224115.082242839

1.0246791.025503380182.438005239

MASTER

PARCS

Difference

Burnup(GWD/T)

Kinf

Difference(pcm)

Fig.E2 PARCS/MASTER comparison for P212 with 1 ppm

Bi

679.92677.4027168024-2.5172831976

356.61339.4566892651-17.1533107349

279.47299.302003560719.8320035607

279.13286.90444352017.7744435201

296.42295.7017007173-0.7182992827

307.1306.4942344612-0.6057655388

316.04314.904044506-1.135955494

324.62323.7961499654-0.8238500346

336.32334.9633719269-1.3566280731

353.01350.0334443144-2.9765556856

375.14369.2936428138-5.8463571862

396.02384.7018594522-11.3181405478

405.75388.7607624326-16.9892375674

400.54379.597392474-20.942607526

383.06350.4267310076-32.6332689924

328.07302.2984152442-25.7715847558

304.28272.6595289289-31.6204710711

288.91261.7619140089-27.1480859911

292.97265.9539324481-27.0160675519

309.09280.1837587233-28.9062412767

326.82299.2802229729-27.5397770271

349.38316.9951071599-32.3848928401

MASTER

PARCS

Difference

Burnup(GWD/T)

Critical Boron Concentration(ppm)

Difference(ppm)

Fig.E2 PARCS/MASTER comparison for P112

ki

1.0460871.0460438523-4.3147716

1.0236581.0225271792-113.082083942

1.0183021.019771192146.919202457

1.0180991.018865490876.649078182

1.0190651.019385170732.01707029

1.0196481.020053409940.540993748

1.0201761.020605599242.959917321

1.0206981.021207159350.915933269

1.0214281.022020686459.2686417

1.0225321.023101514556.951449814

1.0240631.024534501247.150117087

1.0254891.02573560124.66009556

1.0260921.02618095588.895575252

1.025621.02567803125.803122491

1.0243751.0238591293-51.587073537

1.0205551.020848648829.364877561

1.0190311.01910550557.450552545

1.018261.018706664444.66644169

1.0188391.019486479464.747941481

1.0205681.021116884354.888431622

1.0222411.0232688786102.787860461

1.0247381.025485297474.72974348

MASTER

PARCS

Difference

Burnup(GWD/T)

Kinf

Difference(pcm)

Fig.E2 PARCS/MASTER comparison for P112 with 1 ppm

kb501

1.0116421.0116515547

0.9898840.9898889023

0.9874040.9874017257

0.9866890.9866930018

0.988030.9880257966

0.9891330.9891266407

0.9907460.9907390203

0.9931130.993102068

0.9871480.9871479478

0.9838910.9838836078

0.9862530.9862625451

0.9563350.9563380319

0.8530260.8530301867

HELIOS

PARCS

Burnup(GWD/T)

Kinf

PARCS/HELIOS comparison with 500ppm

sm

1000043290000000000000

47964500000000004796000000000000-0.9381938726

17369300000000000173700000000000000.4030099083

24399200000000000244000000000000000.3278796026

2750270000000000027500000000000000-0.9817217946

28379900000000000283800000000000000.0352362059

2898280000000000028980000000000000-0.9660902328

2946440000000000029460000000000000-1.493327541

2985110000000000029850000000000000-0.3684956333

3016500000000000030160000000000000-1.6575501409

30425500000000000304300000000000001.4790225304

30647200000000000306500000000000000.9136234305

3084020000000000030840000000000000-0.0648504225

31009200000000000310100000000000000.257987952

31257000000000000312600000000000000.9597850082

3156300000000000031560000000000000-0.9504799924

3157400000000000031570000000000000-1.2668651422

3139410000000000031390000000000000-1.3059778748

3104440000000000031040000000000000-1.4173248637

30546500000000000305500000000000001.1457941172

2992350000000000029920000000000000-1.1696492723

29197800000000000292000000000000000.7534814267

2839220000000000028390000000000000-0.7748607012

27529400000000000275300000000000000.2179488111

2663470000000000026630000000000000-1.7646153326

25736700000000000257400000000000001.2822156687

2486290000000000024860000000000000-1.1663965185

2403290000000000024030000000000000-1.2066791773

2325310000000000023250000000000000-1.3331555793

2252010000000000022520000000000000-0.0444047762

21827700000000000218300000000000001.053706987

2117120000000000021170000000000000-0.5668077388

20547500000000000205500000000000001.2166930283

19956300000000000199600000000000001.8540511017

HELIOS

PARCS

Difference

Burnup(GWD/T)

