CROSS-SECTIONS USED IN CALCULATIONS
VISTA is capable of using any reactor and fuel type if one group neutron cross sections are provided. For the purpose of this publication, 7 reactor types with 9 fuel types (7 uranium fuels and 2 MOX fuels) were introduced to the system. One group neutron cross sections of those 9 fuel types are given in TABLES 9–17.
TABLE 9. ONE GROUP NEUTRON CROSS-SECTIONS FOR PWR URANIUM FUEL (BARN)
239Pu 58.6100 106.2000 0.001120 2.41E+04
240Pu 104.0000 0.5840 0.000448 6.56E+03
241Pu 38.6800 118.1000 0.007518 1.44E+01
242Pu 31.7200 0.4146 0.002307 3.75E+05
241Am 118.8000 1.1230 0.000328 4.33E+02
242mAm 98.0400 466.2000 0.005670 1.41E+02
243Am 49.4870 0.3959 0.000207 7.37E+03
242Cm 5.8010 0.5591 0.000053 4.46E-01
244Cm 13.8200 0.8746 0.001048 1.81E+01
TABLE 10. ONE GROUP NEUTRON CROSS-SECTIONS FOR BWR URANIUM FUEL (BARN)
Nuclide σc(inc σex) σf σn2n T1/2(y)
235U 11.21000 50.00000 0.001969 7.04E+08
236U 8.24900 0.16480 0.001935 2.34E+07
238U 0.91900 0.08083 0.004039 4.47E+09
237Np 34.07000 0.46150 0.000210 2.14E+06
238Pu 37.27000 2.48800 0.000123 8.77E+01
239Pu 63.07000 114.10000 0.000818 2.41E+04
240Pu 111.10000 0.52660 0.000328 6.56E+03
241Pu 41.51000 126.30000 0.005496 1.44E+01
242Pu 33.07000 0.40380 0.002245 3.75E+05
241Am 121.30000 1.12500 0.000319 4.33E+02
242mAm 234.2638 1210.7879 0.004338 1.41E+02
243Am 51.58100 0.38520 0.000202 7.37E+03
242Cm 6.03300 0.55540 0.000052 4.46E-01
244Cm 14.39000 0.87090 0.001019 1.81E+01
TABLE 11. ONE GROUP NEUTRON CROSS-SECTIONS FOR PHWR URANIUM FUEL (BARN)
Nuclide σc(inc σex) σf σn2n T1/2(y)
235U 28.6400 159.10000 0.001391 7.04E+08
236U 5.6590 0.10750 0.001487 2.34E+07
238U 1.1650 0.05424 0.002779 4.47E+09
237Np 58.6300 0.29150 0.000046 2.14E+06
238Pu 142.5000 5.08700 0.000109 8.77E+01
239Pu 123.1000 267.30000 0.000587 2.41E+04
240Pu 144.5000 0.33290 0.000268 6.56E+03
241Pu 115.6000 339.40000 0.003755 1.44E+01
242Pu 23.8100 0.25170 0.001105 3.75E+05
241Am 393.37000 2.19100 0.000069 4.33E+02
242mAm 849.4000 4166.0000 0.000658 1.41E+02
243Am 76.274 0.06523 0.000045 7.37E+03
242Cm 12.1400 1.67700 0.000010 4.46E-01
244Cm 23.1900 1.03790 0.000217 1.81E+01
TABLE 12. ONE GROUP NEUTRON CROSS-SECTIONS FOR RBMK URANIUM FUEL (BARN)
Nuclide σc(inc σex) σf σn2n T1/2(y)
235U 17.9000 93.0000 0 7.04E+08
236U 5.6900 0.0920 0 2.34E+07
238U 0.8670 0.0452 0.00226 4.47E+09
237Np 41.9000 0.2610 0 2.14E+06
238Pu 74.9000 3.0500 0 8.77E+01
239Pu 113.0000 210.0000 0 2.41E+04
240Pu 122.0000 0.3040 0 6.56E+03
241Pu 79.9000 238.0000 0 1.44E+01
242Pu 24.7000 0.2210 0 3.75E+05
241Am 179.9000 1.4600 0 1.41E+02
242mAm 432 2775 0 4.33E+02
243Am 42.4200 0.1680 0 7.37E+03
242Cm 2.6400 0.8310 0 4.46E-01
244Cm 10.6000 0.9780 0 1.81E+01
TABLE 13. ONE GROUP NEUTRON CROSS-SECTIONS FOR AGR URANIUM FUEL (BARN)
Nuclide σc(incσex) σf σn2n T1/2(y)
235U 19.0000 84.0000 0 7.04E+08
236U 6.1700 0.1200 0 2.34E+07
238U 1.0600 0.05640 0.00226 4.47E+09
237Np 52.0400 0.3060 0 2.14E+06
238Pu 118.4000 4.4200 0 8.77E+01
239Pu 125.0000 240.0000 0 2.41E+04
240Pu 142.0000 0.3526 0 6.56E+03
241Pu 101.000 319.0000 0 1.44E+01
242Pu 31.2000 0.2650 0 3.75E+05
241Am 179.9000 1.4600 0 4.33E+02
242mAm 432 2775 0 1.41E+02
243Am 42.4200 0.1680 0 7.37E+03
242Cm 2.6400 0.8310 0 4.46E-01
244Cm 10.6000 0.978 0 1.81E+01
TABLE 14. ONE GROUP NEUTRON CROSS-SECTIONS FOR GCR URANIUM FUEL (BARN)
Nuclide σc(inc σex) σf σn2n T1/2(y)
235U 19.0000 96.0000 0 7.04E+08
236U 6.3000 0.13000 0 2.34E+07
238U 0.8800 0.06000 0.00278 4.47E+09
237Np 48.0000 0.30000 0 2.14E+06
238Pu 118.0000 4.00000 0 8.77E+01
239Pu 139.0000 249.00000 0 2.41E+04
