<%BANNER%>

Optimum Boiling Water Reactor Fuel Design Strategies to Enhance Reactor Shutdown by the Standby Liquid Control System

xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID E20110113_AAAADV INGEST_TIME 2011-01-13T20:58:19Z PACKAGE UFE0005364_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES
FILE SIZE 80166 DFID F20110113_AACMXB ORIGIN DEPOSITOR PATH fensin_m_Page_049.QC.jpg GLOBAL false PRESERVATION BIT MESSAGE_DIGEST ALGORITHM MD5
25254ea5c4921dbbde1e06e8af6a4ca7
SHA-1
8c18506749edb4dd3c2f6da7900db92e2d751e2d
43186 F20110113_AACNBT fensin_m_Page_041.pro
6758a4bdc7c4d6a4fab080c4de834dba
5e71149d4566e95543b09b92904fc1b632b034bf
14635 F20110113_AACMWN fensin_m_Page_068thm.jpg
23f32ed57162d24fb7aa7b94f9d51765
cdbc730f976d6f32a431fa7a23ccf34f7f6b8fa9
841 F20110113_AACMVY fensin_m_Page_099.txt
03738bebac700415efbfb8df38d7d43f
a0dca3a98a962ab22abbc9b2b8ec85deec158846
21257 F20110113_AACNCH fensin_m_Page_076thm.jpg
420ca8c2117cfa21da5918ac1a3b0a93
aa3f1b2fb9a445ccf0001d1c49e4a34eaa651cca
108521 F20110113_AACMXC fensin_m_Page_071.jp2
9ee556f792aa2a00192e8b0b1ff49bd4
15621d8c4affa38f55dee59b8d9aa7f466e92999
1830 F20110113_AACNBU fensin_m_Page_098.txt
dec84fd52395a837e94c071ed1c560a3
317052c06768fcb9816dccb85a916ae09e6f5e85
35804 F20110113_AACMWO fensin_m_Page_053.pro
603883aa8fa35af725b26870c136b3e8
d13900fd78dc4bb296bfa2a3caaa7f9358163537
1988 F20110113_AACMVZ fensin_m_Page_076.txt
b94f1696d9519850cb2ff9cd223c8b05
5bf962ad727eefe26310c6ffe52c548822512960
83205 F20110113_AACNCI fensin_m_Page_046.QC.jpg
87d7ecf24c1086a1c53fe45d3a2a3ff1
ac1080ec4f70ded8cef6094c5a463f7128f98829
24140 F20110113_AACMXD fensin_m_Page_015thm.jpg
34a727e49bc4ebaa1988cded47874565
d24303b399ce0fb7f87ac272123f15f4a245dc2b
1053954 F20110113_AACNBV fensin_m_Page_067.tif
591531973457d58554f80ce44871e4a1
31a88d2770e4d5891d8f56d1117ef8d39e7a1494
23012 F20110113_AACMWP fensin_m_Page_037thm.jpg
460b1dc09bca91178431f88aaba356b2
f3dded25fc0855f954512714f2e4b7067e184e86
45995 F20110113_AACNCJ fensin_m_Page_083.pro
d0543f9c587a9042d1c5d89617f989e3
2aa337ebf758929abf298281caadd097394be87e
2377 F20110113_AACMXE fensin_m_Page_008.txt
5c6b3781761e81cb6fe885b660c19dc4
ac76efa5d67a963196de4f813e82bd7f848ce458
78616 F20110113_AACNBW fensin_m_Page_052.QC.jpg
dac7caa657882bd3e053ef637f50a8fb
4ffb98f051ea86b4047b82a8a06c03143ddb07c6
50857 F20110113_AACMWQ fensin_m_Page_067.pro
50271cda47608a0351e9f28b4c223ebc
297565bc762686a068f03af3917e08c1e2daa0f7
76780 F20110113_AACNCK fensin_m_Page_048.QC.jpg
01879f6a483728150765f2c83168ec9b
59847c5f6c214ea52960b03f1d3999955847758b
104991 F20110113_AACMXF fensin_m_Page_042.jp2
491c2ea06934337acfec77118d5881b5
003585c47436f81e348231e266b4925a7a8230c6
34505 F20110113_AACNBX fensin_m_Page_082.pro
6a43acad9daf866a1bb60cb0ed8ee3ca
ef80830e159c6f3474a5b10ad30bfe2063274301
F20110113_AACMWR fensin_m_Page_032.tif
8bebd6fdd010579ac6ea2bb6f56740d0
73c9424c67c14dadb28cdf36c9ca17ff35b8915d
1966 F20110113_AACNCL fensin_m_Page_016.txt
ddfc4d6912b7675fdf1542d30facda63
055986f708e9a95139adadb4ec2fef0a9b7bd0b6
F20110113_AACMXG fensin_m_Page_059.tif
74c314b47c347cbde032f737f51dfbb2
19ec74571e1ba691d670cf84108b5f7fc42b87fa
11634 F20110113_AACNBY fensin_m_Page_101thm.jpg
e4881a71c2c24b84d07481c195e7aa89
a572c97565e2e6d7790146039299365b2c312425
1051978 F20110113_AACMWS fensin_m_Page_006.jp2
5cd6f9b0289930bfccaf2dd19169c6d6
7cd92854ac98019f7a4425fd5dc47118919ca63e
F20110113_AACNDA fensin_m_Page_026.tif
1c789dc90898480381f596660c3a0377
724f51af10c5e98e5995200e370b80674d0bfa74
1051985 F20110113_AACNCM fensin_m_Page_072.jp2
f8b437c4e68b4fee6dd7047e54d51fcf
1a71c070278796e7a112264cad151dab42b5ba24
F20110113_AACNBZ fensin_m_Page_094.tif
71b92f9c672a0da7bfda27a8448d69c4
905cd45a55a6c51795a551c476df53b4412f04b4
106434 F20110113_AACMWT fensin_m_Page_016.jp2
9f929b08cbba61191a575481d8023ce8
9c52cb223eb70a6949164486385e274b0380e553
195559 F20110113_AACNDB fensin_m_Page_051.jpg
5f7bc335cb647a964a5bd209f846c5c0
11ab77467b557101ffcaa97d6f2211b84f511ef8
49235 F20110113_AACNCN fensin_m_Page_023.pro
803394948c63b7fe0101e8bc5e1d79f8
8e75f99cb40d2dc893fa51b224d72cdf3502d09d
F20110113_AACMXH fensin_m_Page_092.tif
4a7a2b8d221048b9afba6a9a1429c5e7
5e92e2ef90f2270390dcc775ee68a1cc68c46825
48029 F20110113_AACNDC fensin_m_Page_042.pro
1cc256924c7a9ae6b90c4a58d566d768
87ba1724ae85919afe979be82ccb52e73f1a8da6
27450 F20110113_AACNCO fensin_m_Page_018.pro
ba6a85cbdae58b66a7af5fe8b8636374
c23f5a51ed6d5fbdd3b556efc2bd73befdca8e50
F20110113_AACMXI fensin_m_Page_088.jp2
0efa019e691dc22a6bf2eccf61299d6b
f1dc0ffac283470bbc4d53c3aa1397ab8e7563ae
22387 F20110113_AACMWU fensin_m_Page_100thm.jpg
9b3dd05197e77ef59aaad0abb4235ef2
239c40558819bf38a446a370f4dc4d2af9a163bd
34696 F20110113_AACNDD fensin_m_Page_043.pro
e801a2de5b0166f806650d6a3bd77574
8ea25e3b927a33a9f2925bfe03d1194dc519b910
F20110113_AACNCP fensin_m_Page_039.tif
0ab29c133fc6df4d3f574ec98a4c0a9f
8d023fb331df2ea61679ab4807b0ccbcb7af26ef
22620 F20110113_AACMXJ fensin_m_Page_013thm.jpg
dd26d6cc96d7985f562aca38b4989303
3e18b8e8b8d8afbe4e33a4d68544e73053a67b82
21624 F20110113_AACMWV fensin_m_Page_095thm.jpg
b44499d20b354ffcb043b8566a293e16
919d6c20435f80b7dd1bcd42ff1879b82fe86966
2046 F20110113_AACNDE fensin_m_Page_075.txt
075d408323e8d5b9304be2dcef24de24
e54c980f693aaad75b7d99479b76cb8d80747304
76169 F20110113_AACNCQ fensin_m_Page_090.QC.jpg
3eead2195c2553da38884b218853f1a5
1b957cfb6398d84b77232e65c4c34d15f17e6317
93156 F20110113_AACMXK fensin_m_Page_041.QC.jpg
73e68fc5ea000d28be413dcbd396e152
cb9577c36e36d1ab1c55a07005a195232e088642
46953 F20110113_AACMWW fensin_m_Page_018thm.jpg
bdc5171dc566eb20d8ee670e6be390dc
0f2c2ddc4a76b9d8d8350fc0c60cafecda94fabf
87091 F20110113_AACNDF fensin_m_Page_093.QC.jpg
29350df5449cee6ed44128fe60b69eed
02a1f1dae3804b8a0496d7009eb255d83f944470
109581 F20110113_AACNCR fensin_m_Page_036.QC.jpg
50b8f48220d2fe221c630ca8129f452f
aeb3a30f729cbdd21233761ef8ff296947e55f59
163922 F20110113_AACMXL fensin_m_Page_061.jpg
6e7f6378880658ebe8cbc1c5a0accd65
2b57b0d7ba2f509191aada5df5ae749c6dc33f42
74469 F20110113_AACMWX fensin_m_Page_015.QC.jpg
4c3eb3d21277c749dfcbc0ddf305fdb8
846294010c7f4763cfe46e718d10bf3d342de7e5
F20110113_AACNDG fensin_m_Page_031.jp2
3ef242aa876f43458e33b9ffa086237e
fc23e0658656c983221f69ae2afc5ac5984d58b6
79932 F20110113_AACMYA fensin_m_Page_081.QC.jpg
2c93ae8c71273cc2f6e267dbb883fb81
da0d80c897754009f5be446528fdac4b091883d0
108544 F20110113_AACNCS fensin_m_Page_024.jp2
f4875444a7f7c35387e8e523b04d9b7a
3085738fb7672c2f3c29305dffe26dd8166688ed
F20110113_AACMXM fensin_m_Page_033.tif
e4dd090eccd5401e81f7bc9e59d96b71
74d7125474d9fd7083eef1580045d3f2402f8571
80024 F20110113_AACMWY fensin_m_Page_096.QC.jpg
7e50c4a580f7ccbbefa98779dea277cb
ef824af83419665ddb6a8d50dc98145390f94067
101894 F20110113_AACNDH fensin_m_Page_076.jp2
66a2b33cfed211d876762ea028926c0c
049cdc0cf2026141944ca4f8c03f3b3af08d13e7
1585 F20110113_AACMYB fensin_m_Page_090.txt
d7dbc00b450bbafd58461f25300e9c03
d80853e33678dd4c7cdfe5227d7ba0f08b975337
49073 F20110113_AACNCT fensin_m_Page_035thm.jpg
9a06c5f3089337871a1f35ade75177e1
039f517dab4c61bd59066ad96768acd538dcfa1f
1704 F20110113_AACMXN fensin_m_Page_097.txt
fe00b711595eff5745bce9f81611c5da
29949a4ee92f9599943af8556102c8c5172d747e
1051914 F20110113_AACMWZ fensin_m_Page_036.jp2
0a14affe244764347966c30782d00904
2b86e72e65fd775e63e526800c59929e43ac8680
2142 F20110113_AACNDI fensin_m_Page_041.txt
c4937602966de582eed01d40848b583d
152cca19ff75863fe7ccc729f9240cd2fc645947
19033 F20110113_AACMYC fensin_m_Page_084thm.jpg
7a45e24a591528551e1d251d190cabf5
d776398634a3782ab508484ac1b4e5997659d785
23042 F20110113_AACNCU fensin_m_Page_070.pro
f174e9b578280f710f79dd6f7113207c
ab9993e0b8670118827264999bdf642052b75acd
150175 F20110113_AACMXO fensin_m_Page_027.jpg
c20b520802d5ed81dcd86533b84a88eb
602c96bce0c213a797f331b628adeb2eb4a349f9
204685 F20110113_AACNDJ fensin_m_Page_048.jpg
fb1b013609bb21e07623cc6ab28d1ce5
186fc02ff3e9ddf31ec002f01ed66307f7b4815c
36270 F20110113_AACMYD fensin_m_Page_093.pro
2ae7e4a96fc587c0e0e15c6ea9728b07
e28e6d6a4ba61a87107cba7ecb4e5d374d63dff2
100170 F20110113_AACNCV fensin_m_Page_029.jp2
95212a915927f6e3cd41b8dfb49ba6dd
ecf71d7cb5bb28a0b99d7b5511ecb1b48d7c4cda
10318 F20110113_AACMXP fensin_m_Page_026thm.jpg
60939f6637494911409acb261b25b1b5
4c46f825bbbd778ad292785ddde7b51c8b8fb857
2178 F20110113_AACNDK fensin_m_Page_017.txt
6ed5816d533ceeb372da9a6e4253d4f8
9e85adf5c371b842f41dc1f009a9aa9c58513054
209414 F20110113_AACMYE fensin_m_Page_065.jpg
792a16318731bdaa2b2728bb260d1772
b47c5a4e5ceb32d373ef50b615482b5ef97f58fd
F20110113_AACNCW fensin_m_Page_091.tif
d34c82c27b74cea9923da144930efd0e
2c8bf60e43adb60c5c645a5c7f1d16f098e5e065
80178 F20110113_AACMXQ fensin_m_Page_031.QC.jpg
b9c7a2e6e33e8a59b983b15dad40ac1a
801d4a19d9ba00e3ee712f2e35039788d2e2a85d
25271604 F20110113_AACNEA fensin_m_Page_043.tif
d9fa17f2fea8c8f04e3298dbb0b04e74
5bc03320eb010e70e7cfd77ffa70da9111c8a2f7
50002 F20110113_AACNDL fensin_m_Page_030.pro
dd3b88221d496f8c9872382583723c51
89a314b4436c72ca9f66bfbc1095b482d18a3b11
108735 F20110113_AACMYF fensin_m_Page_014.jp2
cb852f8cdec3ee9d15e2af38058974ac
348009fe55d897136d35f33e5107e409edad9b11
35363 F20110113_AACNCX fensin_m_Page_039.jp2
5ba4df94526ce6dbab524a53d074c537
691e68d50e887515def0756c334a06d5f6dcfabd
108290 F20110113_AACMXR fensin_m_Page_030.jp2
43117baf58557bf6167e33a227a27b8a
15a54b7c02d289f6363d2b25a472ac48c2736499
1998 F20110113_AACNDM fensin_m_Page_021.txt
43e65457278f70d81a75ddf42161381a
c461c0b33763a8ef3a2d1319e12b52acf868b0f5
78511 F20110113_AACMYG fensin_m_Page_065.QC.jpg
55b8a42e6d33a0894d45ce5005272bdc
eaab230ac53e7703b751dc77efe1cf2a93b5d6e6
1775 F20110113_AACNCY fensin_m_Page_069.txt
6cea3a5dd356768897dca9a7f4e6e345
f99aaf7562c6b1f4d73d7897dd73d9c652be2dc7
192656 F20110113_AACMXS fensin_m_Page_082.jpg
766d5cd582f89a881414e5579dc556ba
a302f24a428f02d79b1b53e4aedbaf8b23ac3af0
79132 F20110113_AACNEB fensin_m_Page_063.QC.jpg
2c356dd5ee73946439a2f6b58f3f8b61
d52628d661606583597c4d34339f0521eb80cfdb
303694 F20110113_AACNDN fensin_m_Page_036.jpg
163e848c70b6fd6708668ef02582284d
ca35cf1a331affac745d31564f5e3333017d8750
1980 F20110113_AACMYH fensin_m_Page_014.txt
9159ded35fe456f230880582972562d8
ad5909ac91df9807e7857038096129e2a935dd64
F20110113_AACNCZ fensin_m_Page_035.tif
56b67f018662bcf7458357b5bf4fca40
be5f66e5ac866e2274e4b94fbb97e01a89c7f86d
34881 F20110113_AACMXT fensin_m_Page_101.QC.jpg
a70c28cd3f3f4aee84a8dc7a20343f8c
c543858d9922acf14036fffd92a9341302f74a9e
1716 F20110113_AACNEC fensin_m_Page_038.txt
423a2ded712569e02cc7095e931e2c25
a8e8a177b34b9f641b9f176bbed476b00a65a80d
88354 F20110113_AACNDO fensin_m_Page_026.jpg
dff923dade9f932df1f374b6c16583c5
8caee3bfe9fb811471da3897c95c097f9aabb427
88041 F20110113_AACMYI fensin_m_Page_028.jp2
c5d25f5795224f082f963c166e9bd483
4a4b5a2c12b3f39878d10d0c09cbea175506ebad
45014 F20110113_AACMXU fensin_m_Page_086thm.jpg
a13e8c371db70773c2fe19532c4184fb
89a13c141c018bf318261f943ed0303b57c7b72e
46467 F20110113_AACNED fensin_m_Page_075.pro
1898cc638d6336813eeaa889df4a68cf
fafbbeb53f7a444c54b53c7238c90018d9b0a43e
78305 F20110113_AACNDP fensin_m_Page_030.QC.jpg
b0736c1a38f393571c0e469da3962215
15b772584bcefb71fc0aa717dcd56e330390298c
183105 F20110113_AACMYJ fensin_m_Page_033.jpg
cc1b332824ad5616ecf13699d0007757
63367fa839911c2ce90fb02d0e2726ef5f147ae5
57759 F20110113_AACNDQ fensin_m_Page_058.QC.jpg
1b365bf9934e9bba2c7fa1472d962715
bebf23d20e174d27bfbed30906119414c169c334
1377 F20110113_AACMYK fensin_m_Page_081.txt
4a0a0c04776ad1fb3b99d0ad7074264b
5034b216bc62de3070b08fedf77fe5ae9d984ae3
91121 F20110113_AACMXV fensin_m_Page_087.QC.jpg
44198db90e366bf1883d4e5e8911c67a
83c3bf6fcae44d6f35c51b5b8a6f2c772cc17b19
109642 F20110113_AACNEE fensin_m_Page_059.jp2
55ffb9a66a52d67f90293be23789d090
c7c1754e31182309b81694b4da115175ee575876
56521 F20110113_AACNDR fensin_m_Page_085.QC.jpg
b5b7045e22f01760ea27f94ba5fde6ff
314539d68f07cae737c34a5171d8687fcdef7504
1572 F20110113_AACMYL fensin_m_Page_057.txt
9fab2950c118c035b14acd27afe15db1
505f451bf8904a448ba677fc68f1c922e37cb2ef
112166 F20110113_AACMXW fensin_m_Page_021.jp2
98c196ebf8b18a68775825042808f097
bc82b4a8322929863984cf7e8ea32b234db65d5f
6090 F20110113_AACNEF fensin_m_Page_002.QC.jpg
203578b7cab6f253b6f73d5cd8d372f5
11e3fed00989dde52621958c055c5be2bdd8fa29
265304 F20110113_AACMZA fensin_m_Page_008.jpg
9423ab3a1ec3b41b187de59b20c45672
fb72be856f5096c3fb4dd1d39f2f13276560ea00
F20110113_AACNDS fensin_m_Page_045.tif
791afba5e089cb32931cdac7a96834d0
de19684280e6fda1c3e64b32f71ae5fe3843b74a
2771 F20110113_AACMYM fensin_m_Page_003.pro
6844bb7ab78e58111e60ef6684a661d8
894bc70e0e8a8bad046fc2d2970f49a840b493bd
64304 F20110113_AACMXX fensin_m_Page_055.jpg
4e907ae32933074ca9ebcefd667d49c0
a2a66dca6e58a8e28ae3f9d94a7ff28644ea3789
35982 F20110113_AACNEG fensin_m_Page_027.pro
1b4748034de85081e064a61cec0dc561
b74688834676bc1d0ffff5e1c1b1453ccc990784
F20110113_AACMZB fensin_m_Page_004.tif
3ef75553b21bc99830c38a79567852a2
341fc3bebc3b1cce4394bc870e5a054fdbb83628
2299 F20110113_AACNDT fensin_m_Page_072.txt
ccf3f746e90676fbc983282baf08ec16
61b428faa92e8571785bb55858c2f60e6057f5d9
F20110113_AACMYN fensin_m_Page_071.tif
caa489200523b23de703e55a111f7ceb
7e39a32e444c6f2b9db75c3b3228717d739ea74b
55479 F20110113_AACMXY fensin_m_Page_009thm.jpg
571d16ae47efc5d2dfda7ae556c8f64a
cfd598f9f3dce903eda79a31737e048c8b6a61e1
1846 F20110113_AACNEH fensin_m_Page_029.txt
8bb4f5999e4c0f68ca073d3451c76065
fff5308a2f2a1ea33ecd5849f94f082c858cfc66
F20110113_AACMZC fensin_m_Page_100.tif
39054cdfff0e925aff9582cdb89bf822
821e01b393271fd697ba7d9d0773c32bb501652a
195126 F20110113_AACNDU fensin_m_Page_029.jpg
c1358c70037cad64393c30dec9de93b9
20dad6c068ee90a15048de2a6d0d0ed6d4053809
88426 F20110113_AACMYO fensin_m_Page_083.jp2
f2a28ad215f43dbdf8584a631faf9a91
783f5a8996613d1508970cde729abc7f30658761
F20110113_AACMXZ fensin_m_Page_023.tif
4c567b3d5bc62ebb0fdacde9887a291e
7775adbdfcd635696bbdf4ef9f3fcd31ab2d059c
F20110113_AACNEI fensin_m_Page_095.tif
0f06f1ee6630160ad2fed333ad30f91f
275898ec7d4b48ff6c5c442cbd9572905186c11b
1815 F20110113_AACMZD fensin_m_Page_028.txt
514a29a5d9d4f8de6caf7a93273c28db
955cd41622c0009ea66f859932ed5c5cbc360df3
1923 F20110113_AACNDV fensin_m_Page_013.txt
8eba635a2bf06cec7270f20b3b7e2b1b
3fbe5aaf48b2176a9e74b134a40dbfea4f81dd01
23486 F20110113_AACMYP fensin_m_Page_029thm.jpg
f2e56f7066a4e2aee7acace271b48d05