Nsm

Relative Difference(1E-4)

012 PARCS/HELIOS DEPLETION COMPARISION

xe

1000024920000000000000

27004100000000002700000000000000-1.5182879637

270364000000000027040000000000001.3315382225

271067000000000027110000000000001.2174111935

271876000000000027190000000000000.8827553738

27252900000000002725000000000000-1.0641069391

272856000000000027290000000000001.6125721993

272900000000000027290000000000000

27270300000000002727000000000000-0.1100097909

272268000000000027230000000000001.1753125597

27160700000000002716000000000000-0.2577253164

270765000000000027080000000000001.2926338338

26983200000000002698000000000000-1.1859230929

268876000000000026890000000000000.8926047695

267669000000000026770000000000001.1581468157

26552900000000002655000000000000-1.0921594251

262362000000000026240000000000001.4483804819

25862400000000002586000000000000-0.9279881218

25434100000000002543000000000000-1.6120090744

24954600000000002495000000000000-1.8433475191

244280000000000024430000000000000.8187326019

238589000000000023860000000000000.4610438872

23252300000000002325000000000000-0.9891494605

22614100000000002261000000000000-1.813028155

21952400000000002195000000000000-1.0932745395

212779000000000021280000000000000.9869395006

20603500000000002060000000000000-1.6987405053

19940400000000001994000000000000-0.2005977814

192953000000000019300000000000002.4358263411

18671100000000001867000000000000-0.5891457922

180688000000000018070000000000000.664128221

174889000000000017490000000000000.6289703755

16932500000000001693000000000000-1.4764506127

16401200000000001640000000000000-0.7316537814

HELIOS

PARCS

Difference

Burnup(GWD/T)

Nxe

Relative Difference(1E-4)

012 PARCS/HELIOS DEPLETION COMPARISION

K

1.046041.0251010.3852284

1.022521.0225321.1

1.019771.0197790.5

1.018861.0188810.9

1.019391.019143-0.1

1.020051.0194060.7

1.020611.01974-0.1

1.021211.0200730

1.022021.020349-0.5

1.023111.020626-0.6

1.024551.020929-1.3

1.025751.021233-1.2

1.026191.021633-0.7

1.025691.022034-1

1.023871.022578-0.9

1.020871.023123-1.9

1.019131.023835-2.3

1.018721.024549-1.2

1.01951.025151-1.3

1.021131.025754-1.3

1.023281.02598-1.1

1.025491.026207-0.5

1.02731.025963-0.8025325

1.028091.0257190.5807028

1.027051.024817-0.1222589

1.023111.0239110.320948

1.015411.0224220.2844346

1.003881.020920.7077976

0.989241.0200490.0798062

0.9725631.0191680.9377816

0.9548341.018967-0.0131073

0.9367731.018765-0.4085402

0.9188191.0191460.4658752

0.9012381.0195390.0082925

1.020335

1.021159

1.022207

1.023299

1.024375

1.025503

1.026375

1.027304

1.027685

1.028118

1.027597

1.02711

1.025186

1.02326

1.019489

1.015674

1.010014

1.004276

0.997057

0.98974

0.981483

0.973121

0.964299

0.955369

0.946333

0.937191

0.928165

0.919036

0.910151

0.901167

HELIOS

PARCS

Difference

Burnup(GWD/T)

Kinf

Difference(pcm)

PARCS/HELIOS comparison for P112

Sheet1

P002K1ppm

MASTERPARCSDiff (PCM)dif(C-I)

SpectrumSpectrumSpectrumKinfKinfNxeNsmNxeNsmNxeNsm

DayBurnupCritical *)Infinite **)CriticalInfiniteCriticalInfiniteHELIOSPARCSDKPARCSPARCSHELIOSHeliosHELIOSHeliosDnxeDnsm