240Pu 185.0000 0.38000 0 6.56E+03
241Pu 107.0000 255.00000 0 1.44E+01
242Pu 25.0000 0.30000 0 3.75E+05
241Am 391.7000 2.19100 0 4.33E+02
242mAm 849.4 4166 0 1.41E+02
243Am 75.8140 0.06523 0 7.37E+03
242Cm 12.1400 1.67700 0 4.46E-01
244Cm 23.1900 1.03790 0 1.81E+01
TABLE 15. ONE GROUP NEUTRON CROSS-SECTIONS FOR WWER URANIUM FUEL (BARN)
Nuclide σc(inc σex) σf σn2n T1/2(y)
235U 8.1400 35.1100 0.00430 7.04E+08
236U 6.4000 0.2100 0.00270 2.34E+07
238U 0.9600 0.1000 0.00570 4.47E+09
237Np 29.7400 0.5300 0.00150 2.14E+06
238Pu 25.2100 2.4100 0.00014 8.77E+01
239Pu 49.2000 86.5700 0.00150 2.41E+04
240Pu 153.0700 0.5800 0.00140 6.56E+03
241Pu 30.9200 92.4900 0.00310 1.44E+01
242Pu 29.8700 0.4200 0.00200 3.75E+05
241Am 95.7900 1.0200 0.00076 4.33E+02
242mAm 130.4300 564.78000 0.00071 1.41E+02
243Am 49.0300 0.4500 0.00150 7.37E+03
242Cm 4.2800 1.3500 0.00046 4.46E-01
244Cm 15.4400 0.8200 0.00110 1.81E+01
TABLE 16. ONE GROUP NEUTRON CROSS-SECTIONS FOR PWR-MOX FUEL (BARN)
Nuclide σc(inc σex) σf σn2n T1/2(y)
235U 6.3980 22.6900 0.0032 7.04E+08
236U 8.4870 0.2166 0.0031 2.34E+07
238U 0.8718 0.1105 0.0064 4.47E+09
237Np 24.2300 0.5713 0.0004 2.14E+06
238Pu 15.2600 2.0330 0.0002 8.77E+01
239Pu 26.0400 46.4500 0.0013 2.41E+04
240Pu 43.8800 0.6222 0.0005 6.56E+03
241Pu 16.7200 54.5200 0.0087 1.44E+01
242Pu 25.5600 0.5354 0.0024 3.75E+05
241Am 64.3940 0.8959 0.0004 4.33E+02
242mAm 45.8400 224.4000 0.0066 1.41E+02
243Am 41.9900 0.4455 0.0003 7.37E+03
242Cm 5.3410 0.4676 0.0001 4.46E-01
244Cm 13.8400 0.9332 0.0012 1.81E+01
TABLE 17. ONE GROUP NEUTRON CROSS-SECTIONS FOR BWR-MOX FUEL (BARN)
Nuclide
σc(inc σex) σf σn2n T1/2(y)
235U 8.131000 32.0200 0.002190 7.04E+08
236U 8.624000 0.1792 0.002159 2.34E+07
238U 0.871900 0.0881 0.004502 4.47E+09
237Np 27.960000 0.4995 0.000230 2.14E+06
238Pu 22.650000 2.1590 0.000137 8.77E+01
239Pu 38.520000 69.2000 0.000910 2.41E+04
240Pu 52.630000 0.5540 0.000366 6.56E+03
241Pu 25.010000 78.7700 0.006098 1.44E+01
242Pu 26.200000 0.4607 0.001722 3.75E+05
241Am 86.790000 0.978 0.004741 4.33E+02
242mAm 66.720000 321.6000 0.000218 1.41E+02
243Am 46.200000 0.4163 0.000056 7.37E+03
242Cm 5.767000 0.4963 0.001102 4.46E-01
244Cm 14.520000 0.9094 0.000419 1.81E+01
Appendix V ISOTOPIC COMPOSITIONS OF DISCHARGED SPENT FUELS IN code for 9 different fuel types are presented in Tables 18–26. The tables give isotopic compositions at the time of discharge reactor. However CAIN is capable of calculating isotopic calculations after a waiting period following the discharge. LE 18: ISOTOPIC COMPOSITION OF SPENT URANIUM FUEL (%) - PWR . Burnup (GW·d/t) 235 U 236 U 238 U 237 Np 238 Pu239 Pu240 Pu241 Pu242 Pu241 Am242m Am243 Am242 Cm244 Cm 5 5.00 0.9516030.07139898.0435820.0046530.0003920.3431430.0579410.0110390.0007180.0000480.0000010.0000290.0000050.000002 0 10.00 0.9445430.13291597.2866640.0098440.0012950.4381370.1166170.0343960.0039850.0002900.0000040.0002790.0000510.000026 5 15.00 0.9331740.19331196.6001800.0159080.0026930.4782000.1599110.0587880.0095450.0007280.0000130.0009100.0001640.000118 0 20.00 0.9141840.25328295.9530540.0228550.0046370.4972490.1914640.0808160.0167110.0013050.0000250.0019800.0003440.000322 5 25.00 0.8882640.31273995.3313860.0306400.0071770.5065220.2146230.0996860.0249240.0019650.0000400.0034940.0005780.000680 0 30.00 0.8568130.37144994.7276250.0391980.0103500.5107180.2317310.1154370.0337660.0026640.0000560.0054310.0008460.001228 0 35.00 0.7972180.42431494.1608950.0484580.0143330.5125760.2457200.1297210.0439290.0033950.0000740.0080240.0011570.002091 0 40.00 