ce5fc17a370e1eea158afeaf7b6b3ac851c0e3be
77185 F20110113_AACNEJ fensin_m_Page_027.jp2
79e90faed0815b1a16ec319b0feafc7e
e1c40fef643ff570aae28fe021a01854075b4d36
877406 F20110113_AACMZE fensin_m_Page_046.jp2
c06921ea436a6f1ac440396ff515a976
2ac128faeca282bc9c59fa32485b56fa4262e918
25626 F20110113_AACNDW fensin_m_Page_096thm.jpg
9cefde613975f2ee37bb8a2ce23a823d
fe0d3f5f6ac669d25bf2eb89fe79ae4cce1aacf9
1617 F20110113_AACMYQ fensin_m_Page_084.txt
3c6389c83e676c23d205e67170ce0d81
d7f4620e78b8d0f4c2d110e036c7e9ed8df78315
F20110113_AACNEK fensin_m_Page_002.tif
c4d4edbe41748b3bb61e42a934cbc931
5df1302f8fad10200d7e6ddc63cc1426d6c8352c
F20110113_AACMZF fensin_m_Page_049.tif
d4b8bfb4184a5be7582d40134a44f58c
88e77159ca413aac06a18d653fabea416212269c
18625 F20110113_AACNDX fensin_m_Page_026.pro
33d4f9f7545f85c7bc1d38979662a3d2
33afb326460d778e5dd34a4cb61a06889a191ae8
68239 F20110113_AACMYR fensin_m_Page_004.jp2
a04be0c15c1c4f8671359df3a4a7bd56
758990b4b6b15f2b6e19b9c542965059ef291bbe
F20110113_AACNFA fensin_m_Page_005.tif
1df678d6f7adebf8abf37f0117fd3cc3
c30196c1357157b6d2eae07d0d507bccc9838285
802636 F20110113_AACNEL fensin_m_Page_090.jp2
79a518eacff598130ac9076b3e78b36d
8fbb7277adb2dc534ef500813771b9490e0e56a3
865019 F20110113_AACMZG fensin_m_Page_077.jp2
32482953934fe6ba8cc584e497858fb0
e0ea62aca176a2be2703c75c9711f70887c8dd0a
F20110113_AACNDY fensin_m_Page_066.tif
66457a403a1f4df61736889f5c4ba308
4e8e9048e0c263ccb8d473dfe8f3aa085911166f
2068 F20110113_AACMYS fensin_m_Page_024.txt
7778aac7de33cffcdbaafc8827d061a0
62d64afbf7438268a61778f063452b6f8eaa818a
209907 F20110113_AACNFB fensin_m_Page_014.jpg
e6453e3f8b7b53aee3c1f7befe08d326
7b3cf0c11947dd6b9cc3329a0353c688e6ae7ed7
1844 F20110113_AACNEM fensin_m_Page_051.txt
c60f5cca7a50efbb4b77e1bfff6ee1f6
19816eab8731308605734da7d049c15d845d4050
F20110113_AACMZH fensin_m_Page_034.tif
f3c1a7e40f9ff05e808ce0bb4e32a260
302a5ae257ab79d7c1a6321476302e9237973056
1765 F20110113_AACNDZ fensin_m_Page_011.txt
45d708180d7b18805de519da881a95c0
14d7a792c0adbdb760025d42ce449a17561c7ab3
F20110113_AACMYT fensin_m_Page_054.tif
a06373fba28c0dd3e11ffa3668ba2942
61d8504aaabc9eb0ab3b9bd2a75a9498dc1fedcb
113321 F20110113_AACNEN fensin_m_Page_020.jp2
74435a433b48d9c2e0730bdf4c776687
7b5420cf648ae16c8ea87409adf193bf8159dd48
40410 F20110113_AACMZI fensin_m_Page_056.pro
8dcf49d5d3c5366e034bc6e374963079
7934642faab5a49691a62764302ec19db966e7ab
80638 F20110113_AACMYU fensin_m_Page_022.QC.jpg
9d06ead883dc913b06107ec2b639efc2
6ced97a227d44dabdbddd79b000d217d53fdc75d
94422 F20110113_AACNFC fensin_m_Page_097.jp2
c94b175914272b6da0a90fbe91ef5827
8b620e8614856249dba2f3a5d00d3a903693e6ba
85021 F20110113_AACNEO fensin_m_Page_102.jp2
80a75c903549feaaf9f8ab0c85281826
c0d04c41d13f6587639d08a13403e6fea638efd5
48523 F20110113_AACMZJ fensin_m_Page_015.pro
cdcca125e38c9bb7f1ccfaa118696ed0
61874d9ad3587fe1ee4fedbda7baaaf4e5a91dc4
944068 F20110113_AACMYV fensin_m_Page_041.jp2
322bb87b54c6888d5f2d892a814198cf
a7c45c750e9c36bb9d9e2e0e9e227d5b891d39f9
46927 F20110113_AACNFD fensin_m_Page_013.pro
7d29a0feeff20b088f94a8a52a534f74
acd817106b8f9939ff0d7989499e0046423260aa
95046 F20110113_AACNEP fensin_m_Page_095.jp2
310d56452058647f409d85ca08edf7ea
92658ea50d986edf6b529863e6e5eac67c8763fc
97471 F20110113_AACMZK fensin_m_Page_088.QC.jpg
fa7e64f5867b537a443b89721b7d3bb3
74474211fee10e9e6d5aae20b4d586a25f51d44e
F20110113_AACNFE fensin_m_Page_016.tif
fa057fa23dab8a3d374665e54872294f
8cf9c7a7c37dc51823ad142c1678d8488aa8cdd2
163598 F20110113_AACNEQ fensin_m_Page_060.jpg
d0a062a98537c8b4e39c72e2166e9182
5bc67667a6e15d924ad88ee184c47476cefb4648
570 F20110113_AACMZL fensin_m_Page_055.txt
040fd3a672bed6e1640331aa4ebe8baa
4678df20375d5582f0b9dc3c8204194ae4d9f624
F20110113_AACMYW fensin_m_Page_065.tif
35e46c44e43f745b8afef61f94dd0e1d
c80aad41dcff830314b254c06c598976608a55a7
198382 F20110113_AACNFF fensin_m_Page_041.jpg
b433b1dc21a307be22390758ea15bdce
e5f218da470c070a3ecab10fa10824346bc1128f
77140 F20110113_AACNER fensin_m_Page_089.QC.jpg
e389b6f56efcfbab9be3ca672456c1c8
5d9c9e3675d01a79ab3e1896915e93cac8a8f2cd
43608 F20110113_AACMZM fensin_m_Page_061thm.jpg
e25a8f2763c5d2be4c0b7531a74927a9
e3aea75fef735a58fd6fb0d0a00934e3790fb02b
51759 F20110113_AACMYX fensin_m_Page_020.pro
b0c9e41ed6a22076cbbc7a5573143aff
89e60f00f3acd91518c1836d9cc28ec5b2248422
F20110113_AACNFG fensin_m_Page_048.tif
42ed609e21c78a78857a422736c21ac1
281101e97063d6a58b83e4bbbdbf7820f3ea33f8
F20110113_AACNES fensin_m_Page_021.tif
13497d57da19a5e3386a1d0a854bb87a
e695ba4dea0b9154a8289bc5ce865c9740614576
7195 F20110113_AACMZN fensin_m_Page_003.QC.jpg
b3da38372ebd3eefbeac9a5d03258e5c
56349c9c1854c88c7dd496164c2f3eb1746d5b6f
36477 F20110113_AACMYY fensin_m_Page_073.pro
16a28024d1cd9b388c9a43399d9bd6ae
1bca2c1cbba378af27d581ba2e953968e7f8ec52
201096 F20110113_AACNFH fensin_m_Page_087.jpg
a19157eb43dfc7d7f7efbf6ad9b0563e
787181adbeb9e8d1c1e777c03fa382801469e064
43148 F20110113_AACNET fensin_m_Page_006thm.jpg
871a92b797bd3755b0ba2039c8a1ba94
20e55994d32c1fa426db81583235d7f56bdcaad9
115488 F20110113_AACMZO fensin_m_Page_054.jpg
6b6277fce83e8a8060eebdf0c4db082b
5c04de0aeada62981e95ef7ef4bba6050b22811c
32307 F20110113_AACMYZ fensin_m_Page_064.pro
fbb2ab5a7ffe3bd491fea1a0c0ec9616
570090d0697c073d32d743bc0c4665ed252ba02d
118802 F20110113_AACNFI UFE0005364_00001.mets FULL
3ff115fb3a03305a86b06f134c1e1e2f
2ea084d2fb8779f7a3eebe4129741b491456368a
78432 F20110113_AACNEU fensin_m_Page_062.QC.jpg
8d6d8d3fe52aa2a95e4936b52af3bfc6
335e5047bd2c2b579adf68d55040282494df2b25
105120 F20110113_AACMZP fensin_m_Page_007.QC.jpg
2ee879de51a72b3e5936573a36712d68
af12cf33c6ee04038166d8b5d1ef4ddd22fa3c98
F20110113_AACNEV fensin_m_Page_062.tif
dd8a88e8b95a3237dee877e0b81006bb
822730e6e41cbccf878df9aa0faf97874bbcd90c
211091 F20110113_AACMZQ fensin_m_Page_059.jpg
ea6d1bae6521f78fa46cffbafe6493b8
2c438db91411d0bec0b8bc6ea880ed0089d6850e
38478 F20110113_AACNEW fensin_m_Page_054thm.jpg
3cf381b15376add28d6a355b8b803933
4f24a31331d5638931fb4a60634e627aeb65dea8
80464 F20110113_AACMZR fensin_m_Page_059.QC.jpg
7200a689a20abb5d5459abd71cdb5015
afdd3e07440b40b1fead75fcf0db5643856b1b13
166621 F20110113_AACNGA fensin_m_Page_040.jpg
9d2693665705eec3958b403acf2f33fe
ecc5462a911c209fc1907838636be206c392dfd5
15358 F20110113_AACNFL fensin_m_Page_002.jpg
daef279af782df2f64527f16d5ebbe33
5a7e1408459c1a337b690221cd86f48216e3f45c
F20110113_AACNEX fensin_m_Page_077.tif
1e4a46e07aedeedff4748dd6296b2dcc
e0f0734f77147d663a02408405f6e0b3ff700491
89644 F20110113_AACMZS fensin_m_Page_011.jp2
9516e47706c8291b8cd0b1d5178fa0ba
0108dcbe095d5999b4abd21150ed3f6e220ba391
203723 F20110113_AACNGB fensin_m_Page_042.jpg
9cc401f92fe0bfa0c47dea08aac1eddf
f1b6de629dc95510e5c7a5f3eaec869d159878e6
22248 F20110113_AACNFM fensin_m_Page_003.jpg
7d6cb979700a59b7a1b60c3563c7464f
50a46efba26ac8a87f444c9a6b3718358ab07a51
F20110113_AACNEY fensin_m_Page_085.tif
b37b1020ec88334fbae160e856783973
5d17032d4fc8b7433348b943e1b5e0db772da944
F20110113_AACMZT fensin_m_Page_012.tif
3e51e516cd5aeb4fbb9a8a9a04678951
9e00decabca19b855eaa9cbed583d76d553e33cc
183406 F20110113_AACNGC fensin_m_Page_043.jpg
4c1b30b1135f7ea48090cbee078b0756
95e86a4a6c8258e543b59b8d71e8dcacec719413
136162 F20110113_AACNFN fensin_m_Page_004.jpg
9f8824f16eaf2ba51256117d6e245e19
60f07ba2d5c06dc574a3009edc03c3b290d2121d
168049 F20110113_AACNEZ fensin_m_Page_085.jpg
88721d2613eccb774ed854d22e20bd25
0e03555f2ac09c190a87cd9d1166994283012cd0
50210 F20110113_AACMZU fensin_m_Page_014.pro
72ce9b89dd273c5090ca87f9d7cbc19b
ced30628fd0466f8b9b8adafd29b870421390a9c
266904 F20110113_AACNFO fensin_m_Page_007.jpg
6e767eeb026b4d08742b286d616569ed
8b5c103b6a786f3a6b5b2dbf9d9f8a14bdc10aa1
5904 F20110113_AACMZV fensin_m_Page_002.jp2
2795d3860031b9e0d8b6f9974267d281
81f6e6d6688208a92297a0f6ffb4385935931004
199534 F20110113_AACNGD fensin_m_Page_044.jpg
2abd28a482993921c239a6d5c5741c6e
78c4b9d6131031f67dcad1cc44f4fe6947a80445
198739 F20110113_AACNFP fensin_m_Page_010.jpg
6f5ce683a257a44a7152f74b41463030
306d9009e8423e2a779629cfe991beaffb818795
180385 F20110113_AACMZW fensin_m_Page_062.jpg
56e14231f6c076577d07503fb68a8a7e
0e2150c9bad87e67bf366be6aa1219a4981d20ac
174744 F20110113_AACNGE fensin_m_Page_046.jpg
ebb00442c472c9764b552e378f55ca8d
c11c0efdff6d4265f5ba9a56a68eb756042f89b8
182194 F20110113_AACNFQ fensin_m_Page_011.jpg
7d5ed622b4bbefdbce9fdc82f627902c
e43c7a19b3f26eb9324d36acabed524859a5ec14
324081 F20110113_AACNGF fensin_m_Page_047.jpg
ca4915ab562f11eb91e042a8d1ab0f6d
076444637d2331ff63e6368cf6eb4d87770dd73e
189404 F20110113_AACNFR fensin_m_Page_013.jpg
ee3193fd856956b23f3c5d18d3dc096b
9a36a04f8138b8bbbbe38caf9e989d916df28f22
218336 F20110113_AACMZX fensin_m_Page_021.jpg
2ae4ee9ca0cc25d0fa2f91f135ddaf02
2f42f1806091ea99cc5c4f055c8bbdebdc537b77
212073 F20110113_AACNGG fensin_m_Page_049.jpg
89de8639dd70b6bd6e4252a230aef5c0
c38e495b48b925ac942f224f17197b7647c49add
205626 F20110113_AACNFS fensin_m_Page_016.jpg
59d1b9c156faad0ccc0b31250c266480
2bac61af353551f7cbff59cd8174ab3a3be0191f
48743 F20110113_AACMZY fensin_m_Page_099.jp2
c6858ebcf13d490343af17b2e7a829fa
b8f2f56cf8ae47c31ee6e3ff1c557f6507bf4bd2
407238 F20110113_AACNGH fensin_m_Page_050.jpg
0ca7bed1351970d719b008431b65a5ef
97bff7511e80e737e6fcb7e0507df3ac851fe711
202014 F20110113_AACNFT fensin_m_Page_017.jpg
0db3e8e161ca5c020e81d77ad5636de3
95dfc0dcc27b0acdcf484e2b62c64aa2328b70d3
39890 F20110113_AACMZZ fensin_m_Page_011.pro
bf02502e9896b611c4565f93651eddf0
a456c57eae445480a037f6a645b43c961ea88c12
178740 F20110113_AACNGI fensin_m_Page_056.jpg
2f48eba03be7ff17c70b3d3844f88212
793813d78d61dbce69609639faa09993631fe540
201056 F20110113_AACNFU fensin_m_Page_018.jpg
d9a9fd66d9400951d63ddd3ef4b0268e
cfc5176820e4a7d5cf07d10b6d63c2293e3ea846
205811 F20110113_AACNGJ fensin_m_Page_066.jpg
5878a2accd927c0eaaf62f9b7df72121
3b5c6fee9dccdf96d137e2fb8aadaa679e1a58da
279054 F20110113_AACNFV fensin_m_Page_019.jpg
33fffc80db644ba1fe7b77b0f5ef3fe4
04333d621951a4eb9c194ed5c905d61dd4b0d3f6
247586 F20110113_AACNGK fensin_m_Page_070.jpg
daa1c7d06dfcfdff866c4c7c31f4b469
c4e7c95149c347afda4d78a42eb477dd7654236d
219889 F20110113_AACNFW fensin_m_Page_020.jpg
e1cab196e1d68abde249413dc71e128e
fb51fa933f1677fd4489486c272e623f6bf443f1
248408 F20110113_AACNGL fensin_m_Page_072.jpg
93fe01e183aa9eac7dd6e8b104fe0b30
46e7d6df73fb3b441627c52504d3f74b09c6df73
204152 F20110113_AACNFX fensin_m_Page_023.jpg
179295cca8e0b74e22b34bb79700fada
98c3f9ba50392f8e0bc094377f187819181610ca
112894 F20110113_AACNHA fensin_m_Page_022.jp2
7a120066a13873eac78b9dcc37790fc3
d512b987f043e95d142579c8560658f17400357e
248519 F20110113_AACNGM fensin_m_Page_074.jpg
2fde1129550fb22c983224b861be81f0
8998e8d253281d3200184b3deda9f6ac0593a513
206750 F20110113_AACNFY fensin_m_Page_030.jpg
6b1d5fceb03a2b67ee41ab52e86922bd
e830fe0d6970fdd0a743a265e97e6f8cabf4171d
96112 F20110113_AACNHB fensin_m_Page_037.jp2
fe7194e2fcfa36b7341aa85c8b426277
fce28e11a43e9cde17bf52cd6dddf8bcafdc5aaa
225808 F20110113_AACNGN fensin_m_Page_075.jpg
23134cf70548b3dbf8d7a70885f17410
b86497ad0efec38baeae361c4d2dd5e648991eda
213516 F20110113_AACNFZ fensin_m_Page_034.jpg
600fac724f2b41e68d7f9ca6b014d4c7
672a1a59a4d555f94ffeb6b1efd8ee781313d7bc
881470 F20110113_AACNHC fensin_m_Page_043.jp2
64a620dbfbee71ecc45fbe37ae26eb4b
f075e1f115173aeec00af12386aacf3dfe0c5e36
199306 F20110113_AACNGO fensin_m_Page_076.jpg
492f5b8870917cb0155ada6a0ac4a654
cf0b7db942dda445b111bf9685e94949179843ac
727356 F20110113_AACNHD fensin_m_Page_045.jp2
99debf9249ae811c39c28215a358265f
e2204a8ae816f7856dac95a7007bd158417c7237
168041 F20110113_AACNGP fensin_m_Page_084.jpg
a2e9bbf139b643c2e8733e460fa86229
9e2e5f0c69c745fda524410d6de51f8038b3e118
253681 F20110113_AACNGQ fensin_m_Page_088.jpg
d2b37ba2a824f93d3be8a453bf42b611
cacef8832761d3d85fe2afe84a7a180e2d2a6ef5
100531 F20110113_AACNHE fensin_m_Page_051.jp2
efc70074b9b5a97b6735580c3d20aaac
f2c4d1233e9cfd6271430db458a443b58b40aa08
158920 F20110113_AACNGR fensin_m_Page_090.jpg
b8d82f51e4c09c25ed38835d2bd9c23e
586de25d18b9390c4e08c599dc4e4b99ea10a88b
31975 F20110113_AACNHF fensin_m_Page_055.jp2
d762ede065c408203238477a56106e20
70f294677b2e6bfd63407dc8ac0191780468e059
212453 F20110113_AACNGS fensin_m_Page_092.jpg
465b5ee58d934117707562f5b968fd35
9677e472017c39e11ea560ddee7c5eb3c477ac5c
1051949 F20110113_AACNHG fensin_m_Page_057.jp2
4bd67d5e385e3a57832ca3a7de1359aa
c47332d3850d2083c64865acc3f9e7ff5a64d2bb
22013 F20110113_AACNGT fensin_m_Page_094.jpg
81a28347d319863282e8b368699962f2
76639e2c5e95f4a5c1de5ed1922fa668453b2feb
509238 F20110113_AACNHH fensin_m_Page_058.jp2
ab0f803bfe3f4c738c46f324869a2cac
cd593aef795606b589d188a5cefada766cc694ac
182085 F20110113_AACNGU fensin_m_Page_097.jpg
f56d5fe576eb58ece2ec8b54c0fe25bb
ebace6791232848fec42bf7d7155f454ace2e7d5
832313 F20110113_AACNHI fensin_m_Page_060.jp2
773d8bdd30814049c4fe2ffb78cca073
432f4c32094e3d33b91ba9e6f5843189d6a8672d
190537 F20110113_AACNGV fensin_m_Page_098.jpg
e0a686dfd1b72e3927b5889d2b39645a
897d7242c4eb13ab5ff12669320763ad2410bf65
758563 F20110113_AACNHJ fensin_m_Page_063.jp2
2fc4093d77b85791a3cba17b80f5e347
e253b99c3bb4851d95dedfa1c245a3ba8f35da00
170187 F20110113_AACNGW fensin_m_Page_102.jpg
87f34e5ddba3ef280e103230f6ae30d9
827fc32a490923bab396d5b33cccb28551674674
108505 F20110113_AACNHK fensin_m_Page_065.jp2
b2823a7bdb10fc30be2c8bdb83456345
94416e31e67432eedf942c8410a90b907acc1dd3
9345 F20110113_AACNGX fensin_m_Page_003.jp2
26b2ae83bbe63d40274147a76b08bafc
f15368fb8adf809c899ec57bbc0f6fe7ac15a898
F20110113_AACNIA fensin_m_Page_007.tif
89aa77db29229ec558836027d808912b
5463d79d8246159ca15f4dd9add9e5787ab9d1e0
95270 F20110113_AACNHL fensin_m_Page_069.jp2
659fc26094b3a233ccfbd3f03afc81c8
21ba7ade4f03c0bfbebe115c755e4e1f8ee46022
98341 F20110113_AACNGY fensin_m_Page_013.jp2
0d35a01f2294508bc0872057926533d0
87d012f1c03c0202fe603738d2f078fe0bc1ad7d
F20110113_AACNIB fensin_m_Page_009.tif
b216821f5c98330a2c126df11c126c5c
baa10bf2e57ea8ce97f967f7805e154a9c139888
F20110113_AACNHM fensin_m_Page_070.jp2
478d907c4458b42ebf396e90fa547322
4298d8cbb27bd2b805961bff57a4c22bd92c4cfd
1051748 F20110113_AACNGZ fensin_m_Page_017.jp2
3274fe98fce7bb10b1fc59fe79b0679d
a9959a19b40a6997a9dcb9192d643b58174cd5ea
F20110113_AACNIC fensin_m_Page_011.tif
5b4a1a416876b1bfd122b7b9a02847d5
2e3505d013c0e9281fdf3caec21207874379004a
913058 F20110113_AACNHN fensin_m_Page_073.jp2
d7537f542e17438c6c830b02b6fafea0