0.000.001.046041.046091.046031.04604-1.1-4.3-1.30.001.046041.046040.3852.492E+154.329E+151.000E-201.000E-201.000E+041.000E+0401.025101

5.730.151.023601.023661.022531.02253-106.9-113.10.10.151.022521.0225311.1002.700E+154.796E+152.700E-094.796E-092.700E+154.796E+15-1.5183-0.93820.151.022532

19.110.501.018221.018301.019781.01977155.5146.90.40.501.019771.0197750.5002.704E+151.737E+162.704E-091.737E-082.704E+151.737E+161.33150.40300.51.019779

38.211.001.018111.018101.018881.0188776.676.61.21.001.018861.0188690.9002.711E+152.440E+162.711E-092.440E-082.711E+152.440E+161.21740.327911.018881

76.432.001.019111.019071.019401.0193928.932.01.72.001.019391.019389-0.1002.719E+152.750E+162.719E-092.750E-082.719E+152.750E+160.8828-0.98171.51.019143

114.643.001.019711.019651.020071.0200536.140.51.73.001.020051.0200570.7002.725E+152.838E+162.725E-092.838E-082.725E+152.838E+16-1.06410.035221.019406

152.864.001.020161.020181.020621.0206146.543.01.74.001.020611.020609-0.1002.729E+152.898E+162.729E-092.898E-082.729E+152.898E+161.6126-0.96612.51.01974

191.095.001.020621.020701.021231.0212161.050.92.35.001.021211.021210.0002.729E+152.946E+162.729E-092.946E-082.729E+152.946E+160.0000-1.493331.020073

229.256.001.021401.021431.022031.0220263.159.31.06.001.022021.022015-0.5002.727E+152.985E+162.727E-092.985E-082.727E+152.985E+16-0.1100-0.36853.51.020349

267.517.001.022501.022531.023121.0231062.657.01.97.001.023111.023104-0.6002.723E+153.016E+162.723E-093.017E-082.723E+153.017E+161.1753-1.657641.020626

305.678.001.023991.024061.024551.0245356.147.21.28.001.024551.024537-1.3002.716E+153.043E+162.716E-093.043E-082.716E+153.043E+16-0.25771.47904.51.020929

343.919.001.025491.025491.025751.0257426.324.71.69.001.025751.025738-1.2002.708E+153.065E+162.708E-093.065E-082.708E+153.065E+161.29260.913651.021233

382.0910.001.026151.026091.026201.026185.78.92.410.001.026191.026183-0.7002.698E+153.084E+162.698E-093.084E-082.698E+153.084E+16-1.1859-0.06495.51.021633

420.3311.001.025581.025621.025721.0256813.85.83.911.001.025691.02568-1.0002.689E+153.101E+162.689E-093.101E-082.689E+153.101E+160.89260.258061.022034

458.5512.501.024371.024381.023911.02386-45.7-51.65.012.501.023871.023861-0.9002.677E+153.126E+162.677E-093.126E-082.677E+153.126E+161.15810.95986.51.022578

573.1715.001.020601.020561.020921.0208531.929.46.915.001.020871.020851-1.9002.655E+153.156E+162.655E-093.156E-082.655E+153.156E+16-1.0922-0.950571.023123

649.6017.501.019061.019031.019171.0191110.67.56.117.501.019131.019107-2.3002.624E+153.157E+162.624E-093.157E-082.624E+153.157E+161.4484-1.26697.51.023835

764.0620.001.018281.018261.018761.0187148.644.75.720.001.018721.018708-1.2002.586E+153.139E+162.586E-093.139E-082.586E+153.139E+16-0.9280-1.306081.024549

840.7222.501.018751.018841.019541.0194979.164.75.222.501.019501.019487-1.3002.543E+153.104E+162.543E-093.104E-082.543E+153.104E+16-1.6120-1.41738.51.025151