0.7381100.47528493.6014070.0583150.0190470.5125370.2559870.1413080.0543930.0041010.0000910.0110970.0014760.003278 0 45.00 0.6799440.52425493.0468660.0686950.0244980.5113670.2634340.1505620.0649400.0047610.0001080.0146130.0017920.004836 5 50.00 0.6055550.56508592.5162080.0793800.0308940.5097180.2694210.1586910.0765750.0053720.0001240.0189820.0021180.007048 0 55.00 0.5365810.60305691.9853660.0903170.0380280.5075570.2734780.1648840.0880260.0059020.0001380.0238140.0024210.009839 0 60.00 0.4873530.64485891.4368390.1016470.0455950.5049520.2756240.1688690.0978690.0063550.0001500.0284360.0026680.012847 5 65.00 0.4277090.67742390.9056310.1128430.0540320.5023090.2771870.1722570.1084740.0067280.0001600.0339000.0029060.016829 5 70.00 0.3848960.71438290.3580540.1243780.0627730.4994410.2776190.1741830.1173140.0070430.0001690.0389130.0030900.020907
TABLE 19: ISOTOPIC COMPOSITION OF SPENT URANIUM FUEL (%) - BWR Enr. (%) Burnup (GW·d/t) 235 U 236 U 238 U 237 Np Pu238239 Pu240 Pu241 Pu242 Pu241 Am242m Am243 Am242 Cm244 Cm 1.35 5.00 0.9385950.07369598.0636850.0039340.0003290.3332430.0586520.0115180.0007850.0000720.0000000.0000320.0000070.000002 1.70 10.00 0.9230930.13647497.3204410.0089320.0011740.4218850.1166450.0352780.0042950.0004350.0000040.0003060.0000700.000029 2.05 15.00 0.9046000.19774096.6445640.0150360.0025810.4582100.1586840.0595710.0102000.0010810.0000090.0009920.0002170.000130 2.40 20.00 0.8794870.25825696.0062540.0221740.0046300.4749560.1888430.0810930.0177360.0019230.0000170.0021470.0004370.000354 2.75 25.00 0.8481490.31798595.3918500.0302630.0073850.4827870.2106710.0992170.0263100.0028750.0000260.0037740.0007080.000746 3.10 30.00 0.8120190.37669394.7942700.0392090.0108860.4860690.2265600.1140850.0354810.0038730.0000360.0058460.0010060.001344 3.40 35.00 0.7488500.42917294.2324850.0489110.0153220.4872910.2393960.1273900.0459930.0049050.0000460.0086190.0013390.002285 3.70 40.00 0.6869350.47945793.6769860.0592540.0206010.4868670.2486410.1379740.0567590.0058890.0000560.0118980.0016690.003580 4.00 45.00 0.6267600.52744293.1257020.0701420.0267100.4854820.2551950.1462460.0675450.0067970.0000650.0156350.0019810.005276 4.25 50.00 0.5517840.56682592.5971950.0813130.0338710.4837040.2603460.1533840.0794050.0076210.0000730.0202740.0022950.007686 4.50 55.00 0.4827760.60304592.0669410.0927290.0418450.4815060.2637070.1586830.0910310.0083210.0000800.0253990.0025760.010732 4.80 60.00 0.4336990.64300691.5195810.1045210.0502380.4789460.2653280.1619200.1009020.0089110.0000860.0302530.0027930.013987 5.05 65.00 0.3756110.67327790.9884390.1160780.0595340.4763690.2664130.1646060.1114980.0093800.0000910.0359790.0029980.018295 5.35 70.00 0.3340340.70792590.4409810.1279640.0690960.4736080.2665110.1659890.1202370.0097730.0000950.0411890.0031480.022677
LE 20: ISOTOPIC COMPOSITION OF SPENT URANIUM FUEL (%) - PHWR . Burnup (GW·d/t) 235 U 236 U 238 U 237 Np 238 Pu239 Pu240 Pu241 Pu242 Pu241 Am242m Am243 Am242 Cm244 Cm 1 7.00 0.2369560.07104798.5833030.0025960.0003330.2658760.0957960.0181180.0039370.0001830.0000020.0001230.0000600.000010 0 15.00 0.1230990.12874797.6593090.0065570.0015470.2897480.1739390.0452340.0224400.0007920.0000070.0014130.0004330.000244 0 20.00 0.0820470.16169297.0896900.0095190.0028060.2907310.2006200.0562890.0388430.0011570.0000100.0031770.0007330.000732 0 25.00 0.0649540.20501796.5075330.0129680.0042990.2896700.2140590.0621610.0529650.0014480.0000130.0050950.0009580.001409 LE 21: ISOTOPIC COMPOSITION OF SPENT URANIUM FUEL (%) - RBMK . Burnup (GW·d/t) 235 U 236 U 238 U 237 Np 238 Pu239 Pu240 Pu241 Pu242 Pu241 Am242m Am243 Am242 Cm244 Cm 5 5.00 