585144056640253a5dfbe8f7046a16162bc9d169
F20110113_AACNID fensin_m_Page_017.tif
49c417f4001633bf3297c4afe50c7d08
5c1c4289f9d9945fabfbbdd945b76fe12d6be4ff
1040437 F20110113_AACNHO fensin_m_Page_075.jp2
9390dd8fd8236dc534e251208d51a0c5
61c7fe0cc2116e6ae969d45ce5296aa30432b098
F20110113_AACNIE fensin_m_Page_019.tif
013df692be386a840d15e46a2aa59de2
2d19805f87665e8f532a511c3916adde1dc3e0f2
740871 F20110113_AACNHP fensin_m_Page_079.jp2
2310d6c357fea763aca986474e5d970b
0a4409c6000c063c96c4f7fe29f9282d50f4b579
948829 F20110113_AACNHQ fensin_m_Page_080.jp2
d56c89d429ad50eee99c9dfa107625fa
b7a6c106594038026c9e072e124626edd07b830f
F20110113_AACNIF fensin_m_Page_022.tif
8da9350ab5cd21766fc48156703adf7c
c910d72c385946064547a0c8e83a2e7bfc9d138c
880292 F20110113_AACNHR fensin_m_Page_081.jp2
0ede73e29c976092a6f7b059a5b6ab5a
40bfa16ab368fc592bfa139a65ffa2227a5e382e
F20110113_AACNIG fensin_m_Page_025.tif
4454a86578cc400f56ddb05b1a2f1b87
dab20a4352bcc47e52c1d7f49e44faca95bfb05e
83420 F20110113_AACNHS fensin_m_Page_084.jp2
fd03dab04c60bb873a2be2bea70dd3cf
c2d1ee70a7a9b282995d90ed9c0eb6ca0d120430
F20110113_AACNIH fensin_m_Page_027.tif
5cdeb78af0829d5ea3aa3241f27e90c7
d48171f61ed38314b34c4936f7280f081bef135e
863810 F20110113_AACNHT fensin_m_Page_086.jp2
bdccfb1a29c10ccf459a6c6a9caaf46c
d454d169517684efb4e920af53bfd346ab20c88b
F20110113_AACNII fensin_m_Page_029.tif
7d13d70e2eff463b5afcfdcd325ce50c
1585fe98d7ac88e04072513fd21d384d9d78b3be
795849 F20110113_AACNHU fensin_m_Page_089.jp2
f9a69028555b4bfe73235647e7e9d092
c5b07ecafc971776087d0a884bc5a49efc1e1002
F20110113_AACNIJ fensin_m_Page_030.tif
574ddd90b4fcb4ac9796981bf58a1880
dbf29af8141ef93438f362145f7d6c34c1a2262b
108720 F20110113_AACNHV fensin_m_Page_091.jp2
cfb7e0e198a0b9ded6924388e3a2e3cd
9d174eadcb2579bf32e353ce753c29e573397b83
F20110113_AACNIK fensin_m_Page_031.tif
64a322f1668afb84d6ff8568e70c9abb
b818685ebcfbe48de44e6026e021ebdf29d1a802
10297 F20110113_AACNHW fensin_m_Page_094.jp2
5b32e2b454f2435044a6df0aaddadb2e
254ecba0e76acd994f8c318181d4af884ba63af6
F20110113_AACNJA fensin_m_Page_080.tif
6af568090eb2cd037c4d0835a25f1c4f
46ed3a220b6c302cfe4728da776390277a5f94b1
F20110113_AACNIL fensin_m_Page_037.tif
9137ca572917a612115f244d07981991
49119651c5043fd05b390443ed6569baedaac1eb
97458 F20110113_AACNHX fensin_m_Page_098.jp2
5737f0004f957564685e269cbe46be61
b1323fba78db8f15d3cfdb400867708c3f8bc3e0
F20110113_AACNJB fensin_m_Page_083.tif
840466e7c1b19a5352093820e6aec489
3b21e8197067956ed144f6a2feb0874910644253
F20110113_AACNIM fensin_m_Page_044.tif
60ac24f69fa22cd86d957ca3d2d9be3f
f12ae61e202020882ddfded762382d2b1601d46f
51315 F20110113_AACNHY fensin_m_Page_101.jp2
d07efc540c3135d3bd18e7902e570b0a
6ec5181a54f09097c02a2f7ea147870d2fe30c54
F20110113_AACNIN fensin_m_Page_051.tif
26b9be9b5de14a6368a3fb1f26f9050b
4bfddef50acaf5147f9cdac648473c3459bff8d0
F20110113_AACNHZ fensin_m_Page_006.tif
d73305b424b1c8e12622bdd367da7bd7
8b2ad1e3b2e593e9df87780d13e56c9e88cb9a90
F20110113_AACNJC fensin_m_Page_086.tif
0532f1d988d9f249860f6a9f7dbf736b
a3e4dd7ec35eefef1797fa26fa46ea98a8269518
F20110113_AACNIO fensin_m_Page_055.tif
b58eedb8d80bfe248e24ad3220eac493
60df16b115b43131fe629163b0873aacb5f921a8
F20110113_AACNJD fensin_m_Page_087.tif
2b4e5a75de1aeaf917641551e556b678
ef070f95c9c21f09ba227ec85617399a387b9de6
F20110113_AACNIP fensin_m_Page_057.tif
cfed36edb050262f69e73b848e6dbd2f
6a832c9840c09ed2c6fbb07c5aada32927c84fda
F20110113_AACNJE fensin_m_Page_089.tif
79a4a39886475dd5416d22153fea432c
50fca79d4050e1a83fa16a6492e1c1b395674fa1
F20110113_AACNIQ fensin_m_Page_058.tif
490bdf67b08153bc7e5b6205f293a079
10a24d4435bdb39ff77e0ac5ac72be21576b5665
F20110113_AACNJF fensin_m_Page_098.tif
724feec0abf920a2e5c2b0831e29dc39
22524bc6ec2aa6ac807fef26d9e9bcce7997c646
F20110113_AACNIR fensin_m_Page_061.tif
c4a07a6ef4b3d8368ca2f3b227655632
f6a7258860363761d46eac517c445214ff9495b4
F20110113_AACNIS fensin_m_Page_064.tif
882aaad5ec4a5a5ef61300650b72fe0f
5a9a784dbabd7a581ac1efc3ca49b5af078b8ae7
F20110113_AACNJG fensin_m_Page_099.tif
b01d41995769082f256a71826b118e63
2cd2f9374b73b85d1584f779906b39bcc19bb050
F20110113_AACNIT fensin_m_Page_068.tif
168765c1ed8e3fdeb4535279983367b9
fbc7afd3a8bbef53ef761d6b476dc32884f3f7ba
F20110113_AACNJH fensin_m_Page_102.tif
7715b3a159de51a417a37fc584b916e8
de5b33457955359775fca55fb01b96f1248b5bd5
F20110113_AACNIU fensin_m_Page_069.tif
727589078b29c92ee61421a78e8ef619
be551a39f554f01514e6ea10133a42c5ae1407b3
9308 F20110113_AACNJI fensin_m_Page_001.pro
a728d5931d6996a99ddbfbe218f45a06
ab281cc151260bc2fca4f9c8ab9c7825e1bc1a1a
F20110113_AACNIV fensin_m_Page_070.tif
ec3d1eb0f7dea5c1d57efeebfea3323a
38e484e214fcdd1809f4ae634ec2f6ad39d85ef0
29955 F20110113_AACNJJ fensin_m_Page_004.pro
af636ea8503b0f8ad6568a1edba93043
09f0c79abb55a71ba661a0815cee3638b5ede2ed
F20110113_AACNIW fensin_m_Page_072.tif
6b76a60d14caee62ca561a5f28efa948
b2c5ca0e9f89e0456f262a8ec1a01a89515977ac
71340 F20110113_AACNJK fensin_m_Page_005.pro
aa0cf6dabd64a6f81601ea7d67b90c02
6ea2d257c5109ccaa7c81950c2246a4c38c8cd39
F20110113_AACNIX fensin_m_Page_073.tif
cec2625d7aec519c79088091ddd97be9
0c9949d824c57696793281ae8c750906d723b2d1
28018 F20110113_AACNKA fensin_m_Page_045.pro
3855a50fb5d5be1cc8814bfc8734e399
b8c7fe3946ae50f43c8d5364596a7082a7b24ce0
55615 F20110113_AACNJL fensin_m_Page_007.pro
bb58f54edb6955fb95c7d47ef12214ca
9688098ea2ff3c252802ee7f7d53677c673bbefa
F20110113_AACNIY fensin_m_Page_075.tif
121d8d822043f50edd29a780c805756a
77452ec76acc7af7805e1aaac0421a297334778c
64060 F20110113_AACNKB fensin_m_Page_047.pro
814b9ebc0370da858622de4311949abe
7e32d5d1a30104790da2cb0870d3581473ca7e70
36342 F20110113_AACNJM fensin_m_Page_010.pro
d5d70ed4e0c5613600ab825ebbdd18af
96ff4b7d07df4f408c6fe63a3293685cd24d46ad
F20110113_AACNIZ fensin_m_Page_076.tif
02fb8e1e10f87be699cbaeb381b9cf9b
4128aee55ce7eb868e7e0c505147e003e460bc70
49875 F20110113_AACNKC fensin_m_Page_049.pro
13435e07774cfaa7c7165623645d310b
ecdd26e7481bb8d4267243a396bd195b0234c5d7
25490 F20110113_AACNJN fensin_m_Page_017.pro
b6c767321cc6ad5803ba9fa7b302f6ab
3d6baabbf99bb1cf74940f5fa7e856fec6c44974
45962 F20110113_AACNKD fensin_m_Page_051.pro
9fafcf97b2f140c72a07e32c1506ba0b
a9a5b03dc73714f38e9dd1fbebae14db0137e56f
26286 F20110113_AACNJO fensin_m_Page_019.pro
b7e9773ad5160d4f7ae1aa7863807e59
2a4f89a5ed3fd080c5ae17624be6c493d16b04a1
18331 F20110113_AACNKE fensin_m_Page_054.pro
ce87337cb4e3b8e8f5ae9619298d2c43
c672f6a326610180e094d1e020cf4211b92a6c7d
51117 F20110113_AACNJP fensin_m_Page_024.pro
b01ca73886aea15b0acd516ac909375d
8775753d8355213e5cdd43c116e38d50cfb6b82b
13343 F20110113_AACNKF fensin_m_Page_055.pro
491cf7005690b0d820b84273311cbdd2
44eff6a3ce61417636d892d19d74982668406c3c
53528 F20110113_AACNJQ fensin_m_Page_025.pro
d895d293c10345e822f7c073b79ec6c0
0cd28cfdfdca3bc04f7e268f3a71c60fc920a013
32508 F20110113_AACNKG fensin_m_Page_057.pro
0022d707684fcffcc52c8fcc296430ab
a5f208929c86ad3b714c19dc470ea3b914482084
41417 F20110113_AACNJR fensin_m_Page_028.pro
3494a4b5e965b843f50c438095bcd5cf
7ea8f37dc173271b8bed87d087aa890a53e354d7
45741 F20110113_AACNJS fensin_m_Page_029.pro
f66541c4d07b5f53029c0a1424b1c75c
74358ed1e2ee552788aae90d5f6148ea80fe1807
14026 F20110113_AACNKH fensin_m_Page_058.pro
506267c4e8d80f1d855de25fb40133b7
6105e84f7655083369a93c147369903657354f8b
51678 F20110113_AACNJT fensin_m_Page_031.pro
6743ec19d051954588bdb6aedb3b56cd
7fad3aadd2eab04a0a8090d47a04a7b7a3038ff2
50377 F20110113_AACNKI fensin_m_Page_059.pro
22886ed71a8bcaa979bb40363bfee172
a18c33bd77190caf3c95dc678f309e74e2576ffc
48658 F20110113_AACNJU fensin_m_Page_032.pro
9fa428fd854756c9d3864e9689016f4c
3f53e7a25caeb74409b1678ae785c3286b914eb8
31275 F20110113_AACNKJ fensin_m_Page_061.pro
a8717f5ba51d5ae2bf4ea4a7cf634274
e9471a247949814cf79d1c08eecc4bbd7e687bdf
43542 F20110113_AACNJV fensin_m_Page_033.pro
9e86c3698d6235e92c2e724b6eb6d754
ae80a8e86a31dff1605d70dd84fa94d755b5ed1f
34258 F20110113_AACNKK fensin_m_Page_062.pro
ea50b342204232c9476251a16ba0fdc0
548fd70bda0f005547a14322d372191c95f84b29
35554 F20110113_AACNJW fensin_m_Page_035.pro
7206605f9bf2718a2ff3133a3e69e151
3ad2599bf4df105e6341bc875c08ec8965fd8335
1470 F20110113_AACNLA fensin_m_Page_010.txt
c1ba813dc103098f87bda8b2ba9a0170
37708488d51a4ade3faabc3d6c61f752c873c26e
34305 F20110113_AACNKL fensin_m_Page_066.pro
f211aec34471962f55754132107dd9b5
9b09c7a2a96e3e4df847e7482165a6643c8e8868
70183 F20110113_AACNJX fensin_m_Page_036.pro
0b5db7248c212bb9395e14b8f7238310
a234221b5992fc25aacd5f495a9787d687477f0f
1751 F20110113_AACNLB fensin_m_Page_012.txt
846d01f137b5aa7f0d8dd3ee972fb941
7eba789a0e8c3334af2f9387c8abd76363d4eab9
43218 F20110113_AACNKM fensin_m_Page_069.pro
42734f3dde7221b26820ed8670310e3a
a5e171b07c1a90f29ef84abc74a5d7ad16b9d7cd
37375 F20110113_AACNJY fensin_m_Page_040.pro
96cf9f32f48ae513d4e8c3b9eb24f86c
9c4a9d5bce5feafd3a6a587502ddc98f2aed7016
1414 F20110113_AACNLC fensin_m_Page_018.txt
40893fe271fbb89dc59a0cbcf4507cc8
368acd0f8900cc9f685b4f5028be6d70b522a33f
52045 F20110113_AACNKN fensin_m_Page_072.pro
c96a192530e181c299b50443bd2adba6
ec1ea3f036aa3bfb8999423153e00ce3c8831143
48359 F20110113_AACNJZ fensin_m_Page_044.pro
44929f9ada83fb908a7ef12ce24eaf23
7f2e24ef4cbdfa9502ce8727b87ec91082bb059f
1096 F20110113_AACNLD fensin_m_Page_019.txt
11db8b21c331b2e26e9b50d309f7585c
a2f4f22ef1ed3566ff1149216ed45decf591c69a
34158 F20110113_AACNKO fensin_m_Page_077.pro
9116bc587c66b468c7fc0e33320def2d
d4447bcb1494c0da11ff737983e4ed79b390e4ed
2067 F20110113_AACNLE fensin_m_Page_020.txt
5783dac6a20a8963a2afb59dd010ff77
4925545adb5a415f36698fede8abe0ebf916134b
25846 F20110113_AACNKP fensin_m_Page_079.pro
37761b01c03a58a4924da903d8caea66
c78d6c7d5cb89d0cd42a3b8afe0fe2165cb4a0c3
2055 F20110113_AACNLF fensin_m_Page_022.txt
6960cce2f17db37c5ae43d343e84a227
4a2e9fe25edb55175b5a60319102031b550d0a7e
37068 F20110113_AACNKQ fensin_m_Page_080.pro
40c66b7e4e90801fecef1de5c8362336
61b5c33268c04f878c0ed18c16e16f6fcebc9ffb
2240 F20110113_AACNLG fensin_m_Page_025.txt
84ad2e7a0d376f341b1cc59154c052fd
37efbc2421dabde2736f4f62a0b10ce7f2475f35
37309 F20110113_AACNKR fensin_m_Page_084.pro
fca1e051c2598f75ae241e506e321915
00202b78eb040dfba5aa4a6d369b7fd2db0c5f30
1971 F20110113_AACNLH fensin_m_Page_030.txt
8705f144b4abae7d5d0129cc5c086d09
f61d532d7acfd2ed11a3998d93436178d2ab674a
34721 F20110113_AACNKS fensin_m_Page_086.pro
5fd09272d9350abb2eb5b7a372d65bfd
60fa3be39e3c47de0a65cd62e88299402c2e4cbd
37496 F20110113_AACNKT fensin_m_Page_087.pro
f1c7789e21bbe0a33104e9fe145f5844
28f35f4bd903df7f0fc83086d28c19e6a96a258b
1836 F20110113_AACNLI fensin_m_Page_033.txt
d05ff5bc4aea2c98369bcf9d2e48729f
7323b29fb2c5909e6cc3bb8f5b26c40d5f66d65b
53689 F20110113_AACNKU fensin_m_Page_088.pro
a63d099be332de4d06fa5741198cc6f6
c5a342c7547339cabec64f8c0d8d1af0372eb657
1503 F20110113_AACNLJ fensin_m_Page_035.txt
11fee5ea0114f5d1faa07f7cfd427e35
e99db4529524ab45d7f4d323d8137158e1eb87aa
3377 F20110113_AACNKV fensin_m_Page_094.pro
025913b8cfbc6423501d1135294a4291
e25684c9834a1e16f996bf80782cd4b896ea4446
672 F20110113_AACNLK fensin_m_Page_039.txt
dbfdaf88ca5f5ec290deb030d9b66c57
96f792a20009e466cd16781294aa0cbfb2a9e273
50398 F20110113_AACNKW fensin_m_Page_096.pro
e094086530782612dad9b54dabb252ad
00f852bf49838ef4af3c0731fc50c4c11c55b5c8
1593 F20110113_AACNLL fensin_m_Page_040.txt
6464398be9486ac079f5e04676029e9a
78be80c204463ffc056ea61658336f06d1c18abb
38749 F20110113_AACNKX fensin_m_Page_102.pro
508babcaee7ee69e4d0655bc693f6564
6f9bae66df2a87796dbe08c41f1078fd5baced14
1978 F20110113_AACNMA fensin_m_Page_096.txt
844967e5e6acf42b28be4154d9659483
169426fa379d8d7c7000726c2cc8cf5901b3c6fc
1626 F20110113_AACNLM fensin_m_Page_046.txt
335c5054d04010b737d111f27009cd67
68611f9464ba4c17889fe42c8717784142f48b16
507 F20110113_AACNKY fensin_m_Page_001.txt
2580fee35dc595e040c07ec8401a5294
c19fa6be102aa3d6d0790b674cb0345bd8171f9b
2078 F20110113_AACNMB fensin_m_Page_100.txt
dbd549740a37d30d2d8591d389e3f538
bd99fc4677e4ec2184282c00dfa45a9680c4cf51
5832 F20110113_AACNLN fensin_m_Page_050.txt
5be857970abf62397ee3680df73424df
c330eab5cbf6948c5afd6253d3acfcd6c3af1e91
2288 F20110113_AACNKZ fensin_m_Page_007.txt
6362e33700df8a101a93e7ed9815d815
83a43ac4db6ee8e33e414b8fc3890f7499ba4fd4
1578 F20110113_AACNMC fensin_m_Page_102.txt
9f7643ecc0e55161925cff472f64c4d6
8139d34744a5035de1610ef2d52f8ec4b578e820
1144 F20110113_AACNLO fensin_m_Page_052.txt
d69f9d2ba4bf7bff75d8c80140ebef8e
aee3e5afabbc72e75b81aa05fc1bb652fe122da1
21625 F20110113_AACNMD fensin_m_Page_097thm.jpg
f5f77110cdfd86074c68df32c975bc75
58ce40f0ca4bce16fe586be17e0510dc27b2ba7b
799 F20110113_AACNLP fensin_m_Page_058.txt
d7287e77cac8565abd2f627ff8751d49
d8ad481d0ad0468c62992f5087e63371236b86e6
141439 F20110113_AACNME fensin_m_Page_050.QC.jpg
bb991fba1f57391605e62b625ba74d71
3980e97444990c0bd16834ec8b6c13fe9ed1a0ae
1996 F20110113_AACNLQ fensin_m_Page_059.txt
d787b2fc7be47fa2f0e4cbb1ec685e3e
ee9530811fb4c461018f7df6bb959c7e7bb8efd1
20804 F20110113_AACNMF fensin_m_Page_040thm.jpg
1663f4f4f55c72fc0ef3b3035c136bf4
ce4eb244fa66a7ae2de794f2afd41b2c035e9634
1531 F20110113_AACNLR fensin_m_Page_061.txt
1b3eff99d2aaf76d2e785b390dd36c60
f0f2fd1466f45b7edabe367c46697275f08daecd
45849 F20110113_AACNMG fensin_m_Page_005thm.jpg
755eeafbf7ae9b30701597cf8a9e8468
f392c801492b0383cdb6d6dbca9629718e94c052
1587 F20110113_AACNLS fensin_m_Page_063.txt
ca7c7409eed982a69827cfac3526a4eb
7d6ad1733fb6962b5f4dc4667352ec3d43957c8b
21272 F20110113_AACNMH fensin_m_Page_028thm.jpg
2fed97617c4c9d077093c1b46318368b
1ba6cd3f3ba984a54b304930f439ad38263b354b
1549 F20110113_AACNLT fensin_m_Page_064.txt
566b187cf4d28ba719b4af9b249c5740
f9b30a23dd17b628b15c4f7adb279e06e6af772e
78007 F20110113_AACNMI fensin_m_Page_060.QC.jpg
136c076fb394b48180275bb4273f8b9a
36fe1755fba505b65a2de00d5f9bcb2f91ed9fcc
1964 F20110113_AACNLU fensin_m_Page_065.txt
9b6ba736a9b4ac85b18cc6c8913b1db8
8c8a65d83ed7a1db10518c0c131e6efd63f8dd6d
1047 F20110113_AACNLV fensin_m_Page_068.txt
a56376ad30fd99d901ba4ce2dc594a30
51b3ee403c0f32d9cbf06cf200223152db86737f
122831 F20110113_AACNMJ fensin_m_Page_047.QC.jpg
4b873a4925eaae6514bef9ab98b04413
05b81a6ff8f5fcafef4ab17ae5766b69d3c984de
1632 F20110113_AACNLW fensin_m_Page_073.txt
a353dd48541542ea900a872576158066
c11e82a3a8066a1014ee33075a9724625bfcba8b
21509 F20110113_AACNMK fensin_m_Page_092thm.jpg
7b2f19f50a794372e4c46f65836b1862
3dab6a448bc8bc774b709f8743879bd46e3c139b
1180 F20110113_AACNLX fensin_m_Page_079.txt