955.3425.001.020501.020571.021161.0211266.254.94.125.001.021131.021117-1.3002.495E+153.055E+162.495E-093.055E-082.495E+153.055E+16-1.84331.145891.025754

1031.7827.501.022151.022241.023301.02327115.1102.83.027.501.023281.023269-1.1002.443E+152.992E+162.443E-092.992E-082.443E+152.992E+160.8187-1.16969.51.02598

1146.5030.001.024681.024741.025501.0254982.474.71.830.001.025491.025485-0.5002.386E+152.920E+162.386E-092.920E-082.386E+152.920E+160.46100.7535101.026207

32.5032.501.027301.02729-0.8032.325E+152.839E+162.325E-092.839E-082.325E+152.839E+16-0.9891-0.774910.51.025963

35.0035.001.028091.028100.5812.261E+152.753E+162.261E-092.753E-082.261E+152.753E+16-1.81300.2179111.025719

37.5037.501.027051.02705-0.1222.195E+152.663E+162.195E-092.663E-082.195E+152.663E+16-1.0933-1.764611.751.024817

40.0040.001.023111.023110.3212.128E+152.574E+162.128E-092.574E-082.128E+152.574E+160.98691.282212.51.023911

42.5042.501.015411.015410.2842.060E+152.486E+162.060E-092.486E-082.060E+152.486E+16-1.6987-1.166413.751.022422

45.0045.001.003881.003890.7081.994E+152.403E+161.994E-092.403E-081.994E+152.403E+16-0.2006-1.2067151.02092

47.5047.500.989240.989240.0801.930E+152.325E+161.930E-092.325E-081.930E+152.325E+162.4358-1.333216.251.020049

50.0050.000.972560.972570.9381.867E+152.252E+161.867E-092.252E-081.867E+152.252E+16-0.5891-0.044417.51.019168

52.5052.500.954830.95483-0.0131.807E+152.183E+161.807E-092.183E-081.807E+152.183E+160.66411.053718.751.018967

55.0055.000.936770.93677-0.4091.749E+152.117E+161.749E-092.117E-081.749E+152.117E+160.6290-0.5668201.018765

57.5057.500.918820.918820.4661.693E+152.055E+161.693E-092.055E-081.693E+152.055E+16-1.47651.216721.251.019146

60.0060.000.901240.901240.0081.640E+151.996E+161.640E-091.996E-081.640E+151.996E+16-0.73171.854122.51.019539

23.751.020335

MASTERPARCSDiff (PCM)P002K501ppm251.021159

SpectrumSpectrumSpectrumKinfKinf26.251.022207

DayBurnupCritical **)Infinite **)CriticalInfiniteCriticalInfiniteHELIOSPARCS27.51.023299

0.000.00680.7679.9677.53563677.40272-3.2-2.50.001.011641.011650.95528.751.024375

5.730.15356.7356.6339.54854339.45669-17.1-17.20.150.989880.989890.490301.025503

19.110.50278.8279.5299.48496299.3020020.719.80.500.987400.98740-0.22731.251.026375

38.211.00279.0279.1287.07052286.904448.17.81.000.986690.986690.40032.51.027304

76.432.00295.9296.4296.02361295.701700.1-0.73.000.988030.98803-0.42033.751.027685

114.643.00306.5307.1306.88835306.494230.4-0.65.000.989130.98913-0.636351.028118

152.864.00315.6316.0315.31584314.90404-0.3-1.17.000.990750.99074-0.69836.251.027597

191.095.00324.0324.6324.29900323.796150.3-0.810.000.993110.99310-1.09337.51.02711

229.256.00335.9336.3335.46014334.96337-0.5-1.415.000.987150.98715-0.00538.751.025186

267.517.00352.1353.0350.59012350.03344-1.5-3.020.000.983890.98388-0.739401.02326

305.678.00373.4375.1369.87032369.29364-3.5-5.830.000.986250.986260.95541.251.019489

343.919.00395.1396.0385.46802384.70186-9.6-11.345.000.956340.956340.30342.51.015674

382.0910.00405.3405.8389.74913388.76076-15.5-17.060.000.853030.853030.41943.751.010014