0.8705000.07677898.2937140.0016910.0001110.1914090.0438020.0059060.0005350.0000620.0000010.0000110.0000060.000000 0 10.00 0.7895960.14429497.6803720.0042500.0004670.2355680.0918050.0188320.0032650.0003890.0000140.0001260.0000560.000007 5 15.00 0.7133350.20980997.1010840.0076060.0011550.2502380.1282660.0320840.0082450.0009720.0000520.0004540.0001700.000035 0 20.00 0.6379540.27393296.5394870.0117090.0022590.2553900.1552600.0436470.0149920.0017150.0001250.0010650.0003340.000107 5 25.00 0.5639470.33654995.9877280.0165110.0038300.2568580.1752750.0531610.0230590.0025280.0002350.0020060.0005250.000247 0 30.00 0.4924980.39742395.4411650.0219620.0058950.2567500.1901590.0607660.0321010.0033420.0003850.0033080.0007230.000483
68 TABLE 22: ISOTOPIC COMPOSITION OF SPENT URANIUM FUEL (%) — AGR Enr. (%) Burnup (GW·d/t) 235 U 236 U 238 U 237 Np 238 Pu239 Pu240 Pu241 Pu242 Pu241 Am242m Am243 Am242 Cm244 Cm 1.35 5.00 0.9009630.08209898.2176780.0017850.0001380.2184620.0544680.0078660.0009150.0001220.0000020.0000250.0000110.000001 1.70 10.00 0.8507240.15367797.5636670.0044370.0005700.2606620.1071440.0221830.0048840.0006900.0000250.0002380.0000840.000013 2.05 15.00 0.7995150.22411996.9534320.0078820.0013930.2734210.1445120.0351410.0113770.0016200.0000860.0007860.0002250.000060 2.40 20.00 0.7442250.29400896.3667090.0120580.0026670.2773860.1708310.0454560.0195020.0027380.0001960.0017310.0004020.000168 2.75 25.00 0.6858950.36313395.7943160.0169010.0043990.2781400.1895470.0533390.0286160.0039090.0003550.0030940.0005880.000364 3.10 30.00 0.6260380.43118695.2309530.0223540.0065650.2775880.2029600.0592610.0382970.0050460.0005610.0048770.0007670.000675 TABLE 23: ISOTOPIC COMPOSITION OF SPENT URANIUM FUEL (%) — GCR Enr. (%) Burnup (GW·d/t) 235 U 236 U 238 U 237 Np 238 Pu239 Pu240 Pu241 Pu242 Pu241 Am242m Am243 Am242 Cm244 Cm 0.71 0.01 0.7088580.00018999.2886920.0000040.0000000.0012250.0000010.0000000.0000000.0000000.0000000.0000000.0000000.000000 0.71 1.00 0.6131360.01600499.1706790.0004050.0000110.0882170.0078430.0005800.0000210.0000060.0000000.0000000.0000000.000000 0.71 2.00 0.5371510.02844699.0631700.0008490.0000450.1377310.0230670.0030560.0002230.0000570.0000010.0000030.0000060.000000 0.71 3.00 0.4732090.03881798.9602920.0013280.0001090.1682660.0403140.0073200.0008150.0001960.0000070.0000150.0000260.000001 0.71 4.00 0.4178150.04770698.8593410.0018390.0002240.1878120.0574940.0128650.0019620.0004420.0000230.0000490.0000680.000003 0.71 5.00 0.3691130.05542898.7589470.0023760.0004110.2005300.0736430.0191730.0037740.0007910.0000530.0001190.0001350.000009 0.71 6.00 0.3260400.06216798.6585360.0029350.0006920.2088310.0882850.0257880.0063080.0012280.0001030.0002390.0002250.000023 0.71 7.00 0.2878150.06805498.5577290.0035090.0010830.2142350.1012440.0323580.0095760.0017260.0001760.0004270.0003340.000048
LE 24: ISOTOPIC COMPOSITION OF SPENT URANIUM FUEL (%) — WWER . Burnup (GW·d/t) 235 U 236 U 238 U 237 Np 238 Pu239 Pu240 Pu241 Pu242 Pu241 Am242m Am243 Am242 Cm244 Cm 5 5.00 0.9922630.06596397.9045390.0050590.0004740.4320600.0615970.0211110.0012930.0000760.0000010.0000580.0000080.000004 0 10.00 1.0238000.12256697.0794700.0099760.0014460.5515470.1125210.0602130.0064680.0004330.0000050.0004880.0000730.000052 5 15.00 1.0478620.17897996.3437870.0154470.0028600.6042020.1452320.0977040.0145780.0010440.0000130.0014790.0002280.000215 0 20.00 1.0613330.23586095.6575130.0215700.0047600.6306420.1665260.1295340.0244490.0018230.0000250.0030550.0004680.000555 5 25.00 1.0650130.29309295.0034310.0283470.0071920.6444570.1806240.1554470.0352680.0026960.0000380.0051720.0007750.001117 0 30.00 