faef37d11fb8fa48eaabf25859f9c5a6
a957a6edc26393662072408d029461c72d91a173
24196 F20110113_AACNNA fensin_m_Page_044thm.jpg
e5b06a773f434dadf8c67cdad3e22fad
c6aedb35cd09a36c4de50e9f026231e6f1f197ae
86477 F20110113_AACNML fensin_m_Page_073.QC.jpg
94831e6bd7a7b36750edac93cfd29866
dc88a0244f2325c7341c273a9484f6e1fd09473b
1567 F20110113_AACNLY fensin_m_Page_085.txt
0ec6cc58c7fcdae780f1a79dfddd144e
2b04b6124ced992ba08a5e66f8017fca8f100be1
153980 F20110113_AACNNB UFE0005364_00001.xml
59446a6817e74f6bf06d1bb7417c3e2f
db2b47c271f8d41b46011b6065acb9068761eb39
43139 F20110113_AACNMM fensin_m_Page_089thm.jpg
80076687b438e9a1ec94ad68ffc3144c
53796ee6fe49696912603fd27df596f6993ce207
1553 F20110113_AACNLZ fensin_m_Page_086.txt
aa7dfb6eb263d01a3f0de2962e24d19e
f01516c882cbd7d42bddc7912db702f35494d3a5
3789 F20110113_AACNNC fensin_m_Page_003thm.jpg
23e0f5c173a980444822785587ffc872
c983f141bd7a9b80d4fbf0886299bde25b9ea8c5
69893 F20110113_AACNMN fensin_m_Page_033.QC.jpg
20abcad9f180c84fb137533bca432f4e
5a6baa0c2637d5c63ab6cf77c646062ed3b169a8
52709 F20110113_AACNND fensin_m_Page_004.QC.jpg
5e028013d0cef62fd6ffd54428b51491
30e92403373eb3e8a6053c611bf2da052d3419cd
45562 F20110113_AACNMO fensin_m_Page_075thm.jpg
87775b101a43ab4036b5d1d06d47be9c
096f3cb93548e3b2bc8e490d45b18d473984b739
48740 F20110113_AACNNE fensin_m_Page_007thm.jpg
aff019c68b8f74e4103f0896eb8396b8
a6bef613dfe6ade04acd14bd3c5a59743fccb28c
57272 F20110113_AACNMP fensin_m_Page_084.QC.jpg
32a2651ad110aad6c5f64666863343d7
7e7904aa3324149d811bd642ba48e5faddb00140
48370 F20110113_AACNNF fensin_m_Page_008thm.jpg
aa2030ca588b8afda0563eaf2e8473a5
2399cfa21e894c86a84ed544bc5e43339bf380e0
78812 F20110113_AACNMQ fensin_m_Page_044.QC.jpg
7f57f0061fb8316b861cef893c93b2ce
ec13a75860e9d88fc7810976999dea398b558d20
109271 F20110113_AACNNG fensin_m_Page_008.QC.jpg
83fa6d390f56b804bd565fc4d5bb0690
2e9c1a673a977a9b4a9653729c247217876b3230
70191 F20110113_AACNMR fensin_m_Page_069.QC.jpg
1920d57b731cacc2168e55ba1f39a724
d9b440e0be3eca2b020c4f01317c1f3584d71268
41799 F20110113_AACNNH fensin_m_Page_010thm.jpg
4c9eecaaa3e7519aceb039fc67100e37
83eaf564e2fa8bf39ad10f4bda67df0413b1660b
48944 F20110113_AACNMS fensin_m_Page_078thm.jpg
f6a35afaefb5bdd956537cb0ec887e84
7358eab05af61fd72be947f9436898d59a2f553f
19366 F20110113_AACNNI fensin_m_Page_011thm.jpg
0026caf5f3a0536cdf90323e2606e5f0
1e5a1dee6f54a7c5fa4145e9e911fa6abd60104a
78482 F20110113_AACNMT fensin_m_Page_045.QC.jpg
50c6001d1b39a51775ec9c4444325bbb
8f44ef9b155b2473da9dc9b08880b2e42ea54582
22992 F20110113_AACNNJ fensin_m_Page_012thm.jpg
82daf7e917ca904d4af06250aae79130
94c5d64162c6b6016f329b765c213de858ed01aa
66703 F20110113_AACNMU fensin_m_Page_091.QC.jpg
7fc849a496f75ac5acb36defddac918f
6775b7f704e74a3893d1120a443611774aacf5ad
43271 F20110113_AACNMV fensin_m_Page_045thm.jpg
8a03c2bfc3b9ec64dc06965fd8b395bb
352cc0fc1b8f4b7c4bd3ccac422cdb1fda4384cf
72303 F20110113_AACNNK fensin_m_Page_012.QC.jpg
24bd06d55834cbf58f89eb32f8a94bbe
76797d588bbd5e9af71fc9b3182d06e35e676a72
46548 F20110113_AACNMW fensin_m_Page_074thm.jpg
3ef254ec67870696a958c6167c05b19a
2542fe984b73ae527237bd583fb051ae243c68d5
45492 F20110113_AACNNL fensin_m_Page_017thm.jpg
a7df73359d644823e530818b59dfedd5
2f9fa10f0aac9d62867fa3089f1cf507e5679239
78869 F20110113_AACNMX fensin_m_Page_071.QC.jpg
e7722e0f11cb2867278107efb4e6efc2
07a51918758ca403c703c1271bfe72a3d0eb71f4
85835 F20110113_AACNOA fensin_m_Page_043.QC.jpg
3c6373349cce324d03e48ffa21bcb47d
e4d2c79c85ddbc2b813b01ffdca422a68580a0e7
48065 F20110113_AACNNM fensin_m_Page_019thm.jpg
9a913fb0c5d7fa22f02de3114a051d6d
9cca30680b2e6e958cfce422e2e4de1ddbae3e25
21773 F20110113_AACNMY fensin_m_Page_091thm.jpg
e8fc473f6e45afb2b30258a3d12fcc5e
3687063bb6a00b28520a8428713c448284676a6c
22631 F20110113_AACNOB fensin_m_Page_051thm.jpg
d476b1fda31ed9b99b5fb37e7d6473d5
ec7e04be6abbe6153b3fedb59c771fbbf9a77246
26191 F20110113_AACNNN fensin_m_Page_021thm.jpg
ca52a271310102b2d25b7e021bedb67a
f4e17727dcb14b9b0d169c709df4ff5196fb5464
25416 F20110113_AACNMZ fensin_m_Page_031thm.jpg
eb0cd74e137955f2b3e83a4109780cd2
a0968f03dbbea42e510c17e95aad15ba829b0e16
42646 F20110113_AACNOC fensin_m_Page_052thm.jpg
08fc75ee1728d73782fa312fc1a62d23
24010745d854fb4f44362394a6d617609c3b522f
82862 F20110113_AACNNO fensin_m_Page_021.QC.jpg
3a8f8caf3aa603eda0f0c212f85c2092
2e189f9091fcc80d1709424253a86ba362ce7246
90490 F20110113_AACNOD fensin_m_Page_053.QC.jpg
44f1f3ab2471418fe5d142ee51419483
ca5e58396eb1fca6f9478e524b2425f8164877e8
30539 F20110113_AACNNP fensin_m_Page_026.QC.jpg
81664530cc094ecb39afd8c28ea98327
0225c8b0a8346d0a937abdd32b6b6765c1ab599a
58525 F20110113_AACNOE fensin_m_Page_054.QC.jpg
9d96f9917edd607d9989aea4f9eba3d7
ace1afada50629ead57f04c47a0c402071f87ddc
57868 F20110113_AACNNQ fensin_m_Page_027.QC.jpg
f2e2b20c07ab865a2a440ec5c9ff226a
9325431cb9f7a92f6286f3712872420a07c15b45
26202 F20110113_AACNOF fensin_m_Page_055.QC.jpg
66d9f8b16324331d3a7f76e2d693d8e3
bee04187ccd9c721cc229b5ccb09de687cc6bdb4
24205 F20110113_AACNNR fensin_m_Page_032thm.jpg
f59e843a05ed28e793a2d64cb4702eb9
06a81337ec82aa6e347c1a489a28045a89c76635
65644 F20110113_AACNOG fensin_m_Page_056.QC.jpg
20c5fc65caf9b736527aab6d78099a3b
a16b29c1c8fc8f44808dbbcb72d854dc88a4ab9e
78474 F20110113_AACNNS fensin_m_Page_032.QC.jpg
08362e694f37198c816176ade7993a59
62710ea6c72ce06b452919c1c5cf6aa3f96ad349
46411 F20110113_AACNOH fensin_m_Page_057thm.jpg
edd05b216e9199f9e8c3f8e0174c22ea
307ad375275906e9243050817455d5d2b9b178ab
22956 F20110113_AACNNT fensin_m_Page_033thm.jpg
252bee9c42690fe624e8a56153744629
88dc33016d6ea35aa09ba13c9380e7f5e0da19e7
43275 F20110113_AACNOI fensin_m_Page_060thm.jpg
7976bb576df940b3cc7b9b8de034d30d
10f3d714a452e171f76baa8de1218b8d3ca18f56
26084 F20110113_AACNNU fensin_m_Page_034thm.jpg
0728b211dfb2d58b7b91bae34d4efbf1
86745b6372687dce853075157ac5416887486cdc
44253 F20110113_AACNOJ fensin_m_Page_062thm.jpg
226c3f8cbcbdd6f2da1732deb3fcd80f
476830eeb31a773f26463f006f5220b9546bb66e
79917 F20110113_AACNNV fensin_m_Page_034.QC.jpg
ed43c9b77d361d72099851d3487999ed
bbe79377bb494922936d1c35ca6ed4b3eca58c76
44591 F20110113_AACNOK fensin_m_Page_063thm.jpg
16327afacc334d9eaab470068386b14b
b4ec6057c5b9bfa21a233a813409aaff8ae416aa
104934 F20110113_AACNNW fensin_m_Page_035.QC.jpg
2dd5cec93f4ad5788c5f01cb64acdcbe
d44a07b5664aac11420ccd9a052d44d347ee4bfe
66403 F20110113_AACNNX fensin_m_Page_037.QC.jpg
6e049d60b8a687ca0705a79a5d28e6b2
9d21409cf193acaa6cb2e83c5f595432d984396f
64514 F20110113_AACNPA fensin_m_Page_102.QC.jpg
3e2f5e60ba56f401ddad590976d85ee1
2730c5638728987247e98f245f02b36571f00617
47319 F20110113_AACNOL fensin_m_Page_064thm.jpg
ff8515a160030b4ef2e566cc82a7f04c
a6592cbaa8af9bb4437864992ae1df11182ee24d
9596 F20110113_AACNNY fensin_m_Page_039thm.jpg
cffc522b78d24f49a61d6dade0f86c44
856584ed9e912fb0d99a471cf673c0dde2ffc809
89852 F20110113_AACNOM fensin_m_Page_064.QC.jpg
ed3ac39487a00fd98f92f93485528546
b131b9e0704c619f39dd26d3e73a8ee4bfc232f6
27945 F20110113_AACNNZ fensin_m_Page_039.QC.jpg
3597c7986f78b1418af2f6d7b57e9600
5c37dc37efbc55214e7486b03e62d6d0e108bab3
92813 F20110113_AACNON fensin_m_Page_066.QC.jpg
3ad11ac1dd5e168f498ef8c0474d977a
aa370c7d75efcccd1df357f618fcadc984fda474
44547 F20110113_AACNOO fensin_m_Page_068.QC.jpg
3d15b8886f4be3f1dad6afcdaecfea14
5ff3d445d632bfb4ac170ee68f72d6210dc0b297
21631 F20110113_AACNOP fensin_m_Page_069thm.jpg
5afb67fa7a7c4cc946923c73b705d7e8
ae5e05a7c53f3a11d54cb4b05e7c9f3f863ad2d1
102730 F20110113_AACNOQ fensin_m_Page_070.QC.jpg
e6e098f13d7f3710302ece3941512150
482696020399a2c436fd8c93b89abe6d19df0dcb
25374 F20110113_AACNOR fensin_m_Page_071thm.jpg
5bc3e415eed5d5aea8fbbcc18610e5c8
6834ec7b09f71f3fc17752b9cdf10949e382a8bc
65251 F20110113_AACNOS fensin_m_Page_076.QC.jpg
16ff8e2390e8a0d0aecd57606939e4c0
fdb9e2c96d8a7425a41b0c5c3418bb28d9d6d611
45094 F20110113_AACNOT fensin_m_Page_077thm.jpg
52e3608178fccd9b87bc6d1a579596f5
b65f21ad3ed4838110a800201632a479deb630b4
44165 F20110113_AACNOU fensin_m_Page_079thm.jpg
7c396f9e8101d88a917dea084220b739
2ae94b6fc823a83b0f7b5abc9883546d7857e211
77218 F20110113_AACNOV fensin_m_Page_079.QC.jpg
97ef17de244a1bb86f1e3ee4e799e7ed
04b98f54674a6fea71047a734367b323d5a55d88
46016 F20110113_AACNOW fensin_m_Page_080thm.jpg
a38a202bd166263b0520d44c65f3f78e
1b0afbbd61db6ffae3a5ce16c56aade2117f3560
44139 F20110113_AACNOX fensin_m_Page_081thm.jpg
2f23e961880dbff863432800026ca177
0aa24afc93179a17b9e4ac039cbc28c41c3b66d2
4119 F20110113_AACNOY fensin_m_Page_094thm.jpg
002ac033a2abdedf48933b67c68e0873
77fce97be9ecff077c6f8184b617fbe1300bde3b
72147 F20110113_AACNOZ fensin_m_Page_100.QC.jpg
e4d1907796850c26812a24e3ee25aa18
ba675686b8316fc2759e7023d70689ac16144655
54532 F20110113_AACMNK fensin_m_Page_038.QC.jpg
8910fd357a5617c9f7401ae9e665695c
f6a0642e430b585ac79ae27b28e3c0154128cffd
1051954 F20110113_AACMNL fensin_m_Page_050.jp2
a293829881c46df95caca0f3090ac4e2
8e7373965c0f04029936a23929d9aac7ae4846e3
105126 F20110113_AACMOA fensin_m_Page_044.jp2
384694892edc11c9a1bf6546620dea15
6badfe1424516a1ad2dfa168c38f914bb3321515
120 F20110113_AACMOB fensin_m_Page_002.txt
9b96ad1f68745bbb2cefeb8163915d90
06db4e4de46758ca9821df88dff1874bb17525c5
49266 F20110113_AACMNM fensin_m_Page_072thm.jpg
4f9d48d93824acab96389967703b0ae1
3fa0148ae1b39ff8514c25fe5b83067c0661cf28
107022 F20110113_AACMOC fensin_m_Page_072.QC.jpg
9713d98bab12aadc2d0dba5360620b36
d5e66656430daab37e0fd09727a387cc5dbd81fd
1051960 F20110113_AACMNN fensin_m_Page_066.jp2
485345d118e51b762609e421bd2cce25
d2ddb680fa0e2e6ac021aff877e2460bf0e64630
9330 F20110113_AACMOD fensin_m_Page_094.QC.jpg
5e23b9bb7ed5360479cc8fb76b698861
bcd99058f249b2cc93cabd208b5966b109d3ebd1
219437 F20110113_AACMNO fensin_m_Page_100.jpg
44bd90d849e8a5148d5973d229dc6fb3
139af593e7d411f7cf2b6c0225d3afb61e9e48b8
F20110113_AACMOE fensin_m_Page_024.tif
1ba5687d7cc62d8b889b8b04c6e6e865
6eaa1ed766fb3577c5c6bce0ec3a3089b9223ed6
68928 F20110113_AACMNP fensin_m_Page_039.jpg
72d60c2f0b2ba5ab4cca92bec145ce1f
70489ca3c4b2e5d5086467d5aa5712ee34392669
F20110113_AACMOF fensin_m_Page_047.tif
80ed57b723f7e6efc60b33688dee4ba1
55826af372e14544341ccb19d01b8d8aa458ed29
93347 F20110113_AACMNQ fensin_m_Page_057.QC.jpg
e9d52a604d7d197dbd1ffd25eeba8adc
37ecb9b24c2b45245bb1f1cf3e07718de3ea582a
822075 F20110113_AACMOG fensin_m_Page_064.jp2
c25e26039c7b0cb345e4e0abe1b6a95c
f67edce585b35726a6184f47e93477d975230aaf
76214 F20110113_AACMNR fensin_m_Page_016.QC.jpg
04529b3f57357dbf279254d3d44d6fc6
71e0a7615b0f872f1f01b647f72e136f972a7366
47239 F20110113_AACMOH fensin_m_Page_088thm.jpg
76b67f96495417af8927aadc9ac50cd3
e94bb3012f78376d97ebb57dafab99ae870c00b3
49018 F20110113_AACMNS fensin_m_Page_016.pro
e6101f9ea62a72af51708526eec22a2b
67afa86d3b10a5c50f016a119ceee19f45201891
810 F20110113_AACMOI fensin_m_Page_026.txt
c36e13bebc344cde2b9ebed861652d87
4b06c4395813e86ff9279903fcb7bfaa36d192d4
225532 F20110113_AACMNT fensin_m_Page_025.jpg
e58e1ea45efffd420bb57427ddd95836
a7a9f7eaebde24e7ee4588bf83f611a37da7a3df
F20110113_AACMOJ fensin_m_Page_052.tif
4be58802754346e144040a899d042fd1
f701360cae87ced48c4b02c9974ea159a9a4f452
938487 F20110113_AACMNU fensin_m_Page_093.jp2
7d8ac402e577c940663a3acce2524e67
6f59e80ed30f143789b7fe9e75f2943d0439e210
132488 F20110113_AACMOK fensin_m_Page_009.QC.jpg
4fcbf9fbae75d93ca5e0ceec17065040
cabccc8aae9e0217113885991e75fe3cf6631ec0
14511 F20110113_AACMNV fensin_m_Page_039.pro
afe294ad24363b77d15f8231363ea39a
e29620af8ea4550e72592c5d1fdad1aa52a02c57
113568 F20110113_AACMOL fensin_m_Page_025.jp2
bbd88869b83420cfdc0465395e9150ac
91744960b270a9ff96810384a41adf8b50fa53f8
2098 F20110113_AACMNW fensin_m_Page_092.txt
0f46a4af8962c20a2fa9fca447b36c1e
3e39d604d3563a003a4f2498c1f9d8a3fae5e0fb
25376 F20110113_AACMPA fensin_m_Page_020thm.jpg
65a9b207c97ac8b987d67b860d9ce3c8
1b38da547c8840aa9152ed638a78539404313cee
F20110113_AACMNX fensin_m_Page_079.tif
db6048145469ff0d48e7f3fa7cb8c26b
ebd5bb34b2fbfe6d48f561fba7e3087c1eaef70c
24996 F20110113_AACMPB fensin_m_Page_023thm.jpg
115366b6d44daf59cbd7b9ff7978714a
91f15a51434e662da9c83dca1b52cbf0df0a4961
44572 F20110113_AACMOM fensin_m_Page_098.pro
1f89de9d2cc5b5a01685ea5cadd46162
f5aa35c82fdaf36f5f1fd98e53e695ce7bddd1d6
23678 F20110113_AACMNY fensin_m_Page_016thm.jpg
00b1a0356f53f7531e495d8fdf658285
cb52dcf776aa8603e14d91a6a0fcfc89c1a5f023
161871 F20110113_AACMPC fensin_m_Page_089.jpg
331d5ad4458841f9bb2b7c14c9c61318
2968c177b5aab48f580da6b390552f0ab508d63a
165110 F20110113_AACMON fensin_m_Page_063.jpg
e4a5e1d21dedaa3838e12407107aa8df
f56b0b3e9839db113336eebcc59bb640d74089b2
195 F20110113_AACMNZ fensin_m_Page_003.txt
f550cc1b07f67a8c9db3f805a9d54a34
45a6d91ca31d6b23a89cc412de6535e01a799a58
86940 F20110113_AACMPD fensin_m_Page_082.QC.jpg
fa203078649b7a5137f5772dea2a11ce
c01dfbb13856b84f7260ee7e8868a6f8156b3079
25579 F20110113_AACMOO fensin_m_Page_065thm.jpg
71fd02d993a0ad10df075eeceff1a873
ca4cae463b18d12053d1f37e1da523cb0a3d902f
20277 F20110113_AACMPE fensin_m_Page_102thm.jpg
2b06e279c0fe79a370c7200490b6e093
35ab9812eda70cdaf293cf02c762fc6ebcb5eda0
64806 F20110113_AACMOP fensin_m_Page_028.QC.jpg
a48726c3d3a1ea4e54edb6c8fea286c7
0069ab4ed8d8fa134afc9e45eadc0f673b4fd348
22157 F20110113_AACMPF fensin_m_Page_098thm.jpg
6e1f3f65fcdecc30bce42371dfd2f5c3
4de9fdc9e9990677e381cbc678231f5a5efff5d6
19203 F20110113_AACMOQ fensin_m_Page_083thm.jpg
31fa533cfdc2b70cabb079055a35d8f9
d86324c55bb88d98100f8e52164ec8186ca60d86
82897 F20110113_AACMPG fensin_m_Page_020.QC.jpg
671ed3670bf18292ee90746f62854644
b82e0a1c90ef503b62aabaf8f06b71dd7b5727c7
95449 F20110113_AACMOR fensin_m_Page_099.jpg
a1da3ba08deb50ec390ca6c4e1e966bf
63aa8d85a178c5fbc959e0b397bc3f78cf123dab
729348 F20110113_AACMPH fensin_m_Page_052.jp2
320614604d9bcd6d18377527c79fb83a
1b7ed72f3d233b2d05ea68f3d4118caf0e191c9a
76412 F20110113_AACMOS fensin_m_Page_025.QC.jpg
bc100537c79a3b7e0a10ce39b9b1a58f
b7e8ace1132004ef7f1dc5c5a7e2b3f2742763a0
2132246 F20110113_AACMPI fensin_m.pdf
5495776e7fad35dabab5913559ba2948
8cf84dabe029651d0e886807ad78dbdc72d17251
169146 F20110113_AACMOT fensin_m_Page_028.jpg
48d141c3a4bdf5b6b6f20d2384e1c99b
ed1762d739c3ccf310a3abbad2c37d401896c4da
25366 F20110113_AACMPJ fensin_m_Page_022thm.jpg
bcc572e41680056800e690acbccb76bf
908d504bd7788a34ee413665411f62e8a174eb2f
24876 F20110113_AACMOU fensin_m_Page_014thm.jpg
71c8b0a171225b7f6a35b6fb89a02c63
a2fc289370b99dd79df4c05e201069c23935abc3
219981 F20110113_AACMPK fensin_m_Page_078.jpg
d541a71e16e3d89194349396fbc89830