420.3311.00398.6400.5380.79789379.59739-17.8-20.9451.004276

458.5512.50381.4383.1351.75260350.42673-29.6-32.646.250.997057

573.1715.00326.8328.1303.84647302.29842-23.0-25.847.50.98974

649.6017.50303.2304.3274.13894272.65953-29.1-31.648.750.981483

764.0620.00288.7288.9263.27597261.76191-25.4-27.1500.973121

840.7222.50291.8293.0267.46732265.95393-24.3-27.051.250.964299

955.3425.00307.7309.1281.68199280.18376-26.0-28.952.50.955369

1031.7827.50325.9326.8300.82674299.28022-25.1-27.553.750.946333

1146.5030.00346.9349.4318.63329316.99511-28.3-32.4550.937191

56.250.928165

57.50.919036

58.750.910151

600.901167

VerificationMaximum Difference 0.3%Compared with MASTER (KEARI)Problem 2 Checkerboard small core with vaccum B.C.

Ckinf

1.1800391.180746

1.1455611.145188

1.1367971.139271

1.1339161.134727

1.1277061.127578

1.1210241.120844

1.1141471.1141

1.1072511.107379

1.100431.100745

1.0937371.094251

1.0871831.087881

1.0806751.081578

1.0741831.075312

1.0677481.069097

1.06141.062959

1.055161.056925

1.0490441.051016

1.0430511.045224

1.037181.03954

1.0314221.033982

1.0257791.028518

1.0202381.023173

1.0148061.017933

MASTER

PARCS

Burnup(GWD/T)