1.0601960.35044694.3719790.0357520.0101940.6514740.1900500.1761510.0465090.0036080.0000520.0077710.0011270.001938 0 35.00 1.0228720.40308093.7830810.0436780.0138980.6552260.1969390.1939300.0588400.0045440.0000670.0110690.0015270.003154 0 40.00 0.9826580.45478493.2051170.0521060.0182530.6562820.2014360.2077850.0711560.0054450.0000820.0148330.0019380.004754 0 45.00 0.9399810.50545192.6350570.0610010.0232760.6556490.2042720.2184430.0832610.0062880.0000950.0190010.0023440.006772 5 50.00 0.8753320.54940492.0940930.0701330.0291170.6542610.2062090.2273730.0961460.0070710.0001090.0239550.0027610.009489 0 55.00 0.8125580.59151291.5563610.0795440.0356380.6520470.2071910.2339120.1085600.0077620.0001200.0292700.0031500.012782 0 60.00 0.7686900.63782990.9992140.0894610.0426630.6490630.2073390.2379740.1192680.0083650.0001310.0343330.0034790.016289 5 65.00 0.7086770.67635290.4654210.0993180.0504780.6459820.2072130.2412330.1304820.0088780.0001390.0401060.0037950.020727 5 70.00 0.6658440.71940289.9132450.1096440.0587160.6424820.2066410.2429110.1398990.0093210.0001470.0454060.0040490.025239
70 TABLE 25: ISOTOPIC COMPOSITION OF SPENT MOX FUEL (%) — PWR Tot Pu (%) Burnup (GW·d/t) 235 U 236 U 238 U 237 Np 238 Pu239 Pu240 Pu241 Pu242 Pu241 Am242m Am243 Am242 Cm244 Cm 1.29 5.00 0.2359300.01283797.6564230.0047630.0157330.9510650.3485430.1682950.0741970.0021970.0000370.0121300.0003530.001984 1.82 10.00 0.2036020.01895096.6647020.0076050.0212971.1410300.5088930.2520520.1109940.0055780.0001180.0261250.0012500.006872 2.43 15.00 0.1828710.02250595.7342500.0095210.0280281.2547620.6562360.3415490.1540070.0103230.0002380.0426300.0025600.014147 3.12 20.00 0.1687210.02466894.8198000.0108310.0361341.3387420.7965720.4342610.2024700.0165780.0004020.0614340.0041750.023375 3.89 25.00 0.1588450.02596193.8982190.0117080.0458421.4125030.9362650.5301650.2558390.0245400.0006130.0821930.0060080.034049 4.75 30.00 0.1519310.02666992.9541790.0122640.0573551.4865101.0808740.6301820.3137860.0344670.0008790.1045580.0079980.045639 5.60 35.00 0.1460280.02718992.0296500.0127310.0698221.5492571.2168810.7257560.3716840.0457370.0011860.1275750.0100350.058073 6.52 40.00 0.1417640.02739291.0735150.0130180.0842061.6197131.3621300.8258630.4332660.0591980.0015520.1516020.0121460.070740 7.50 45.00 0.1387390.02735190.0790320.0131730.1006151.7011921.5195800.9313730.4984740.0751640.0019840.1764190.0143160.083279 8.46 50.00 0.1356150.02734189.1108810.0133790.1177761.7719061.6669381.0305430.5619260.0922810.0024530.2012800.0164500.096279 9.48 55.00 0.1332760.02717388.1062440.0135170.1368921.8541571.8264721.1345210.6283360.1119960.0029900.2266320.0186140.108909 10.66 60.00 0.1324820.02666886.9784190.0134880.1596071.9790122.0289051.2577420.7036330.1369030.0036490.2528550.0209010.119853 11.80 65.00 0.1311460.02627485.8835540.0135850.1828872.0920352.2193271.3730070.7761930.1630090.0043450.2788150.0231200.131150 13.11 70.00 0.1309980.02559384.6463870.0135840.2100442.2577732.4598311.5091330.8580840.1956510.0051900.3052770.0254500.140274
LE 26: ISOTOPIC COMPOSITION OF SPENT MOX FUEL (%) — BWR t PuBurnup (GW·d/t) 235 U 236 U 238 U 237 Np 238 Pu239 Pu240 Pu241 Pu242 Pu241 Am242m Am243 Am242 Cm244 Cm 1.29 5.00 0.2310340.01286997.8284750.0028350.0152380.7853110.3602160.1556610.0792220.0014720.0000430.0117470.0002170.000199 1.82 10.00 0.1960940.01909596.9333970.0046700.0200310.8920250.5226020.2272940.1214610.0028070.0001380.0281420.0005480.000752 2.43 15.00 0.1742900.02265296.0729490.0059280.0256430.9521730.6700800.3031520.1704070.0044970.0002800.0489650.0009010.001626 3.12 20.00 