ce16332e2646874128aca5dc6d027a50388d150a
2272 F20110113_AACMOV fensin_m_Page_088.txt
b512d1a238f20b0d6f02d861aca17a05
a672658e8ff78eef402a33fcb82aa564a224a521
93429 F20110113_AACMPL fensin_m_Page_005.QC.jpg
4c1c1ab04d7a466cfdee62fcda84eebf
ba3383aed9c440147a8f0798c0a813b80db17cc1
2981 F20110113_AACMOW fensin_m_Page_009.txt
2ab7325aba51af8833f809d2582ab6ea
0061969d9868820e2a3d81f81fce0bd085b8f7fa
1566 F20110113_AACMPM fensin_m_Page_066.txt
acd355a59a0fa474b79c8651da642187
192c8f37f8e0699c9687bb41d590fc68b9bbb850
1051933 F20110113_AACMOX fensin_m_Page_047.jp2
9afab4414075752cc5e553c6ce46e7ed
0bf8bf76e61cb329771499d033f33f65d2b09138
1965 F20110113_AACMQA fensin_m_Page_048.txt
b8ca14cc26e9101fd789e5908e75f69e
70e8bbfa3f92dacc08df0bb316423028c11482cc
73037 F20110113_AACMOY fensin_m_Page_051.QC.jpg
eaac67cdda22c3d98bd5d2a5df4ce4a1
9c8395e30db35c7a3bc58c0a67e0ef20f939b1d0
25273 F20110113_AACMQB fensin_m_Page_067thm.jpg
9050b68d7c6acfcf55ec8bcf7dc73607
d371c0d63d49463adfeebd17994b55aa6ecf7739
69719 F20110113_AACMPN fensin_m_Page_095.QC.jpg
e81547f8b321783a58c6411018df0338
81c846bfa83edf58a4074496811b3f0aa8e262c0
932 F20110113_AACMOZ fensin_m_Page_101.txt
7272fee46ef990e0930efb8273828bbd
a0182634ed5b698ee3c87d6265a377fb02efee9c
24725 F20110113_AACMQC fensin_m_Page_025thm.jpg
9a45743a439eab21f15dd465b04c1e4c
7c84bcffb35f43b34112be7d0c3d72ab269ea641
F20110113_AACMPO fensin_m_Page_036.tif
48636a4c7e7bd10e8c2400091138a66d
474743484e5841f55e29a4aaaff854fb2273f188
38473 F20110113_AACMQD fensin_m_Page_085.pro
247481c6366ac51c81bc1738477e8ef4
9131b4bb8c4678109b60ec021a4f12209ee07bd1
1051964 F20110113_AACMPP fensin_m_Page_005.jp2
cb4615adf151542feaab7c87e1e834f9
e3b476ca1e17531da4b8c22b88b195f5ee8d7ab9
195759 F20110113_AACMQE fensin_m_Page_080.jpg
5da34bb4ee56c39380ef7b37da7d3b1d
1f752b3f2b571aa48b33fe67773c73872c9b7830
19464 F20110113_AACMPQ fensin_m_Page_038thm.jpg
7e5b99ce42f473ce9f80d99c15c58ee1
dddfa204601171b5ea5381906b4d7538005de49a
1686 F20110113_AACMQF fensin_m_Page_027.txt
80c2382f443c7c9c99940da0254c851d
c468ff8e9aeacd6e84a329c53d2517efb0bf7567
96904 F20110113_AACMPR fensin_m_Page_033.jp2
b27e94f0804b8296870823649ee12e02
cea008ea449916426228b6b6eb924dacefa72385
F20110113_AACMQG fensin_m_Page_063.tif
e8908662016f6044312e0d861a8e6dd6
2b876995e5d4fe04f9978ed7f7df7c1c3a2927a2
2943 F20110113_AACMPS fensin_m_Page_005.txt
ed05319bed6fb215d1fd8adff5ce1e0f
4a670ba25b8ee580c161da2a0c77898b25be7b76
45519 F20110113_AACMQH fensin_m_Page_073thm.jpg
d7b668445a9a9c686bf7f40872910f9d
af30919e0d0397fab500c8640c8b076132258de2
1051929 F20110113_AACMPT fensin_m_Page_035.jp2
234c1977bcfc4f1db0a5780e5c320665
2900d02f1363b961bf1defa37879b568ef2a19a4
97917 F20110113_AACMQI fensin_m_Page_078.QC.jpg
0eefd3d34cf4d5c13bb60b71fb4d544a
c0b654680c9f00c23bacb999b418ac6b1378a0a9
78747 F20110113_AACMPU fensin_m_Page_067.QC.jpg
a04a181ae6bf797ecff95ef47e03e371
6058fafe6312caafe4e358cf5158c108a3ff06df
846131 F20110113_AACMQJ fensin_m_Page_062.jp2
83ff981073a53810131d8344ea6d1d1d
40a897730c20c595f7fa90d7329ca8c7acebb9ab
105707 F20110113_AACMPV fensin_m_Page_032.jp2
f6aceaa7d07b6163b623b3535eadc9ab
60710f0cba7cf4ee402dbf2e1ebba8f1aca08ae8
111318 F20110113_AACMQK fensin_m_Page_058.jpg
76d210d55f22ef5430da5aabfa8b36ee
bf9085bbb41437cadd0be9031a2e95d65a8ecbe9
F20110113_AACMPW fensin_m_Page_041.tif
63275bdf35bd9155ab59768f6eaf05f2
05e466cb3f73cea3d137824e1a7637020f799979
2039 F20110113_AACMQL fensin_m_Page_067.txt
45d2152c948921403d5666d71492e733
539a2db0e43946c2645fcc830ae4c1ad34917538
F20110113_AACMPX fensin_m_Page_082.txt
17b842d9ec7e1e1ea71cb6bb45f88dd5
3dc5fdfc0d572a1f2f6e8964ca6ad4b39f99d414
42800 F20110113_AACMRA fensin_m_Page_095.pro
c75dceecf180a13b42259fc50d635d03
8cee71289b2c5e147dfd609bf7551979055fb101
1771 F20110113_AACMQM fensin_m_Page_095.txt
46c81aabb3a89268a74a70fc3d4c9816
a49c5ea2ffb8a4e19947bf028d19075a52934f56
2881 F20110113_AACMPY fensin_m_Page_047.txt
0d85ff70e71cfdd52b892af4e0b1120b
8cbbf48d51e7c4b2160f80ff615b2d1f634dae14
F20110113_AACMRB fensin_m_Page_015.tif
8f860b6e76837345bf5dd484322d16e0
c660013757f9acc083d8d80df428a440fd215956
78638 F20110113_AACMQN fensin_m_Page_010.QC.jpg
15044acaaf789df2aa1ae05e44b45b22
1c63b73d74f1426b54f66ff18e1366e198ff7494
174221 F20110113_AACMPZ fensin_m_Page_083.jpg
e29ad5346bf594cc24e6bb97b16f9c09
fdb034d8c67242af60aa7e05ad4a24943656d12f
46316 F20110113_AACMRC fensin_m_Page_076.pro
e2018faaf006edc33f156cd428e9351d
95573637511efc8d008ae658004944a8a4fb7efd
73087 F20110113_AACMRD fensin_m_Page_029.QC.jpg
21aff5b618658bc707e78df32d8d2e58
434a0d7855420757c6ec71e8c9b9ef70c6e677aa
F20110113_AACMQO fensin_m_Page_078.tif
5af128c5fe064f34dec30df249a6b516
2361dfebe8a5a54c428a5e6d9890a917d12a91b2
26155 F20110113_AACMRE fensin_m_Page_068.pro
db3dbdaf7eb49565cf8f74025964362b
6becd57703cd6dc44713d9ef172b62f4c5f7d4ce
37178 F20110113_AACMQP fensin_m_Page_058thm.jpg
0f1dd9e82ae6b823049d29f198df9521
72ed692fdcee6998640ec0cb513e21f09b8c50e9
214014 F20110113_AACMRF fensin_m_Page_031.jpg
9f8a1b3dc41a31b7a5492444869d30e0
925235add816e494098053c534723f81daf11830
25113 F20110113_AACMQQ fensin_m_Page_059thm.jpg
7cfed4e4388b00783c6ccb0239c09cc4
3fe9085d3b4a76bcd07ad4a58d02fee02bbe0179
51751 F20110113_AACMRG fensin_m_Page_006.pro
13c3bb2967cbc57fd1b7183c18cf37e4
1f723c53dc13ec6266ae57fd28f0ce0c87a48622
1327 F20110113_AACMQR fensin_m_Page_060.txt
290d71811e11b4a9ef064cb066989123
e4de3303f08a129e79626d498002e7cc3d92e823
F20110113_AACMRH fensin_m_Page_008.tif
559de1815ca056bc59db6add67ac37ea
a626a81b102673df0474effb401ce263895fefe8
F20110113_AACMQS fensin_m_Page_040.tif
56efbf6e495acf5ec56b33d91dd0adda
39be85eef993bbd536cadd5bad601bc1d546b764
19063 F20110113_AACMRI fensin_m_Page_085thm.jpg
552acd4d02d554478f3d190d81ede2b0
1e7c0543a48dfad4d9ac6de94dcd0d018cca32ea
44029 F20110113_AACMQT fensin_m_Page_012.pro
7bc6dfe916cff8db3ccfdf57f46b2a1e
19ccb9e726c62d71358b9932338a8eea86e71563
48111 F20110113_AACMRJ fensin_m_Page_036thm.jpg
b13dc22668231674ac40f8c2c5f19a2f
c2439bd47cf34fabc9288bbe10fbc6143e7c07a0
F20110113_AACMQU fensin_m_Page_018.tif
c9d300f9fce82fcf78e57a382e49b0b3
c9934ef98181179a971234b7d8e720c387b10ef1
50338 F20110113_AACMRK fensin_m_Page_100.pro
52034d1c491a162c2b28cd33f77e77ba
e693a9284ab7462856f0e21f83244470bb30b2fd
183754 F20110113_AACMQV fensin_m_Page_095.jpg
4755189a4b89f4ef590c49061c5bde84
3ab7d777491891791e9d0ea13f138567ef916ea4
106931 F20110113_AACMRL fensin_m_Page_019.QC.jpg
97e41681ef21683b7401f7a8ad824e27
92be66b12c321351aa469725b4cae006167ba8d8
F20110113_AACMQW fensin_m_Page_101.tif
be2d4ec3111f6b78b58d160bcf57424e
0744d21b8ff730e84894b65108ab96f3fa894612
88778 F20110113_AACMSA fensin_m_Page_018.QC.jpg
a9ca57fd207e3b818a38d0caf35e6e99
7e389fec7cd359d8f1f73fa2cd53db5f69ab5127
F20110113_AACMRM fensin_m_Page_088.tif
8833905dc58f13074486b2cdc325187c
3244ce1089148309813e25e2e4dbdb04160cac48
16402 F20110113_AACMQX fensin_m_Page_004thm.jpg
7d5cee9e7f3466f49a8ebbd21973786c
7aa6f496bbbfb1d51ed1dc142e86be399614f0c9
1051973 F20110113_AACMSB fensin_m_Page_074.jp2
aeab76a16355fe32fd5fa8f498d0f448
a49d6dbfbc7180469fc462f6b20e20ec3ea9ec7c
76199 F20110113_AACMRN fensin_m_Page_042.QC.jpg
092df147ac508db10b506e6c96067c21
83f4affafc3b67d7c10ce1be5556d97904b1134d
F20110113_AACMQY fensin_m_Page_010.tif
cc552397da9608347e78d49e9c423c4e
f0a0f54dc7af4ce244bd812f132deab45408d2cc
44898 F20110113_AACMSC fensin_m_Page_037.pro
abfd14a8fae5fb97f1a9d3da80da7ed3
abcac59e88d079ecfdf340a7b4ddf89738903e2c
49851 F20110113_AACMRO fensin_m_Page_065.pro
37a77fd8f33467c4edcb46fd96fff042
b4ff7e8b20f6a0403103d9834905a543df188ced
83163 F20110113_AACMQZ fensin_m_Page_006.QC.jpg
4464af3b4e873c19bda3b7284304a706
f81d56ca67093750c3b73f473eae7621243334ce
78506 F20110113_AACMSD fensin_m_Page_014.QC.jpg
3db277a6af3723e2097bd0eab6362dfe
0255e328877ef78c76db4d4163d890eea90afdf9
21227 F20110113_AACMSE fensin_m_Page_001.QC.jpg
4f7edfbff419d8e1f5a1f9ee8d2c082b
22af2132230f6d59edd6396f09f289e87ff18902
21144 F20110113_AACMRP fensin_m_Page_099.pro
17aaf4f6bdb3cc807d129c46ff9d306d
cce19499de876f7519b0e2ab1e0cee8688cf7f9e
F20110113_AACMSF fensin_m_Page_001.tif
ab8e360348490620f8db18e4497c0479
b938006f71716c6ccae712d1d41c869a0204df5d
80140 F20110113_AACMRQ fensin_m_Page_061.QC.jpg
a8a2b3a8f5c359607239ccc6e07382d6
3f7563a834f821881982922a54b42ffd8270d9b5
2099 F20110113_AACMSG fensin_m_Page_006.txt
ee478c511c6ea05b5f2367d64bd5c0a3
170b30eedd6fd5d46d72c09c89f14a564f1daf51
43272 F20110113_AACMRR fensin_m_Page_026.jp2
9c23488931f13929da164ffb2c83d873
befc845a41f32c470d4dcddb61cba89a4a9b860e
F20110113_AACMSH fensin_m_Page_074.tif
f432163ef54fbf17d6b27bb3f5056947
cdbd22b1cf3af5f56e043fee3a751fb7e6d54e8a
189026 F20110113_AACMRS fensin_m_Page_093.jpg
e73bb356fe9a551419a5f980025e4320
de7f2ec9163db2efe6320c1e64d8fad26c801cdf
F20110113_AACMSI fensin_m_Page_081.tif
7070c5c583b7501a0dcdb26b1202b43c
7a34d1f6fbf0614ce2b5b711e728017e8d097e06
203851 F20110113_AACMRT fensin_m_Page_015.jpg
e6ccab61620adab061938a4f0a3c5575
c5f851e5d27d47789983d79af0d08d8973582ac2
F20110113_AACMSJ fensin_m_Page_046.tif
2fdb30da20f360176445444d10e1f723
5aae5dab523e887e46a05bbb50fbd9438b227789
24617 F20110113_AACMRU fensin_m_Page_049thm.jpg
821e2aee39d8110f6d1c658073ec2a78
694b879b4adb0fb027f1ef238341a2d9fa00bc2e
32652 F20110113_AACMRV fensin_m_Page_063.pro
10b74379d48066344d9729da8b3f2847
96320cb60f8018c7b46175dde954658bf8740c9c
31194 F20110113_AACMSK fensin_m_Page_081.pro
b97453f76fc2c5868d3e79e5388dc22a
86b841a11cfa4ddd4580e0e5a9e15206fc9c98ca
217266 F20110113_AACMRW fensin_m_Page_067.jpg
1aa28411e323b23d92ff2564b6fe07c6
1b5346cc29ab1c19c4c058bd0a23173bc19ef68e
1317 F20110113_AACMSL fensin_m_Page_045.txt
e90b81454df626423419f8d56faeaa4a
ecd7c5dbcf4db88be6ad92cca1be94cb2a5835d1
1828 F20110113_AACMRX fensin_m_Page_053.txt
7b7a3a475c9fa5df96d5406f85306316
4d8deacd8ca20a57f15e9eb91b6e783b550b172e
109003 F20110113_AACMTA fensin_m_Page_049.jp2
b63247671409bfe144693e958ec4fb72
72a096243f0909a4c97b00ef19626cfff0c490be
35784 F20110113_AACMSM fensin_m_Page_038.pro
37018e6b50fde67c047126b87bd0b57e
25784b28f3b8a796ee2e95e009d224309f93404b
109857 F20110113_AACMRY fensin_m_Page_067.jp2
d19720bb26ddd4bd15438975d9bcd4da
06129e8d706a270f35c6df3da8a3d0a15958877c
F20110113_AACMTB fensin_m_Page_031.txt
65d9fa7c4b0a5a3641b357c4cec69d4a
732bb6e92e512ef09d57a3bffcc23eb8f3178a64
191073 F20110113_AACMSN fensin_m_Page_012.jpg
28476f86980031da1a18003456ac9ffa
436e0fe17b34df56cbff3e48a83d02d6ec6339d1
F20110113_AACMRZ fensin_m_Page_007.jp2
da3fae4e4bd8dbedb55ce1caf6b06193
254c1e9c98f9c92095a9fd654d766a7eb574f7e7
184041 F20110113_AACMTC fensin_m_Page_037.jpg
e7724d431ee6f96cbb7f624417a3949e
953500ff4ad0d2ec32791b8032c0a0141b24fcac
938031 F20110113_AACMSO fensin_m_Page_082.jp2
25bbc7832ae1497a73f4d6bc18c67bf8
b83443ab5ff6a43211301981fa00424331b26215
F20110113_AACMTD fensin_m_Page_056.tif
4d702cc3f131db50e8beddeade6f2b71
191f9b7d0f636c865db391def6e018dd8fb5157c
27042 F20110113_AACMSP fensin_m_Page_001.jp2
6ec524481ab1ed9b20489ef9712cc75d
100b5665b32c2adfd4b56b8e75cdd68fe3bdf494
2577 F20110113_AACMTE fensin_m_Page_083.txt
fcda3c83421cacbeb76435c5e3f78eeb
a60ea0ee486967a01cf3690e0a92676c9ee83e08
1008478 F20110113_AACMTF fensin_m_Page_087.jp2
40094d16d8296ed8ce2befeb2db46b8f
5ef9fea3b57a12928f7959a1fed3f3a7282c5af7
959207 F20110113_AACMSQ fensin_m_Page_053.jp2
139391c0146c431d08f1c7951433ce55
a90032fecf1586a95c2cfacac4e609756416ed9e
29658 F20110113_AACMTG fensin_m_Page_060.pro
1e12e2be10807cc3200bdd6c2e91aa20
10304b4906ae62afefe4782ad466c529fb32e518
F20110113_AACMSR fensin_m_Page_010.jp2
e964dfff2a5300cd83d30e974f0b49e8
846523ca6d240ef4f58063c0fe7d9a790768ff6c
1976 F20110113_AACMTH fensin_m_Page_034.txt
b113fb9ce7b882903d23f095ab28a260
d7d5ff2d4a5d2d92ff3f5d8da48b542f80c02baa
44894 F20110113_AACMSS fensin_m_Page_093thm.jpg
855a442b7cfca8ee78c21555f528c208
d374fb2bed0328671e5b40ef6609defaf2dcb884
17432 F20110113_AACMTI fensin_m_Page_027thm.jpg
8137b35eaebabaaa3f38d497ebaebaad
e7f6abec618b545b1222a13ca0d35740c1996359
59175 F20110113_AACMST fensin_m_Page_008.pro
c4fec637e361a276fc7932ef153990bc
819bb4c501ca1fffe4004663a839eb0770dbec65
F20110113_AACMTJ fensin_m_Page_084.tif
54f6616b22e51984c80f5a234e181235
46288bb72237285fa5eb6b13be16f7ea1eb076b9
1051977 F20110113_AACMSU fensin_m_Page_078.jp2
ce153fee063f76079a5ddf43d18d5a6b
f2c400a4e003b1465f38a13e418f6b2c5411cb98
85664 F20110113_AACMTK fensin_m_Page_017.QC.jpg
c2527c566b87d40a90a6439fa8310123
285471bb5b68d7c50e7ffbb403f80c21897b886a
F20110113_AACMSV fensin_m_Page_060.tif
2e1875d0bcfc3088fd476f3efec3e6d3
3e9fbedc4123936f7e3d8700fd624c2ab4f9789b
31309 F20110113_AACMTL fensin_m_Page_046.pro
fee9ca52feba3845b8890c549c3783ee
d266a67f45ebb4423e0efd41858bd816174ce094
1915 F20110113_AACMSW fensin_m_Page_015.txt
200b06a21762829201f91fa1a7c0f93f
7eeb05cfa3fda30b512c812060c3359fb43d98f7
60944 F20110113_AACMUA fensin_m_Page_040.QC.jpg
9b373709c69dfcb785dfe116404c7eb5
c1c281f76cd717255d9041ac4bf88f39e55147c0
161849 F20110113_AACMTM fensin_m_Page_045.jpg
69003e53a4692ec726894076d90586c4
021d0c858145dac0e6a6a7f70d9a88527b436f1f
1928 F20110113_AACMSX fensin_m_Page_037.txt
9e93a4660556ddb4a9cbaa2cb70b41a9
7970ffe982cf1b10ea7611f03cbb314245a389cd
23314 F20110113_AACMUB fensin_m_Page_052.pro
6321dbebb7a24d92ff1fef6faa8decd1
b40f64c0f8d62fc97bfa1a77c2f4a85a3b26f2d2
F20110113_AACMTN fensin_m_Page_096.tif
13254bd9b2f596b566e8714ff6bd378b
3e2a778173db5d3685285ff3b355101865cb6bdb
104801 F20110113_AACMSY fensin_m_Page_023.jp2
005f14888e3f35842491efa28f083f20
ea71ad01cafb16fa61f47d0c6e1f66a87029a937
211220 F20110113_AACMUC fensin_m_Page_053.jpg
5b7ca5d2c28a695f677b02bd78157e98
e1a5f1f1a5af430d830c3f21bf2259e731a81ad8
43445 F20110113_AACMTO fensin_m_Page_090thm.jpg
380310f556d99c7c11475e74fd6e9e01
544f2ea69cc68455ffcfb3a925b090341e3d8e4e
49337 F20110113_AACMSZ fensin_m_Page_092.pro
e697988a8bfd67f89939592d987b2624
fcecc7dd4fc6cf93d1f702a3fc389a49c44b01d8
2219 F20110113_AACMUD fensin_m_Page_074.txt
6acd52ea8d03a32f82848b47b40f3b6d
8fbbe788b3d6fd9b8e934e87fb88195df4d82c0f
F20110113_AACMTP fensin_m_Page_090.tif
5647cbb11b72ecc8b51704a5ee85d198
f2e7411592b1d9520e424d95a8dab659b6e2a691
103844 F20110113_AACMUE fensin_m_Page_015.jp2
74a12dc6197fb30115e97957341d260f
94eb5fca3bbc9427a4d64da327f1b673422e947e
2019 F20110113_AACMTQ fensin_m_Page_091.txt
147ba91225eb688d5e588aee49ec230f
ad02e337a03146c0e10032d799a533c0375d7b37