Keff

PARCS/MASTER Comparison

Sheet1

P-303

SearchXsSmpowerPPMTf-aveTm-aveDensity

Conditionk_efftrtr55.821480.04290.040.74568

k-value

Keff

DayBurnupMASTERPARCSDIFFPARCS(4x4)DIFF2x24x4

00.00001.180041.1806241.851.18074650.74188187201.1456111.145594

40.10471.145561.1457716.221.145188-28.43241983630.1051.1452631.145188

160.41881.136801.14010254.741.139271191.02479129430.4191.1395431.139271

300.78521.133921.13569137.731.13472763.030185040.7851.1351041.134727

601.57051.127711.1288891.931.127578-10.06624472921.1781.1315591.131029

902.35581.121021.12250117.031.120844-14.32558689351.5711.1282731.127585

1203.14121.114151.11611157.781.1141-3.78644095131.9641.1250781.12422

1503.92661.107251.10973201.691.10737910.43920930042.3561.1218891.120863

1804.71211.100431.10341245.621.10074526.00527260692.7491.11871.117495

2105.49771.093741.09721289.531.09425142.94704257213.1421.1154981.114129

2406.28341.087181.09112331.581.08788159.01621844813.5351.1123051.110766

2707.06911.080681.08507375.091.08157877.25645936483.9271.1091141.107418

3007.85491.074181.07905419.471.07531297.74198948394.321.1059421.10409

3308.64081.067751.07305463.031.069097118.17512549714.7131.102791.100791

3609.42671.061401.06714507.121.062959138.18169590195.1061.099671.097528

39010.21271.055161.06132550.011.056925158.26402985095.4981.0965791.094302

42010.99881.049041.05560591.911.051016178.85615037175.8911.0935161.091106

45011.78491.043051.05001635.601.045224199.31721454276.2841.0904721.087938

48012.57101.037181.04453678.351.03954218.88533442566.6771.0874391.084781

51013.35721.031421.03916722.281.033982240.04385697197.0691.0844161.081638

54014.14341.025781.03390765.611.028518259.61293783357.4621.0813941.078501

57014.92971.020241.02874810.321.023173281.16259242467.8551.0783751.075372

60015.71611.014811.02369854.821.017933302.70922842768.2481.0753651.072253

8.641.0723731.069158

9.0331.06941.066077

Boron search (ppm)9.4261.0664541.063021

9.8191.0635261.05999

ppm10.2111.0606211.056986

DayBurnupMASTERPARCSDIFF10.6041.0577361.054013

00.00002367.510.9971.0548911.051077

40.10471969.011.391.052081.048164

160.41881861.111.7821.0492961.045285

300.78521829.812.1751.0465361.042426

601.57051756.312.5681.0438051.0396

902.35581673.112.9611.0411051.036809

1203.14121584.713.3531.038431.034041

1503.92661494.413.7461.0357791.031296

1804.71211403.914.1391.0331571.028578

2105.49771314.414.5321.0305611.025891

2406.28341225.814.9241.0279931.023233

2707.06911137.415.3171.0254521.020605

3007.85491048.615.711.0229281.017993

3308.6408960.3

3609.4267872.8

39010.2127786.9

42010.9988702.6

45011.7849620.3

48012.5710539.8

51013.3572461.1

54014.1434384.1

57014.9297308.9

60015.7161235.4

MBD01D54607.vsd

600 MWe SBWR DesignFresh fuel, 69 Once burned Fuel, 69Twice burned Fuel, 45

Total 732 Fuel Assemblies

Fuel Assembly Design (GE 8x8)(8 Gd Rods)Percent Enrichments (3.95 wt% average)2.43.33.74.25.35.6Gd (1.8)

RELAP5 ModelCurrently uses 63 Core channelsModels Vessel OnlyFrom Cold to Hot LegInlet: Feedwater TankOutlet: Turbine SideSimilar Models built for 200 and 1200 MWe

Neutronics to TH Mapping 1 1 1 1 1 1 1 1 1 2 2 3 3 3 1 1 1 5 7 8 8 9 10 9 1 1 5 7 12 14 14 15 13 16 13 1 1 6 12 12 19 20 19 18 17 18 17 1 1 6 11 26 25 23 24 23 22 21 22 21 1 1 6 11 33 27 28 27 28 29 30 29 30 32 1 5 12 26 27 36 37 36 38 34 34 39 40 35 1 1 7 12 25 28 37 44 43 41 34 34 41 42 35 1 5 12 19 23 27 36 43 49 48 45 47 45 46 451 1 7 14 20 24 28 38 41 48 54 50 51 50 51 521 2 8 14 19 23 29 34 34 45 50 56 56 57 58 551 2 8 15 18 22 30 34 34 47 51 56 56 58 57 551 4 9 13 17 21 29 39 41 45 50 57 58 64 63 621 4 10 16 18 22 30 40 42 46 51 58 57 63 61 60 1 4 9 13 17 21 31 35 35 45 53 55 55 62 59 59 856 Neutronics Channels

732 (Fuel), 124(Reflector)

63 TH Fuel Channels, 2 Bypass

Preliminary Comparison of 600 MWe Core TH Properties

ABWRGE SBWRPurdue SBWR (BOC)Power3926 MWt2000 MWt2000 MWtCore Flow Rate52.2X106 kg/hr27.2X106 kg/hr27.0X106 kg/hrPower Density50.6 kW/liter41.5 kW/liter41.5 kW/literMCPR1.171.32--Average Core Void Fraction0.4080.4340.448Core Pressure7.274 MPa7.239 MPa7.22 MPaCore Pressure Drop0.168 MPa0.048 MPa0.038 MPaAverage Exit Quality0.140.1430.157

Axial/Radial Power Profiles (BOC)

Depletion Results

B(GWd/MT)C.R. Notches (798)Max PeakRadial PeakAxial PeakB Average (GWd/MT)0.0004861.7961.3071.30213.91.14561.7431.2801.25415.02.24561.7971.2711.25816.13.34561.8761.2631.27217.24.44561.9841.2621.29918.35.54632.1421.2961.35519.46.64982.3421.3321.44020.57.74982.3271.3501.44421.68.84912.1601.3531.38622.79.94221.8841.3441.25223.811.02171.8361.3251.38224.912.102.0691.3041.36826.0

Other Related WorksVIPRE as a T/H solver for Depletion systemAn EPRI code, with steady state option Used for 200MW and 1200 MW SBWR designUsed for HCBWR analysisUsed for Ringhalls Benchmark problemSuccessfully treat the history effect

Further improvementsPredictor-corrector Time integration methodMicroscopic depletion?

Thank You !