0.1600070.02473995.2135270.0067750.0321400.9986220.8116230.3810870.2250290.0066380.0004770.0733720.0012600.002754 3.89 25.00 0.1505950.02590694.3366220.0073150.0396361.0448030.9554570.4616240.2845670.0093330.0007320.1003180.0016260.004043 4.75 30.00 0.1445470.02645293.4292100.0076200.0482651.0981021.1084360.5460480.3485250.0127240.0010540.1287400.0020000.005391 5.60 35.00 0.1394630.02683292.5367480.0078710.0570761.1448631.2546130.6265720.4121580.0164930.0014290.1581560.0023560.006822 6.52 40.00 0.1362250.02687491.6070120.0079870.0670571.2036551.4148460.7116450.4791330.0211020.0018760.1877350.0027250.008197 7.50 45.00 0.1343550.02665990.6335480.0080040.0783091.2774271.5924990.8020020.5492970.0267290.0024030.2168680.0031090.009458 8.46 50.00 0.1321980.02650789.6847680.0080660.0894701.3430801.7607950.8866550.6173480.0326740.0029770.2462830.0034700.010762 9.48 55.00 0.1308870.02618988.6951280.0080760.1018191.4236691.9459260.9758030.6878580.0397080.0036310.2748880.0038450.011932 66 60.00 0.1314130.02549087.5746880.0079520.1171271.5532042.1843091.0822070.7663410.0492420.0044230.3007280.0042810.012710 80 65.00 0.1311420.02494286.4869960.0079240.1321471.6731862.4100921.1809170.8417060.0591610.0052600.3267790.0046880.013551 11 70.00 0.1322250.02407985.2487900.0078150.1504561.8538622.6958631.2971470.9253020.0723760.0062550.3495370.0051570.013984
Appendix VI
VALIDATION AND BENCHMARKING OF CAIN MODEL
In order to use CAIN code in the VISTA simulation system, one needs to validate the CAIN code against the other available well known codes and measurement results. The validation study was performed for uranium fuels and MOX fuels separately since handling MOX fuels was added to the system later on.
VI.1. Validation of CAIN code for uranium fuels
Different methods and sources were used to validate CAIN code for uranium fuels. For PWR, BWR and PHWR uranium fuels CAIN results were compared with those given by ORIGEN code (Section VI.1.1). Both calculations used the same cross section set which is available in ORIGEN standard library. For AGR, GCR, RBMK and PHWR uranium fuels, validation against WIMS code was performed (Section VI.1.3). In addition, CAIN results are compared with available measurements (Section VI.1.2).
VI.1.1. CAIN vs. ORIGEN
The CAIN burnup calculation was compared with the ORIGEN code for 3 reactor types, which are PWR, BWR and PHWR. Since cross sections and the neutron flux are identical for both CAIN and ORIGEN, these two results should be identical except the small influence due to the assumptions listed in Section 2.5.5.3.
TABLES 27–29 show the comparisons of CAIN and ORIGEN results. The results show that the CAIN code agrees very well to the ORIGEN, and the errors are less than 1–2% for PWR and BWR cases. For PHWR case, the CAIN code also agrees very well to the ORIGEN within 1-5% error except 238Pu. 238Pu concentration calculated by the ORIGEN is 10%
smaller, and this may be due to an inappropriate large 237U cross section in the ORIGEN.
Based on these results, it is concluded that the CAIN model gives essentially identical results to the ORIGEN.
TABLE 27: CAIN AND ORIGEN COMPARISON (PWR WITH 4.0% ENRICHMENT AT
Total 95.360641 95.372575 -0.01
TABLE 28: CAIN AND ORIGEN COMPARISON (BWR WITH 4.0% ENRICHMENT AT 45 MW·d/kg)
Total 95.360977 95.362566 0.00
TABLE 29: CAIN AND ORIGEN COMPARISON (PHWR WITH 0.71% ENRICH. AT
Total 99.278338 99.268354 0.01
VI.1.2. CAIN vs. measurement
Direct verification of the CAIN model was performed by comparing its results with the measurement on discharged fuels for PWR and BWR fuels.