184623 F20110113_AACMUF fensin_m_Page_086.jpg
9deeaac95e1ddb49b017cde9a95b8424
9573877d6c757ce6b55941c7db644c4d7c667b39
2048 F20110113_AACMUG fensin_m_Page_043.txt
c22b48ff191942c2e11116b0293239e8
68992b990a85c02aa4cdfcfa873662ee7c8b892f
63778 F20110113_AACMTR fensin_m_Page_011.QC.jpg
93d4cf9454b846cbea5cf7ec6d2801f4
3a9e9894d4e2b89e13d5aa0a259ca46dde5abb47
1947 F20110113_AACNAA fensin_m_Page_023.txt
7e67d4c285fb18b7cf836b5636652142
4c8f6c243cf35ed4d43131de195c3633faffe634
7715 F20110113_AACMUH fensin_m_Page_001thm.jpg
13b02e65b125d9303665f44fd7c01387
8d7ef1c7ecb98794deee350ef19d14cd36a8093a
F20110113_AACMTS fensin_m_Page_053.tif
762379e8ced5e7f87d22b4aae2e5e03a
1e15c150d6f100a1f8c95df49c439eaa8eab80ab
358066 F20110113_AACNAB fensin_m_Page_009.jpg
1b4fd72192a1f13c1111d04d84438015
c7e9d56747d0cf30b2bba6dfda97c0e3b33ca43c
84728 F20110113_AACMUI fensin_m_Page_040.jp2
10a9f64eb208ab87cbae280bf4952668
7e2514b51b49af7afda8f325da64d43fc261959d
83775 F20110113_AACMTT fensin_m_Page_086.QC.jpg
0a90a290097a37eb54fccf94b79c2752
84ae711d1e1140798d8854d1adac4d69d69579e9
F20110113_AACNAC fensin_m_Page_013.tif
9c93eec21e867d58d20ea19e79d3434c
9657188c224787689a780226fe8a054e14a736d8
1898 F20110113_AACMUJ fensin_m_Page_042.txt
76c6cc8b0b285792d3ab21a53f97d21b
a9ae0dee1b2f081a64d57d208530e82cf0625d06
42761 F20110113_AACMTU fensin_m_Page_097.pro
aa91ddc2f698214b43d486d15832ddce
d16806f0e437d81bc47d5f0ea0e4d13006fdfcc4
3360 F20110113_AACNAD fensin_m_Page_036.txt
cc04d480c694ec55e55a55f227e78b4b
5399b391f216c87777f32184644f6eae395b63f3
99313 F20110113_AACMUK fensin_m_Page_074.QC.jpg
13c148e2d3da27e3235478507ce3633b
e69744aeb9eeab7d22637a5120c0cb64e9962ae8
45807 F20110113_AACMTV fensin_m_Page_082thm.jpg
b753510a5c4180e951888fe8c7668518
60a17d502f62c0ae38f57292339596b4f86dbfbf
12497 F20110113_AACNAE fensin_m_Page_099thm.jpg
31ee75af1620c01038d6ac88dee79820
2035d947c9760d9032ee0c16b72def031faf7b01
109445 F20110113_AACMUL fensin_m_Page_034.jp2
214a50c1c320c50e35fd5a3db3dbab81
d5499f1be8f846b3c0b964ac66f382c49cbc7bbe
F20110113_AACMTW fensin_m_Page_042.tif
5e36be0d20f2dc73f666e34f1ca7c5fd
8715e650af3d0ff1ae626dab2cbd75ef5ac1bc14
219611 F20110113_AACNAF fensin_m_Page_022.jpg
5ad83d4879ccd9e89cd71facbbe36309
9483e2f7760aaa77d2a5ca1f8283d29c25a50b86
183893 F20110113_AACMUM fensin_m_Page_064.jpg
b59aca0ffe60b7db9d9a602b6ee6fb8b
932c17a232bceb5ee278c9cfa8b7974ff94b7a56
115741 F20110113_AACMTX fensin_m_Page_068.jpg
7e8e5aaa075a5e2c13aa357eb8353460
ae640ca83d1d402f06ad3fdda9c41aa75bc7d27c
77048 F20110113_AACNAG fensin_m_Page_038.jp2
ba2c1485db4fd417adfc8001ac9e9b37
f9d2bd07e2e30e8d061fac8ae08895bb05356e2a
59649 F20110113_AACMVA fensin_m_Page_050thm.jpg
6bb82e17faf087b6b50955980ee55aef
31e11eedc25ae875a4d2a408ab1352253bcab225
1051984 F20110113_AACMUN fensin_m_Page_008.jp2
15f0800c1ad15cbee7484ede07bd8678
f8092543136f58bf4064d4c89d29e051037ce83c
1599 F20110113_AACMTY fensin_m_Page_093.txt
b0f8f63daf4734336de9cda7269f0c38
f4cb97df6b5702f2185a0c8f6836ce9ddb4c27e2
106728 F20110113_AACNAH fensin_m_Page_048.jp2
6831bdc4e10473e4f62e918249eaedf3
d98ac88a5fd40d8c429cb9e6f75b78242fb3ecb2
24803 F20110113_AACMVB fensin_m_Page_024thm.jpg
0ce4927fba82a021c071510e9b00bdfb
4119e9cf35f159001d66e178b46d2af4d8955536
1247 F20110113_AACMUO fensin_m_Page_004.txt
92d09a23fab02784a9bad3bd75504045
8a98ea3984c5fe9b6fbfa0e7c18fdc2d644c1261
46543 F20110113_AACMTZ fensin_m_Page_041thm.jpg
81b2b726d9353ead25b584e491611f37
db40a4d0aae20130972e9ec397659689a684b7d1
8330 F20110113_AACNAI fensin_m_Page_055thm.jpg
865a9827d7af89bfb4bf9ae88ca7d7a4
fa2e58266db814f5fb38e1b08ab725c39bd8e769
471992 F20110113_AACMVC fensin_m_Page_054.jp2
50289223e878e05d820d4ab959c1fff0
3978d3603addd00664dad17eae27b74abfb064bb
192492 F20110113_AACMUP fensin_m_Page_073.jpg
995ee1ed9b097d9aa6dd0dc2ebee6d37
23112b99323c828dd6ee4c9439dcb95855c8a83d
21662 F20110113_AACNAJ fensin_m_Page_056thm.jpg
89660da2af7e766438e3f0b5236971c4
53fd7d216fcf889c704a132f68b26537d93c61e6
214486 F20110113_AACMVD fensin_m_Page_096.jpg
4b18ac5484955b7240558db69c42e3ca
38317d6f6f8274f4ac95f457113c3d81052e6b9b
F20110113_AACMUQ fensin_m_Page_093.tif
f6629e5cff17ee9925c7e96cd9b4cfe2
d5ecacf709a8d3e8529466cc45e7fc52a3a680b1
35500 F20110113_AACNAK fensin_m_Page_099.QC.jpg
f3247b74635a7edd1dab01831797faf4
6ff7bf9d78cad607bfebf7a59fb58c497a9ebc97
85695 F20110113_AACMVE fensin_m_Page_080.QC.jpg
ec786c173de75ce8e27686ca55fcf7bc
488bda7b209c449c2de3f5cff7ae02c7e2c05f24
1551 F20110113_AACMUR fensin_m_Page_089.txt
f2d10b64cd6893b8c99ac485a2a301de
c0feca31b73c38f7f55170f0766b6ae0f13c18e1
50922 F20110113_AACNAL fensin_m_Page_021.pro
c1c3055721af332ab6a58fd8fb834901
61c1c26084d10b0d52cd173bb150dedf06487547
45110 F20110113_AACMVF fensin_m_Page_046thm.jpg
fb3d263ad3ae61dc5938f364a02464be
be6ac8e8ff46165bbe4a7dac8314ad95833bd4aa
180641 F20110113_AACNBA fensin_m_Page_077.jpg
4c1ac00653e0844b2b4ab5bd0fe815df
16e3180faba2b2139a8bd999d5370da7a55b50f4
31065 F20110113_AACNAM fensin_m_Page_090.pro
7002f5157935ea4d945693a133c1ce97
25c8f0a34b5560a90f8632d68896d38ed0db5e88
F20110113_AACMVG fensin_m_Page_028.tif
0b66b52599b7e2ea5ba7f77f0facc870
54aa3f1f9b615c3fce9ab5330eed57be4729cfd7
179 F20110113_AACMUS fensin_m_Page_094.txt
e2674d9b640a1387f2bb9e6de1681163
46fb0fc83f3b62ee6f2c07a37b901f8be41db452
1028184 F20110113_AACNBB fensin_m_Page_018.jp2
a393f40389e5ce94aea0e95c21b61b49
3e891174734c5f9002b62ef20847929b99ffd988
F20110113_AACNAN fensin_m_Page_097.tif
0458b760da30323a74f9ccfea20c9f03
3f4979020edf1dc674790448ab9b345dd4e1a01d
68082 F20110113_AACMVH fensin_m_Page_097.QC.jpg
e73be34e575eedf404aa2cf79d535931
6717c55df27e7e0a9498f1b43c418dd89a676a1e
90611 F20110113_AACMUT fensin_m_Page_056.jp2
c7655dc79daa7ebabe1dbe909ee54af7
7d66b24e475266f4fd6cb2a4fd56b85fcf18a91a
70987 F20110113_AACNBC fensin_m_Page_098.QC.jpg
de0d2a790c6348ab384e6b482378044b
baa1e8518604b9bdceafddc41e416adabb8b3ef2
51747 F20110113_AACNAO fensin_m_Page_022.pro
4a29bec8cf7a1af6ad722d4f86c61806
55bef2353bb61ec2a997614a92d7e645ef477c26
3204 F20110113_AACMVI fensin_m_Page_002thm.jpg
e41922443d9987e65ba78a35fd9f4858
8b2729c5f5f1f93b58e24a33eba02f4921699e5f
258820 F20110113_AACMUU fensin_m_Page_005.jpg
7e513e71c20547dc215aef9a866f9171
d58a088e82085f13bdc63712238a642d898fac9e
46578 F20110113_AACNBD fensin_m_Page_053thm.jpg
c212f150eda8cee772b17641b6db45a1
ac77bd133548b7e5ac19a04ebafff8cce87daa69
59611 F20110113_AACNAP fensin_m_Page_083.QC.jpg
1b99d58639f9bb66411b5ba26c760079
71946fbad87763e652add0e14e6a64d362582cc3
98466 F20110113_AACMVJ fensin_m_Page_012.jp2
4c3350a33384f9fafd815af14b8b4441
a6a488a25a1f4f7d2288323c4b48430e1f8ddd0e
1717 F20110113_AACMUV fensin_m_Page_070.txt
0efd3b4c64fdc769ee970d3ac3be472c
1d5a10f003ec472bc1ad0328b1aca9c1e2a80ab4
267741 F20110113_AACNBE fensin_m_Page_035.jpg
e3d7af743b1395b8f48bf478816fad58
18b69ccc00ca627c5dff3f9b96dd5a3397b7da00
1647 F20110113_AACNAQ fensin_m_Page_080.txt
89af5a730f53d47127fd8019fd5486c9
e1f8f8ce9e2ae3625fcbcf1f3da37ac07b31ebbf
214034 F20110113_AACMVK fensin_m_Page_024.jpg
6d614c6dda010cab5a192d3e3a257881
4b964775824c1de85c943d8b363d85d00f8b7fc6
71064 F20110113_AACMUW fensin_m_Page_013.QC.jpg
756e01a2b3d6b55b49b57304e10c4279
816beb76bfc7dccfc6f9ef701dd24454e13811a0
49225 F20110113_AACNBF fensin_m_Page_071.pro
71cabe7b0a4a10e1c0df3fe1c1a317b2
5dc153ff4c1c3186994fe711e1414d6e1e104e25
81767 F20110113_AACNAR fensin_m_Page_077.QC.jpg
bafb6d3e4fe580fec748727cd4234f56
b9ff198278e874a9d00707921885cd484a54ae8c
223129 F20110113_AACMVL fensin_m_Page_057.jpg
934cfa06959c811a0c3cb179678839a8
e2ba3db536e256377938fae24cd8aa9be3e95681
44208 F20110113_AACMUX fensin_m_Page_043thm.jpg
ad2fa8c1859d7ddd61ee8f359dddf475
8a74fb459b9fe11c80a0cfb717e5debd83c5dbc7
108656 F20110113_AACNBG fensin_m_Page_100.jp2
09094837dc681cb22e5fc33982bd38cc
e0770945fba4d5581f8c5d93eb80d255ab4ea16f
F20110113_AACMWA fensin_m_Page_019.jp2
1304e2ac1d986ac069422a9691f4676c
6b79e427cf897e2901bbaba0bd4f8f5217e803c7
97688 F20110113_AACNAS fensin_m_Page_101.jpg
a8de9217b49e29f821d3d72e0b858f08
34d8dd432510a1f48fc756ddb9b4fa006248d1a0
54870 F20110113_AACMVM fensin_m_Page_047thm.jpg
d9d7e11eee7a1b43773dd3e104ac9d3e
222f2a0388b45ea7f4cb7f0ffe6066ee8e11e573
151736 F20110113_AACMUY fensin_m_Page_038.jpg
759d67693dfa040b910a1c823a78143d
4368c5faa1c1673c5edb2e2981cdefd1bd1ad033
51867 F20110113_AACNBH fensin_m_Page_074.pro
6173c2590eddae65e6d428628488a150
f388dedb2355b8b4350c0fb1f91da2fdcf5ecfec
66754 F20110113_AACMWB fensin_m_Page_092.QC.jpg
b90d4df3426a96d1940e592807732334
57cdd72a906c034e0de47493932b48da353de288
49906 F20110113_AACNAT fensin_m_Page_091.pro
04ad4cb50bf2d67b5a7b8547a738d99b
d9d2fb6d008bd6ccc05eae28b0570a9632eadfec
1935 F20110113_AACMVN fensin_m_Page_032.txt
fbcd0b9a46f27dd60696492e2f3dd566
c67b73fe078950f1f8b2919363f59fae6ae5684e
75180 F20110113_AACMUZ fensin_m_Page_009.pro
14d3793eff27ceb71d0727b82a87e057
ccf7569548799ec17f04a7af17dedaea87d75da8
1655 F20110113_AACNBI fensin_m_Page_087.txt
720b054839afeb712279d12496a56e21
e2ea64d830da61bec7b61fac6a94a15f837fe511
F20110113_AACMWC fensin_m_Page_014.tif
61fd44c71efd4cc8a51932c6641b1470
1e71bf8a61933301d293f42c9f6714590f1bf8b8
92115 F20110113_AACNAU fensin_m_Page_075.QC.jpg
04a5a50f10fb27173a9c484fe7521ac3
46eda1d55f603fccc6f56bfcadb70f09f4e48cc6
173152 F20110113_AACMVO fensin_m_Page_081.jpg
6191586c64e4a5a8b8355e1a50489aa4
ac3c88abb9ff44d8687ef0c4439bbf69390c9b2f
1948 F20110113_AACNBJ fensin_m_Page_071.txt
43f4a32ec405dac62a6b609f961bbe46
126b03804d17aeb7ecaa9b8ec30ee62e325b4c39
1520 F20110113_AACMWD fensin_m_Page_062.txt
6d33794e2c109878ef2852f574056cde
24cea1e78b622bee624eddd1e3017534d0abd24a
45937 F20110113_AACNAV fensin_m_Page_087thm.jpg
667205c08e86d54b2d8a377517f068b9
148d063127b9baca5a689458c9129d2d4c63f180
107375 F20110113_AACMVP fensin_m_Page_092.jp2
3a887cfd1221cb595b9478176ca2b16e
30bd02c602b52f7ded283dc1e310f14e06e12935
25817 F20110113_AACNBK fensin_m_Page_048thm.jpg
3e4ee4c1775028a752d5ee1c5fa1784a
598a9773fcbdc02bab447a46951dbf565ea353c1
183415 F20110113_AACMWE fensin_m_Page_069.jpg
3d4fa72179cbe8fd403d722f1550ccad
224b9153212da162c7010edfc5e423fe750b2292
F20110113_AACNAW fensin_m_Page_003.tif
b5c216a3e691962d267a668c3edc1f1c
83952716b30400a15802011436039de33c6b976d
75986 F20110113_AACMVQ fensin_m_Page_024.QC.jpg
9a73d85653cb7efad6d21377005bbc9e
1146a35094805b9e70de2f4f40d32c519384cdf6
109463 F20110113_AACNBL fensin_m_Page_096.jp2
38b70d2b5a9854c05cab330bb4a95f6b
e66f8f7edb4ff0f5b7c95258ba8e599465afe51c
1693 F20110113_AACMWF fensin_m_Page_056.txt
0b81cbd1b908df568afdc1ba8ba856a5
7034e3030a669379725d1fecbf9729a63849b7d7
119356 F20110113_AACNAX fensin_m_Page_050.pro
92c5757f110d46c22a055252d6696785
e58a5571f6dfd2130a4d7919a15d7828746089cf
1557 F20110113_AACMVR fensin_m_Page_077.txt
87cb4b7f8f48b264a0ddd61ac2216057
4c92e5bc1d6c02cd606606247acc35bc7ebcd3e5
46969 F20110113_AACNBM fensin_m_Page_066thm.jpg
4e708a617a760a7e25a0d7b51e973755
14836948b44fcb5ac9a991d16ab35b12911635f8
F20110113_AACMWG fensin_m_Page_038.tif
54c06720e9266c13840eb0ee9c00e0ad
a5b106d3c7c75b7beb45644e4ba06a0948178ca5
162090 F20110113_AACNAY fensin_m_Page_079.jpg
5cf44be800a0f6014bfbdb872a9a6fd9
3f106d0a2f9244e5c8c3be97c8177c7b97423b63
22449 F20110113_AACMVS fensin_m_Page_101.pro
01185d9f1892d0a4a205881acf3b254c
96e2d42caaadebcee0240e2b6ad9a0e1bda1de25
23662 F20110113_AACNCA fensin_m_Page_030thm.jpg
326b371a33b08ecd129d46a8e0bd6d06
96e309f2e3ec52dd5c38ae1c6c2e34f1ad070f72
1304 F20110113_AACNBN fensin_m_Page_002.pro
a7734d79e05dc3b301d2935e58153c11
33f181cc5885aadffce22ca9985b154aff4c9922
50185 F20110113_AACMWH fensin_m_Page_034.pro
01f71542b6a2866015beb78226a994ee
55dbbf60693c20a92015cf20b82e08c81b80b151
40613 F20110113_AACNAZ fensin_m_Page_078.pro
82c90233f7c5c7c8ebe6d3e5f21cc59c
7e8acd0cf7ab5b85577cc2d6037903242644035a
49764 F20110113_AACNCB fensin_m_Page_048.pro
3772c5217fd2dae8a06452584c8ec3ae
ac9e6b09f96591c1415c6fb4e857bb1086741c84
30721 F20110113_AACNBO fensin_m_Page_089.pro
e358c7924ae944b738dddff7d8a1d9f5
b3cddba82709e7fca42e6480bcc07ab97bbb2aec
1911 F20110113_AACMWI fensin_m_Page_044.txt
ac96d08fade52c2d708f30c722443830
d62bee9025743403b38fb1a9b68825eb43cef19e
59402 F20110113_AACMVT fensin_m_Page_068.jp2
aa6ae90162b2c0ec3714e89eb32a2fbf
5bb53bf4f45a4727017d5e3afe9bb553f4068d4a
209608 F20110113_AACNCC fensin_m_Page_071.jpg
62594d2fc30e0de239265907e2a26a75
490e5a08a15b53fd929dd4b42a3e1e8ea79a553b
49467 F20110113_AACNBP fensin_m_Page_070thm.jpg
5e1f4d0e317a7f8e0850c18330a99c82
77cbf445824fb77372e11fa9fd3c1e4af61982f4
83588 F20110113_AACMWJ fensin_m_Page_085.jp2
8cb18694d57714cf3aa46680dc39c12b
e3fef4ec39266f67de8bcf354f83fb24311966f1
213575 F20110113_AACMVU fensin_m_Page_091.jpg
8deff37702ae89d5dc72b3f236cd4f36
aa1a8b08a3df2506bec317a0704e694d8e590864
62247 F20110113_AACNCD fensin_m_Page_001.jpg
6cc9b0641c66acf0dbcb1cd937b39c10
be005d4afdba3ea7a5c69943fd23764b687c52af
742169 F20110113_AACNBQ fensin_m_Page_061.jp2
8bebbcfc109611a05766e2bb57780737
ee118b67b7efab68dedf3356135ca0d0636d947d
F20110113_AACMWK fensin_m_Page_050.tif
084e504f5b58494cec4dd094700c7ef5
b2ecbb9dc432aa3256fa2ec93142b87a4ec2abff
76311 F20110113_AACMVV fensin_m_Page_023.QC.jpg
81c2d5bd90b24026892bc9af16c4efce
6c3007c05aa9919624a77049cddbf9ee419e957a
220606 F20110113_AACNCE fensin_m_Page_006.jpg
4515c62e95fc206c422e0fec2d4cf28c
ad18a77681a335636024b08b29945244c344f816
206081 F20110113_AACNBR fensin_m_Page_032.jpg
0e3a8927cf4cdefc102349a21fb4aa54
0e8d029e3ac8c37b4d52428c42cf7f60c700894b
913 F20110113_AACMWL fensin_m_Page_054.txt
33ac0fb25e4c3c1ca007f697d80662e9
f7d20cba731e4cf36389f5d0dee3cb8e9c095833
1968 F20110113_AACMVW fensin_m_Page_078.txt
09d3c373accd93481c064422874951ed
8494f1b749be88c17c10de9f2df640ea0feaed2e
F20110113_AACNCF fensin_m_Page_020.tif
2ee4788bea92343f90e35d6a58e6a89d
8787eca20a18d78c133c21b4c2b9e2b901ab28b1
23913 F20110113_AACMXA fensin_m_Page_042thm.jpg
8d0e28640aae595e9e948882390cb825
b084b7b03c034a6b7258933b3cbd7783a9db97ed
160255 F20110113_AACNBS fensin_m_Page_052.jpg
2b3096a162c0f7df58aee650eb3bb911
5707492090aa9af42d6007b4b7d364c1695a01d1
F20110113_AACMWM fensin_m_Page_049.txt
0624379c4cdd0090e0af73e979101e86
66e29459df1f35965396c762fd8354d308a49293
F20110113_AACMVX fensin_m_Page_082.tif
b54ae26beb7b5dbaea16e7597f59e282
d9d2d4bcc321301c8b6a79a6651e06af990a3d0a
1051974 F20110113_AACNCG fensin_m_Page_009.jp2
7183fedbabb30a860414a210c21ce73c
cc7a5b3c0daef3499945d8314eef6ea837de8a29



