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 !