There is one report of 220 pages [28], which compiles the results of the open data on the actinide measurement of the discharged fuels from both PWRs and BWRs. This report contains PIE (post irradiation experiment) data for the spent fuels from 7 PWRs and 6 BWRs.
Unfortunately, most of the data are shown in the format of tables, and the only available graphs on 235U and Pu composition are shown here. Figures 42–48 are the comparison between CAIN results and the measured data for 235U, total Pu, and each Pu (239Pu, 240Pu,
241Pu, 242Pu, 238Pu) composition.
In order to verify the CAIN model, two calculations were performed for the 3% enrichment of PWR and BWR fuel. Based on the report, the actual enrichments vary from 2.5% to 3.4%, and this would affect the result slightly. But, in general, the CAIN model agrees very well with the measurement. As can be seen in the figures, there is very little difference between PWR and BWR. Actually, because of the similar neutron spectrum for both reactors, isotopic composition would become similar. Usually, PWR is using smaller fuel rod, and this will cause a little bit higher amount of plutonium due to larger resonance absorption for the same enrichment.
Regarding other actinides such as Np/Am/Cm, another report is available [29]. The comparison between the CAIN model and the PIE data is shown in Figures 49–51 on 237Np,
241Am, 243Am, 242Cm and 244Cm. The CAIN model also agrees well for these actinides. As for the content of 241Pu or 242Cm, the measurement may include the effect of the decay,
meanwhile the calculation does not include the effect of the decay of 14.4 years half life of
241Pu and 0.446 year of 242Cm. the CAIN calculation is done by assuming zero cooling time.
If the PIE has been done after short cooling time, this factor would not affect the results.
Fig. 42. CAIN vs. Measurement (235U).
Fig. 43. CAIN vs. Measurement (Pu total).
Fig. 44. CAIN vs. Measurement (239Pu).
Fig. 45. CAIN vs. Measurement (240Pu).
Fig. 46. CAIN vs. Measurement (241Pu).
Fig. 47. CAIN vs. Measurement (242Pu).
Fig. 48. CAIN vs. Measurement (238Pu).
Fig. 49. CAIN vs. Measurement (237Np).
Fig. 50. CAIN vs. Measurement (241Am and 243Am).
Fig. 51. CAIN vs. Measurement (242Cm and 244Cm).
VI.1.3. CAIN vs. WIMS
For other reactors such as RBMK, GCR and AGR, verification was performed against the WIMS results, which have been provided by the Canadian consultant. The WIMS calculations were carried out in 33 energy groups. Also, just for confirmation, same comparison was done for PHWR. In these CAIN calculations, cross sections given in TABLE 30–TABLE 33 were used in order to keep consistency with the WIMS library. Also, the power density is set to 25 kW/kg for PHWR, 16 kW/kg for RBMK and 15 kW/kg for AGR in order to keep consistency with WIMS inputs. The results are shown in TABLES 34–37.
TABLE 30: CROSS SECTIONS (BARNS) AT MID-BURNUP AGR, 24 MW·d/kg - 2.6% Fuel
Nuclide σa σf
235U 77.40 63.50
236U 5.17 0.16
238U 0.84 0.08
237Np 38.10
239Pu 250.00 160.00
240Pu 115.00 0.43
241Pu 236.00 168.00
242Pu 25.30
241Am 169.00
243Am 49.10
TABLE 31: CROSS SECTIONS (BARNS) AT MID-BURNUP GGR, 4 MW·d/kg - 0.71% Fuel
Nuclide σa σf
235U 115.00 96.00
236U 6.43 0.13
238U 0.940 0.06
237Np 48.30 0.3
239Pu 388.00 249.00
240Pu 185.38 0.38
241Pu 362.00 255.00
242Pu 25.30 0.3
241Am 393.89 2.191
243Am 75.87 0.06523
TABLE 32: CROSS SECTIONS (BARNS) AT MID-BURNUP PHWR, 7 MW·d/kg - 0.71% Fuel Nuclide
σa σf
235U 175.00 149.00
236U 5.61 0.12
238U 1.12 0.06
237Np 58.80
239Pu 391.00 265.00
240Pu 167.00 0.34
241Pu 443.00 323.00
242Pu 20.70
241Am 243.00
243Am 52.70
TABLE 33: CROSS SECTIONS (BARNS) AT MID-BURNUP RBMK, 18.5 MW·d/kg - 1.8% Fuel
Nuclide σa σf
235U 125.00 104.00
236U 7.52 0.13
238U 1.16 0.07
237Np 53.70
239Pu 362.00 236.00
240Pu 186.00 0.37
241Pu 361.00 258.00
242Pu 30.00
241Am 236.00
243Am 58.20
TABLE 34: CAIN AND WIMS COMPARISON (PHWR WITH 0.71% ENRICHMENT AT
Total 99.278356 99.311225 -0.03
TABLE 35: CAIN AND WIMS COMPARISON (RBMK WITH 1.8% ENRICHMENT AT 18 MW·D/KG)
Total 98.144252 98.200370 -0.06
TABLE 36: CAIN AND WIMS COMPARISON (AGR WITH 2.6% ENRICHMENT AT
Total 97.628738 97.698740 -0.07
TABLE 37: CAIN AND WIMS COMPARISON (GCR WITH 0.71% ENRICHMENT AT 4 MW·D/KG)
Total 99.5876 99.5757 0.01
As it can be seen from the tables, the CAIN code agrees very well with WIMS code except several higher actinides. Considering that the CAIN is a one group and one point model, it is concluded that the CAIN code has enough accuracy to meet the requirements of VISTA simulation model.