PAGE 1

OPTIMUM BOILING WATER REACTOR FUEL DESIGN STRATEGIES TO ENHANCE REACTOR SHUTDOWN BY THE STANDBY LIQUID CONTROL SYSTEM By MICHAEL LORNE FENSIN A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING UNIVERSITY OF FLORIDA 2004

PAGE 2

Copyright 2004 by Michael Lorne Fensin

PAGE 3

This document is dedicated to the memory of my late grandmothers Bernice Anker and Edna Fensin.

PAGE 4

ACKNOWLEDGMENTS I would like to acknowledge Dr. Samim Anghaie for chairing my committee, supplying a connection to Global Nuclear Fuels of America, and providing excellent tutoring and advice as my graduate advisor. I would also like to thank Dr. Bob Coldwell Dr. Edward Dugan, Dr. Alireza Haghighat, Dr. David Hintenlang, Dr. Travis Knight, Dr. Alan Jacobs, Dr. Tim Olson, Dr. Benard Mair, Proffessor Jim Tulenko and Dr. William Vernetson for providing me countless hours of instruction in all areas of nuclear engineering and mathematical computation during my graduate studies. I would like to acknowledge Global Nuclear Fuels of America for the sponsorship of its computer codes, time and efforts. From Global Nuclear Fuels of America I would specifically like to thank Dr. Mehdi Asgari, Kenneth Gardner, Roland Jackson, J.D. Kavaal, Thomas Marcille, V.W. Mills, Dr. Brian Moore and Tony Reese for supplying intriguing knowledge and guidance during the course of the study. I want to thank my family for being a constant source of support and pushing me to completion. Without their support none of this would have been possible. iv

PAGE 5

TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES............................................................................................................vii LIST OF FIGURES.........................................................................................................viii ABSTRACT.......................................................................................................................xi CHAPTER 1 INTRODUCTION........................................................................................................1 The Boiling Water Reactor System..............................................................................4 Boiling Water Reactor History.....................................................................................8 History of Fuel Bundle Development.........................................................................10 The SLCS Event.........................................................................................................12 Project Scope..............................................................................................................13 2 MODEL AND METHODOLOGIES.........................................................................15 Standby Liquid Control System and Shutdown Margin.............................................15 Modeling Tools...........................................................................................................17 TGBLA 6.............................................................................................................17 PANAC11............................................................................................................18 Utilized Temperature States, Boron Concentrations and Lattice Types.....................19 Measurement of SLCS and SDM during the Lattice Development Stage.................20 Fuel Bundle Geometry................................................................................................21 Thermal Limit Design Considerations........................................................................24 3 MAXIMIZING HOT-COLD BORATED k DIFFERENCE UTILIZING ENRICHMENT..........................................................................................................28 Homogeneous Enrichment Distribution.....................................................................28 Determining the Most Limiting Lattice Axial Zone and Void Concentration....29 Understanding the Exposure Dependent HUCU### Curve................................31 Enrichment and Boron Concentration Effects.....................................................34 Power Peaking Distribution.................................................................................35 v

PAGE 6

Heterogeneous Enrichment Distribution....................................................................39 Localized Enrichment Perturbation.....................................................................39 Gross Enrichment Perturbation...........................................................................41 4 MAXIMIZING HOT-COLD BORATED k DIFFERENCE UTILIZING GADOLINIUM..........................................................................................................44 Spatial Self-Shielding Effects of Gadolinium Rods on HUCU###............................44 The Effects of Increasing the Amount of Gadolinium Rods on HUCU###...............47 The Effects of Increasing the Gadolinium Concentration on HUCU###...................50 The Importance of Gadolinium Rod Location............................................................51 Fuel Lattice Design Conclusions................................................................................55 5 FULL CORE SLCS MODELING..............................................................................57 Enhancing SLCS by Perturbing the Location of Gadolinium Rods...........................59 Axial Power Shape Characteristics.............................................................................65 Enhancing SLCS through Axial Power Shaping Utilizing Enrichment Differencing...........................................................................................................66 Enhancing SLCS by Means of Axial Power Shaping Utilizing Gadolinium Insertion.................................................................................................................74 6 CONCLUSIONS........................................................................................................83 7 FUTURE WORK........................................................................................................86 LIST OF REFERENCES...................................................................................................88 BIOGRAPHICAL SKETCH.............................................................................................90 vi

PAGE 7

LIST OF TABLES Table page 3-1 Gross enrichment perturbation scheme for figure 3-10............................................41 5-1 Critical eigenvalue at specified exposure points for the gadolinium rod location perturbation cases that exhibited greatest enhancement in SLCS............................62 5-2 Exposure dependent MFLPD for the gadolinium rod location perturbation cases that exhibited greatest enhancement in SLCS..........................................................63 5-3 Exposure dependent MFLCPR for the gadolinium rod location perturbation cases that exhibited greatest enhancement in SLCS..........................................................64 5-4 Critical eigenvalue at specified exposure points for the gadolinium rod location perturbation case and enrichment differencing case that exhibited greatest enhancement in SLCS..............................................................................................71 5-5 Exposure dependent MFLPD for the gadolinium rod location perturbation case and the enrichment differencing case that exhibited greatest enhancement in SLCS....72 5-6 Exposure dependent MFLCPR for the gadolinium rod location perturbation cases that exhibited greatest enhancement in SLCS..........................................................73 5-7 Critical eigenvalue at specified exposure points for the gadolinium insertion into the DOM (case 27) and gadolinium insertion into the PSZ (case 26) that exhibited greatest enhancement in SLCS.................................................................................76 5-8 MFLPD at specified exposure points for the gadolinium insertion into the DOM (case 27) and gadolinium insertion into the PSZ (case 26) that exhibited greatest enhancement in SLCS..............................................................................................79 5-9 MFLCPR at specified exposure points for the gadolinium insertion into the DOM (case 27) and gadolinium insertion into the PSZ (case 26) that exhibited greatest enhancement in SLCS..............................................................................................80 vii

PAGE 8

LIST OF FIGURES Figure page 1-1 BWR pressure vessel system......................................................................................5 1-2 A typical BWR fuel assembly and fuel rod................................................................6 1-3 A four fuel assembly group with cruciform control blade.........................................7 2-1 A cross sectional view of the modeled fuel bundle..................................................23 2-2 The geometric setup of the fuel lattice axial zones..................................................24 3-1 Exposure dependent HUCU660 for the DOM at 3.95% enrichment.......................29 3-2 Exposure dependent HUCU660 at varied void fraction and axial zone for the C lattice at an enrichment of 3.95%.............................................................................31 3-3 Exposure dependant HUCU### curve.....................................................................33 3-4 Beginning of cycled HUCU vs. enrichment in the DOM, at 40% void fraction, for a C lattice............................................................................................................34 3-5 The power peaking distributions at 5 GWD/STU, 3.95% enrichment, DOM, C lattice, and 40% void fraction vs. temperature state and boron concentration.........35 3-6 The power peaking distribution at 5 GWD/STU, CU660, DOM, C lattice, and 40% void fraction versus enrichment.......................................................................38 3-7 The power peaking distributions at 5 GWD/STU, HU, DOM, C lattice, and 40% void fraction vs. enrichment.....................................................................................38 3-8 Localized enrichment perturbation map...................................................................40 3-9 Exposure dependent HUCU660 for different localized enrichment perturbation patterns.....................................................................................................................40 3-10 An example of a gross enrichment perturbation map...............................................41 3-11 Exposure dependent HUCU660 at 40% void fraction, in the DOM, with a C lattice........................................................................................................................42 viii

PAGE 9

3-12 Exposure dependent HUCC at 40% void fraction, in the DOM, with a C lattice....42 4-1 Four sample clumped geometries.............................................................................45 4-2 Corresponding 0 GWD/STU gadolinium worth for the patterns displayed in figure 4-1..................................................................................................................46 4-3 Corresponding exposure dependent gadolinium clumping effects on HUCU660 for the patterns displayed in figure 4-1....................................................................46 4-4 The effects of increased number of gadolinium rods on the gadolinium worth at 0 GWD/STU.............................................................................................................48 4-5 The effects of the number of gadolinium rods inserted on HUCU at 0 GWD/STU.............................................................................................................49 4-6 The effect of increasing the gadolinium concentration for 14 gadolinium rods on gadolinium worth at 0 GWD/STU...........................................................................50 4-7 The effect of increasing the gadolinium concentration of 14 gadolinium rods on HUCU at 0 GWD/STU............................................................................................51 4-8 Gadolinium rod placement diagram.........................................................................52 4-9 Gadolinium worth versus location for 0 GWD/STU, 7% gadolinium concentration,...........................................................................................................54 5-1 Reference base core fuel bundle loading map..........................................................58 5-2 The perturbation diagram for the gadolinium rod perturbation cases......................60 5-3 Exposure dependent SLCS for the reference base case, the case in which the perturbation was made to only all of the fresh low enrichment bundles (case 2), and the case in which the perturbation was made to only all of the fresh high enrichment bundles (case 1).....................................................................................61 5-4 Exposure dependent SDM for the gadolinium rod location perturbation cases.......65 5-5 The base case hot axial power shape with superimposed cold axial power shape...66 5-6 Cold axial power shape perturbation diagram..........................................................67 5-7 Exposure dependent SLCS for the gadolinium location perturbation case (case 2) and axial power shape perturbation utilizing enrichment differencing case (case 11) that exhibited the greatest enhancement in SLCS.............................68 5-8 SLCS enhancement utilizing different magnitudes of enrichment differencing between the DOM and VAN....................................................................................69 ix

PAGE 10

5-9 The hot axial power shape for maximum SLCS enhancement utilizing enrichment differencing...........................................................................................70 5-10 Exposure dependent SDM for the gadolinium rod location perturbation case and axial power shaping utilizing enrichment differencing case....................................74 5-11 Exposure dependent SLCS for the gadolinium location perturbation case (case 2), axial power shape perturbation utilizing enrichment differencing case (case 11), inserting a gadolinium rod in the PSZ (case 26) and inserting a gadolinium rod in DOM (case27) that exhibited the greatest enhancement in SLCS........................................................................................................................75 5-12 The hot axial power shape of the most power peaked fuel bundle caused by inserting a gadolinium rod into the PSZ...................................................................77 5-13 The hot axial power shape of the most power peaked fuel bundle caused by inserting a gadolinium rod into the DOM................................................................78 5-14 Exposure dependent SDM for the gadolinium rod location perturbation case, axial power shaping utilizing enrichment differencing case and the axial power shaping utilizing gadolinium placement case...........................................................81 x

PAGE 11

Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering OPTIMUM BOILING WATER REACTOR FUEL DESIGN STRATEGIES TO ENHANCE REACTOR SHUTDOWN BY THE STANDBY LIQUID CONTROL SYSTEM By Michael Lorne Fensin August 2004 Chair: Samim Anghaie Major Department: Nuclear and Radiological Engineering Licensing a commercial nuclear reactor core involves a stringent amount of calculations that demonstrate the capability of safe reactor shutdown in the instance of an emergency transient event. In a boiling water nuclear reactor the control blades and standby liquid control system are the two independent redundant safety systems utilized for shutting down the reactor. In past fuel designs lower power cores with smaller cycle lengths resulting from lower core average enrichment caused shutdown by the control blades to be the most limiting strategy of the two modes for reactor shutdown. This led to a lesser focus on fuel design strategies for standby liquid control system margin (SLCS). Advanced modern core designs involve higher powers and increased cycle lengths resulting from higher core average enrichments, therefore causing SLCS to now become a more significant shutdown parameter. This study characterized the most limiting fuel design parameters for maximizing the margin for safe reactor shutdown utilizing SLCS while maintaining the demanded cycle energy requirements. xi

PAGE 12

This study examined perturbation effects of certain parameters in the fuel lattice development stage and the 3-dimesional reactor core simulator modeling. Lattice enrichment perturbation response was examined first to determine the effects of average and local enrichment perturbations on SLCS. Lattice gadolinium perturbation response was next investigated to determine the optimum concentration, number of rods, location and degree of clump of gadolinium rods necessary for enhancing SLCS. Axial power shape perturbation utilizing both gadolinium and/or enrichment differencing in certain axial zones of the fuel bundle was then examined on the full core level to determine the optimum strategy for maximizing SLCS. This study concluded that the necessary strategy for maximizing SLCS depended upon the exposure point at which SLCS was most limiting. Certain perturbations utilizing gadolinium exhibited maximized beginning of cycle SLCS; however, these strategies involved a modified operating strategy to meet the beginning of cycle operational requirements while not maximizing the limiting end of cycle SLCS. Axial power shaping utilizing enrichment differencing maximized end of cycle SLCS and increased beginning of cycle SLCS margin but to a lesser magnitude than the gadolinium perturbation. In all cases the amount of improvement to the margin was limited by a maximum value. Therefore if the desired magnitude of improvement needed is within the achievable limits of the examined techniques, the choice of optimum strategy for enhancing SLCS to a desired value depends upon the magnitude of necessary improvement at the most limiting exposure points. xii

PAGE 13

CHAPTER 1 INTRODUCTION Boiling water nuclear reactor cores are major sources of revenue for power producing utilities. If the utility is able to maximize the amount of energy output from the nuclear reactor while minimizing the cost of the reactor operation then the utility will realize an increase in profit. A utility may choose to maximize the energy output from their nuclear reactors in one of three ways. Either the utility may increase the operating cycle length of the reactor thereby increasing the amount of energy per cycle and increasing the amount of time between refueling outages, or the utility may choose to increase the power level of operation thereby increasing the amount of available distributable energy at any given time, or the utility may choose to utilize a combination of both practices [2]. In either of the operational techniques the utility must increase the installed reactivity in the reactor core in order to meet the desired goal. Increasing the amount of installed reactivity in a given cycle as compared with a previous cycle in order to aggressively improve reactor power output is termed aggressive core loading. Aggressive core loading strategies involve higher fuel batch fractions with fuel bundles of higher average enrichment in order to increase the installed positive reactivity in the reactor core [2]. Greatly increasing the core power output in the internal core locations greatly increases the neutron flux and thus greatly increases the exposures of the interior bundles. A twice-burned fuel bundle in the reactor core is at its least reactive state in bundle life and therefore in ordinary core loadings twice-burned fuel bundles can be an excellent power suppressor utilized to flatten the power 1

PAGE 14

2 distribution in the internal core locations; however, in aggressive core loadings the high neutron flux in the interior of the core may causes twice-burned fuel bundles to exceed thermo-mechanically limited peak exposure. Therefore in aggressive core loadings after bundles have burned two cycles they must be moved to the core periphery in order to inhibit surpassing peak exposure [4]. This leads to only fresh and once burned assemblies loaded in the interior core locations. Most of the gadolinium in a once burned fuel bundle is completely burnt up at the end of the previous cycle therefore these bundles are at the most reactive state. Inability to suppress this energy output decreases the available margin to shutdown the core in an emergency situation. Due to the aggressive core loading geometry, the only available power suppression comes from the fresh fuel bundles that are loaded into the core. However, with increased energy placed in the fresh bundles by increasing average enrichment in order to meet the increased power demand, these fresh bundles will have decreased power suppression capabilities. Therefore with decreased power suppression capabilities, the reactor core becomes more limiting in emergency shutdown capabilities. One of the shutdown systems is the standby liquid control system and the margin in which the reactor core is shutdown utilizing this system is the standby liquid control system margin (SLCS). If the reactor core becomes more limiting in SLCS due to the decreased power suppression capabilities of the core loading strategy, it becomes paramount to then determine the optimum bundle design utilized in order to improve SLCS in an aggressive core loading environment. A reactor core is never licensed without being able to meet all the necessary shutdown criteria, thermal limit characteristics, and cycle length requirements. Therefore

PAGE 15

3 operating reactor cores do not encounter a failure to meet SLCS because the reactor would not be allowed to operate if the reactor could not meet the SLCS requirements. Inability to meet SLCS with a certain reactor core fuel bundle configuration is realized and mitigated in the design phase of the reactor fuel cycle. The designer has many options to improve SLCS but any one option may endure a list of consequences some of which may result in extreme economic concern. The designer may request that the reactor cycle length be decreased; obviously if the utility wishes to increase profit by increasing power output this option is not acceptable. The designer may request the utility to increase the boron concentration or enrichment of B10 in the boron solution utilized by the standby liquid control system. However, this course of action is limited by increased aggravation caused from Nuclear Regulatory Commission (NRC) licensing, availability for the utility to plan for the change economically, ample time to complete the concentration increase in time for the next cycle loading, capabilities of the installed accumulator tank to support the concentration increase and ability to keep the boron soluble in solution. The designer may choose to increase the amount of fuel bundles loaded in the cycle and load more fuel bundles with a smaller enrichment; however, this may cost the utility more than what was budgeted and therefore is not a viable option. The action that is demanded by the utility is for the designer to create a core design that meets the utilities budget and does not increase the amount of bundles that are loaded into the reactor core. Therefore the designer must design a fuel bundle with inherently better SLCS characteristics. In order to accomplish this task efficiently the designer must

PAGE 16

4 know the set of limiting design parameters that may be utilized to enhance SLCS, and have a list of effective techniques that utilize the advantages of those parameters. The purpose of this study was to determine the fuel bundle design parameters that were most limiting in achieving the maximum possible enhancement for SLCS, and to determine the maximum amount of available improvement to SLCS by utilizing certain enhancement techniques that take advantage of those design parameters. This will demonstrate the feasibility of designing a fuel bundle and core operating strategy that has the ability to meet SLCS without incurring the costs of adding extra fuel bundles in the design or decreasing cycle power output requirements. The Boiling Water Reactor System The boiling water reactor (BWR) system is a nuclear system that boils water creating steam that is converted into power. The entire BWR system is composed of a reactor pressure vessel system, a turbine system, a generator system, a condenser system and the auxiliary control and heat removal systems. Steam is created by boiling water in the reactor pressure vessel system. The high quality steam then passes through a turbine, and causes the turbine shaft to rotate. The turbine shaft is connected to a generator and as the turbine shaft rotates the generator converts the mechanical energy of the rotating turbine shaft into electrical energy. Once the steam leaves the turbine system, it is sent to the condenser to be condensed into a sub-cooled fluid and pumped back into the reactor pressure vessel system. The reactor pressure vessel system is of primary concern to the nuclear reactor core designer. Figure 1-1 is an illustration of a typical BWR reactor pressure vessel system. The reactor pressure vessel system consists of the control drive mechanisms, the active

PAGE 17

5 fuel, the jet pumps, the moisture separators and steam driers as well as other inlets for emergency core cooling [16]. Figure 1-1. BWR pressure vessel system [16].