VI.2. MOX fuels
VI.2.1. Benchmark of PWR-MOX fuel
In the ORIGEN, there is only one PWR-MOX library. Cross sections used in VISTA which is given in TABLE 16 are identical to ORIGEN code. In the ORIGEN manual, minor modification to U/Pu cross sections due to burnup is proposed. But this modification is complex, and its effect on the isotopic concentration is in the order of several percent. So, the original library cross sections can be used in VISTA.
In order to compare the VISTA and ORIGEN results , constant flux is used in ORIGEN, that is, IRF=2.42E14 is used, instead of IRP=39.2 kW/kg. Also, in order to adjust to 45 GW·d/t, 1 155 days is used instead of 1 148 days as irradiation time.
The result is shown in TABLE 38. The maximum error is in 238Pu (5.3%), but this nuclide is the end of long chain, and the error is acceptable.
TABLE 38: COMPARISON BETWEEN ORIGEN AND VISTA/CAIN FOR PWR-MOX BU=45 GW·d/t
VI.2.2. Benchmark of BWR-MOX Fuel.
In the ORIGEN2, there is only one BWR-MOX library. Cross sections used in VISTA are identical to ORIGEN code TABLE 17.
In order to compare the VISTA and ORIGEN results, constant flux is used in ORIGEN, that is, IRF=1.21E14 is used, in stead of IRP=24.6 kw/kg. The result is shown in TABLE 39. The maximum error is in 241Am (-5.5%).
TABLE 39: COMPARISON BETWEEN ORIGEN AND VISTA/CAIN FOR BWR-MOX BU=45GW·d/t
BU=0
gram ORIGEN VISTA Error(%)
235U 2 781 1 297 1 277 -1.5
236U 0 285 278 -2.6
238U 924 421 907 500 907 292 0
237Np 0 87 84 -3
238Pu 986 1 108 1 077 -2.8
239Pu 43 667 12 210 11 908 -2.5
240Pu 15 762 15 270 15 080 -1.2
241Pu 8 561 7 733 7 735 0
242Pu 3 821 5 492 5 510 0.3
241Am 0 943 891 -5.5
242mAm 0 22 23 (1g)
243Am 0 1 615 1 645 1.9
242Cm 0 139 138 -0.4
244Cm 0 648 670 3.5
total 999 999 954 348 953 608 -0.1
In the above study, it became necessary to recognize the difference on the number-of-fission to energy conversion. In the ORIGEN [16], emission energy for one nuclide fission is calculated by the following formula.
MeV/fission = 0.00129927 * Z2 * A0.5 + 33.12
Some typical values are shown in TABLE 40. Since MW·d/gram-fission is proportional to MeV/fission, and in-proportional to the atomic-mass, MW·d/gram-fission value varies between 235U and 239Pu, which are also shown in the table.
TABLE 40: MW·D/GRAM-FISSION ESTIMATION
MeV/fission Atomic Mass MW·d/gram-fission
235U 201.7 235 0.96
239Pu 210.6 239 0.99
Of course, even in UO2 fuel, there exists Pu fission. So, it is difficult to include this effect exactly in CAIN. Current CAIN uses 0.97 MW·d/gram-fission value for all fuel types. This value may increase 1 or 2 % for MOX fuel, and this will improve the general tendency between current ORIGEN and VISTA. But, this improvement is small, and will not affect the total result so much. As a conclusion, we can use 0.97 value for MOX.
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GLOSSARY AGR advanced gas cooled reactor
BWR boiling water reactor FBR fast breeder reactor
FP fission product
GCR gas cooled reactor GW·d/t gigawatt-days per tonne HEU highly enriched uranium HLW high level waste
LWR light water reactor
MA Minor actinide
MOX mixed oxide
PIE post-irradiation examination P&T partitioning and transmutation PHWR pressurized heavy water reactor PWR pressurized water reactor RBMK high-power channel-type reactor SEU slightly enriched uranium SWU separative work unit
WWER water cooled water moderated power reactor
CONTRIBUTORS TO DRAFTING AND REVIEW
Akbas T. Turkish Atomic Energy Authority, Turkey Deroubaix D. AREVA, France
Dastour A. Atomic Energy of Canada Ltd (AECL), Canada Kochetkov A. Institute of Physics and Power Engineering,
Russian Federation
Onufriev V. International Atomic Energy Agency
Pichat C. AREVA, France
Tombakoglu M. Hacettepe University, Turkey
Yoshioka R. Japan Functional Safety Laboratory, Japan
Consultancy Meetings
Vienna, Austria: 21–23 May 2003, 17–19 March 2004, 18–20 May 2005, 5–7 April 2006.