PAGE 18

6 The active reactor fuel length is approximately 12 feet though actual fuel length may vary according to different types of fuel assembly product lines. The fission power of the reactor converts the sub-cooled coolant into steam. The steam then travels through the steam separators and driers to create a high quality steam that is then send to the turbine. Each fuel assembly is composed of the fuel and water rods, intermediate spacer grids, upper and lower tie plates, and flow nozzle. Figure 1-2 displays a typical BWR fuel assembly as well as a typical fuel rod. Each fuel assembly is encased in a zircaloy fuel box in order to limit flow between adjacent fuel assemblies. This allows the flow to any given fuel assembly to be orificed to maintain a constant exit steam quality as well as limit instability in core thermal performance [16]. Figure 1-2. A typical BWR fuel assembly and fuel rod [16].

PAGE 19

7 Fuel assemblies are loaded into the reactor in groups of four with a cruciform B4C control blade loaded in the center of the grouped bundles. Displayed in figure 1-3 is a typical layout of four fuel bundles with a cruciform control rod loaded in the center of the grouped bundles. The fuel assemblies are diagonally symmetric with themselves and are loaded so that there exists 1/8 bundle symmetry with the four grouped bundles. Figure 1-3. A four fuel assembly group with cruciform control blade [16].

PAGE 20

8 By applying this loading scheme, symmetry may be utilized in modeling the fuel bundle thereby easing the computation time of the fuel assembly parameters [14]. Each BWR fuel assembly will contain fuel rods at certain enrichments that may vary radially and axially as well as gadolinium rods which may vary in placement and concentration radially and axially. The modeling of SLCS will first involve modeling a 2-dimensional slice of a single fuel assembly at certain axial heights and then modeling the entire 3-dimensional reactor utilizing the information from the 2-dimensional model. Boiling Water Reactor History The first two light water cooled nuclear reactor systems commercially available for power production were the boiling water reactor and the pressurized water reactor (PWR). The concept of the commercial PWR was created from the technology developed for submarines by the navy nuclear program [7]. BWR development occurred at Argonne National Laboratory and the Nuclear Energy Division of General Electric (GE) [9]. The PWR concept is generally characterized as a system in which the bulk coolant is sub-cooled and contains boron. The system utilizes an indirect dual-cycle that uses a steam generator. The BWR concept is generally characterized as a system that has boiling in the reactor core, with the bulk fluid containing no boron, utilizing a direct cycle for power conversion (the demonstration BWR/1 plants utilized a dual cycle). The first BWR experiments conducted at Argonne National Laboratory utilized the BORAX in 1953. BORAX-III produced steam-generated electricity for the town of ARCO, ID in 1955. The experimental boiling water reactor (EBWR) was developed in 1957 and ran until 1967. This reactor produced 100 MWt and was utilized to demonstrate the BWR concept for electricity generation utilizing a variety of fuel enrichments. The GE Valecitos boiling water reactor (VBWR) was the first commercial

PAGE 21

9 nuclear power plant to be licensed by the United States Atomic Energy Commission (USAEC). Utilized as an experimental reactor, VBWR examined BWR fuel cycle technology and determined the stable modes of operation. In 1955 Dresden-1 became the first commercial BWR specifically constructed for commercial power [12]. Dresden-1 was a dual cycle plant and fell under the category of BWR/1. BWR/1 designs were basically prototype designs of both dual and direct cycle utilized as demonstration plants that were custom made to meet individual utility specifications. Dual cycle BWR plants eventually fell out of favor because of the enormous capital cost involved in utilizing a steam generator. Ouster creak was the first attempt at standardizing the BWR and marked the beginning of the BWR/2. In 1963 BWR/2 plants were developed incorporating a direct steam cycle as the chosen method of power conversion. The reactor concept utilized internal steam separators and forced flow circulation that pumped core flow through 5 variable speed recirculation pumps. In 1965 GE introduced the BWR/3, the Dresden-2 design, which incorporated the use of internal jet pumps eliminating the need for external flow circulation loops. In 1966 the BWR/4 or Browns Ferry design was introduced. This design was similar to previous designs but incorporated a 20% increase in the core power density improving power producing capability of the reactor and thereby increasing its economic value. The year of 1969 marked the introduction of the Zimmer class of plants better known as the BWR/5. These plants utilized an improved emergency core cooling and recirculation system. Flow control in these reactors was accomplished through use of valve control rather than pump speed control allowing the plants to follow more rapid load change and decrease the capital cost of the control system [12]. The BWR/6 incorporated the used of higher

PAGE 22

10 efficiency steam separators and multi-hole jet pumps as well as improved power flattening through enhanced coolant distribution and burnable Gadolinia zone loading. The original BWR/6 fuel design incorporated an 8X8 fuel assembly rather than the previously utilized 7X7 [12]. The current BWR technologies include the Advanced Boiling Water Reactor (ABWR) and the European Simplified Boiling Water Reactor (ESBWR) both of these concepts utilized passive safety features in order to alleviate the need for complicated control systems. The history of the BWR is one that is based off of evolutionary concepts in order to increase core power and eliminate external moving parts that may fail during reactor operation. History of Fuel Bundle Development Over the years fuel bundle designs have undergone evolutionary changes in order to improve the thermal performance of the fuel and the reactivity features. Each fuel bundle design incorporated a key feature that allowed for increased margin in controlled conditions, transients, and thermal limits. The original fuel bundle concept utilized by the General Electric Company was the 7X7 fuel lattice design. These were fat fuel rods with decreased surface area due to the large size of the fuel rods. The decreased surface as compared to todays designs lead to an increase in the maximum linear heat generation rate (kW/ft) in the fuel bundle leading to an increase in fuel duty [12]. With the creation of the BWR/6 came the inclusion of the 8X8 fuel lattice assembly. Increasing the surface area of the fuel rods by decreasing there width and increasing the amount of fuel rods in the assembly decreased the maximum linear heat generation rate of the fuel rods. In 1988 a fuel design study by Motoo Aoyama, Sadao Uchikawa and Renzon Takeda suggested that extended exposure of fuel assemblies was possible if 9X9 fuel assemblies were utilized with and optimized internal water rod width

PAGE 23

11 thereby increasing the non boiling area inside the fuel lattice to increase moderation capability of the internal portions of the fuel lattice [1]. This design change increased fuel lattice efficiency. Going to a larger amount of fuel rods in the lattice at smaller fuel diameter decreased the linear heat generation of the fuel rod by increasing the surface area of the fuel. The current design utilized today by BWR vendors is the standard 10X10 fuel lattice design. Though the water rod locations vary from vendor to vendor the idea is the same; increase the moderation capabilities of the internal locations of the fuel lattice to boost reactivity in the areas that are most suppressed in power. Because the moderator density varies axially in the fuel assembly, the BWR has a distinct axial power shape. Kazuki Hida and Ritsuo Yoshioka determined that there were optimum axial enrichment distributions that minimized enrichment requirements subject to thermal margins [9]. They proved that increasing enrichment in the top half of the core actually decreases the uranium utilization. Therefore the interpretation of that study determined that fuel utilization was a key design constraint in creating optimum fuel bundles. In order to mainstream fuel designs industry moved away from axial enrichment shaping and fabricated fuel rods of a single enrichment and utilized part length control rods that increased the moderation capability in the top half of the fuel assembly leading to an increase in fuel efficiency. In 1997 Yasushi Hirano, Kazuki Hida, Koichi Sakurada and Munenari Yamamoto created an algorithm for determining optimum enrichment loading schemes for fuel lattices [10]. Holding the position and concentration of the gadolinium rods as the constant, the algorithm optimized the enrichments in the fuel lattice in order to meet

PAGE 24

12 certain thermal limit and local peaking factor criteria. The gadolinium configuration utilized for the study was based off of a configuration that was supposedly optimized only for shutdown margin (SDM) and certain thermal limit criteria based off of previous fuel design experience. However, this method lacked the ability to place the gadolinium and enrichment into the fuel lattice in such an optimum configuration such that all controls were satisfied. If the chosen gadolinium configuration was only optimum for SDM yet not also optimum for SLCS then this method was to only be successful in designing a lattice to meet SDM. What this method was lacking was the rules for understanding how the gadolinium needed to be configured to meet the SLCS, SDM and thermal limit configuration for a given average enrichment. The SLCS Event The standby liquid control system is initiated during anticipated transient without scram (ATWS). The following is a list of the events that occur in the SLCS event: 1. A transient even occurs in which it is necessary to SCRAM the reactor. 2. The reactor control blades fail to insert. 3. A calculated amount of steam is relieved from the reactor to the suppression pool at a rate that will not violate containment. 4. The boron solution is injected into the core at a specified rate and concentration in accordance with 10CFR50.62. 5. The reactor reaches an equilibrium shutdown condition. In 1984 the Nuclear Regulatory Commission (NRC) issued 10CFR50.62, Requirements for reduction of risk from anticipated transients without scam events for light water-cooled nuclear power plants (ATWS rule). The law states: Each boiling water reactor must have a standby liquid control system (SLCS) with the capability of injecting into the reactor pressure vessel a borated water solution at such a flow rate, level of boron concentration and boron-10 isotope enrichment,

PAGE 25

13 and accounting for reactor pressure vessel volume, that the resulting reactivity control is at least equivalent to that resulting from injection of 86 gallons per minute of 13 weight percent sodium pentaborate decahydrate solution at the natural boron-10 isotope abundance into a 251-inch inside diameter reactor pressure vessel for a given core design. [17] This is equivalent 660 ppm boron concentration in current reactor designs. The model utilized for determining if SLCS will satisfy the criteria mentioned in 10CFR50.62 is a steady state point after the transient event has occurred. The purpose of utilizing this method is to demonstrate that the reactor may be safely shutdown after the transient event has occurred. Therefore the event modeled is a cold core (160oC), borated to an acceptable concentration that causes the reactor to be sub-critical by a specified amount. Project Scope This study was conducted at Global Nuclear Fuels in Wilimington, NC. The study included both lattice physics analysis and full core modeling in the 3-d core simulator. The lattice physics work was further subdivided into the enrichment phase and the gadolinium phase. For a reference BWR/3 the following projects were undertaken: 1. Enrichment Phase a. Analyze the effects of homogenous average enrichment perturbation on the ability to maximize k difference between the hot operating condition and cold borated condition. b. Determine the effect of localized heterogeneous enrichment perturbations on the ability to maximize k difference between the hot operating condition and cold borated condition. 2. Gadolinium Phase a. Ascertain the effects of gadolinium clumping on maximizing k difference between the hot operating condition and cold borated condition. b. Resolve the effects of increasing the amount of gadolinium rods on maximizing k difference between the hot operating condition and cold borated condition. c. Analyze the effects of gadolinium concentration on increasing k difference

PAGE 26

14 between the hot operating condition and cold borated condition. d. Determine a methodology for placing gadolinium rods in order to improve k difference between the hot operating condition and cold borated condition. 3. Full Core Modeling Phase a. Establish the maximum SLCS improvement utilizing an altered geometric gadolinium placement within freshly loaded fuel bundles. b. Determine the SLCS attainable from axial power shape perturbations utilizing enrichment differencing in certain axial zones of the fresh fuel bundles. c. Resolve the maximum SLCS gained from inserting extra gadolinium rods into the freshly loaded fuel bundles. d. Conclude the optimum design strategy for maximizing SLCS.

PAGE 27

CHAPTER 2 MODEL AND METHODOLOGIES In order to determine the necessary strategies for enhancing a margin of shutdown it is necessary to have a clear definition of that margin. A model and tools to analyze that model must then be selected that depict the physics of the problem as accurately as possible. After the designation of a model and utilized tools, the design parameters that are to be perturbed within the model must be determined. Finally, all other limiting parameters must be clearly defined so that it may be determined if the improvement to SLCS is feasible and will not cause the nuclear reactor to violate the thermo mechanical limits of the fuel. Standby Liquid Control System and Shutdown Margin The two shutdown parameters utilized for reactor core licensing are SLCS and SDM. SDM is a measure of the amount in which the reactor core is shutdown utilizing all of the control blades excluding the highest reactivity worth control blade. effCHBWEeffkkkSDM (2.1) CHBWE = controlled case highest worth blade excluded If keff = 1 then effkSDM 1 (2.2) Therefore SDM is the reactivity needed to make the system critical or conversely viewed as the amount of reactivity in which the system is shutdown utilizing all of the control blades except for the highest worth control blade. 15

PAGE 28

16 SLCS is a measure of the amount that the reactor core is shutdown utilizing a homogenously dispersed boron poison solution. effBeffkkkSLCS (2.3) B = borated keff If keff = 1 then BkSDM 1 (2.4) Similar to SDM, SLCS is the reactivity needed to make the system critical or conversely viewed as the amount of reactivity in which the system is shutdown utilizing a homogenously dispersed boron poison solution. Both parameters depict the amount in which the reactor is safely shutdown; however, the difference in geometry of the poison causes the physics involved in each shutdown process to be significantly different. Because shutdown margin calculations utilize a control blade, a heterogeneous poison located on the boundary of two sides of the fuel bundle, the power distribution of the SDM case is expected to be skewed radially across the fuel lattice with power peaking occurring in areas furthest from the control blade. SLCS calculations utilize an evenly dispersed boron poison solution; therefore the power distribution in the lattice is expected to follow the power distribution dictated by the actual geometry of the fuel lattice. The two different modes of control have two separate types of lattice reactivity responses. Due to this significant difference in reactivity response, it is possible that the ability to meet specified margin may be satisfied in one mode but not in the other. Understanding the reactivity response to each modes shutdown independently and then

PAGE 29

17 utilizing the commonalities in maximized shutdown in each of the two modes ultimately leads to a fuel design that has maximized margin in both cases. Modeling Tools TGBLA 6 TGBLA 6 is a static, multi-group, 2-dimensional, diffusion theory code with transport corrections factors that assumes infinite lattice behaviors. The steady state multi-group diffusion equation that is solved is [14]: )()()(1)()()()()(''''''rqrrkrrrrrDeggfgggggggggg (1.5) Because of the major differences in fuel bundle design, void fraction history, control blade history, enrichment distribution, gadolinium content and accumulated exposure, the fuel bundles nuclear characteristics in the core are very different both radially and axially. Neighboring fuel bundles also have an influence on the characteristics of the modeled fuel bundle; however, modeling the effects of these neighboring fuel bundles may be a daunting task because each neighboring fuel bundle in the core incurs nuclear characteristics that are unique from every other bundle. Therefore assumptions have to be made in order to be able to achieve an effective and timely approximation of the fuel bundles nuclear behavior [5]. TGBLA 6 makes key assumptions in order to accurately approximate a fuel bundles nuclear characteristics. Because fuel bundle designs may be varied axially in bundle geometry, gadolinium content, enrichment, and void concentration, the influence of axial conditions are considered of primary influence to the fuel bundles nuclear behavior. TGLBA 6 completes 2-dimensional lattice physics calculations at different exposure points for certain axial sections where there exists a known major variation in

PAGE 30

18 fuel bundle geometry. Because in certain defined axial zones the void concentration changes drastically and because the fuel bundle characteristics are also needed for certain temperature states, each fuel axial zone is modeled at 0%, 40%, and 70% void concentration. Though potentially any parameter may be varied by TGBLA 6, the main variables manipulated in a lattice design are the pellet enrichment, number of gadolinium rods and gadolinium concentration in each gadolinium rod. As a result of utilizing 2-dimensional calculations in certain axial zones of the fuel bundle, enrichment distribution and gadolinium content are only varied in the axial zones represented by the 2-dimensional lattice physics calculations [5]. Because the influence of neighboring fuel bundle was assumed a secondary influence on the bundle behavior, TGBLA 6 assumes infinite lattice behavior as a boundary condition. Assuming infinite lattice behavior results in a good approximation of the lattice power peaking distribution as well as an accurate generation of group constants to be later utilized in PANAC11. Utilizing these design constraints and boundary conditions, TGBLA 6 uses the solution of the multi-group diffusion theory equation to generate group averaged cross-sections for 3 energy ranges. Group constants are generated for the fast, epithermal and thermal energy range to be later used by 3-dimensional core simulator PANAC11. PANAC11 After the multi-group cross sections were collapsed and generated by TGBLA6, Panac11 was utilized as the 3-dimensional full core simulator. Panac11 is a static, three-dimensional coupled nuclear-thermal-hydraulic computer program utilized to represent a BWR core by a coarse-mesh nodal, 1-1/2 group (quasi-two group), static diffusion theory approximation. The program was utilized explicitly for detailed three-dimensional

PAGE 31

19 calculations of neutron flux, power distributions, and thermal limits at different exposure steps during reactor core life. The main variable parameters in PANAC11 were the control rod positions, refueling patterns, coolant flows, reactor pressures, reactor power level as well as other operational and design variables [8]. The diffusion equations are solved using the fast energy group. Resonance energy neutronic effects are included in the model by relating the resonance fluxes to the fast energy flux. The thermal flux is represented by an asymptotic expansion using a slowing down source from the epithermal region. A pin power reconstruction model is also implemented to account for the effect of flux gradients across the nodes on the local peaking distribution. Utilized Temperature States, Boron Concentrations and Lattice Types There was a combination of 4 main types of temperature states and boron concentrations investigated in the study. These states included the hot uncontrolled state (HU), cold uncontrolled state (CU0), cold controlled state (CC) and a cold state containing soluble boron (CU###). The HU state was defined to be the operating temperature state with no control blade placed next to the fuel lattice. All cold states were to be defined at a moderator temperature of 160oC, and all the cold uncontrolled states also had no control bladed placed next to the fuel lattice. The CU### condition was designated as a cold lattice containing a homogenously dispersed soluble boron solution at a specified boron concentration. The CC condition represented a cold fuel lattice with a control blade placed in the upper and left side of the lattice. There were two fuel lattice types examined in the enrichment perturbation portion of this study. A C lattice was defined to be a fuel lattice that exhibited the same amount of moderator spacing on all four sides of the lattice while a D lattice exhibited

PAGE 32

20 slightly more moderator spacing in the vicinity of a control blade location. Therefore the radial power distributions of the two different lattices are slightly different in lattice peaking characteristics. Measurement of SLCS and SDM during the Lattice Development Stage SLCS and SDM are both global parameters that describe a margin experienced by the entire nuclear reactor core. Therefore the calculation of these parameters involves utilizing a 3-dimensional core simulation tool. Fuel bundles are generally designed by first utilizing a 2-dimensional fuel lattice physics tool to create average collapsed group cross sections to then be utilized by the 3-dimensional reactor core simulator. An abundant amount of energy groups are utilized in the lattice physics calculation in order to properly model the physics of the lattice. Many bundles within the reactor core will exhibit similar characteristics due to the similar enrichment or gadolinium concentration within the fuel bundle. Therefore by generating these average group cross sections for similar fuel bundles, the 3-dimensional core calculation is significantly faster because the calculation does not involve solving equations at an abundant amount of energies for many different points within the reactor core [14]. The 3-dimensional simulator only utilizes few averaged group cross sections (usually 3 averaged groups). The 3-dimensional core simulation tool utilized for this study, PANAC11 separated the reactor core into a series of 6 in. cubic nodes. A flux was then solved in each individual node. Enhancement to the fuel bundle design therefore involvements modifications to the fuel design in both the lattice physics development stage and the 3-dimensional core simulation stage. Since SDM and SLCS global parameters defined for the entire system,

PAGE 33

21 a separate set of parameters must be utilized for characterizing how fuel improvements in the lattice development stage will affect the full core global parameters. Maximizing SDM and SLCS involves increasing the difference between the hot operating condition and the cold shutdown condition. Therefore in the lattice development stage an enhancement in SLCS and SDM meant and improvement in the difference between the hot operating k and cold shutdown k. The cold shutdown condition related to SDM is defined to be when the lattice is controlled by the placing a control blade next to it. The parameter used to represent the maximized difference between hot operating k and cold shutdown k was designated HUCC, and calculated by the equation: lledColdControngHotOperatikkHUCC (2.5) The cold shutdown condition related to SLCS is when the lattice is controlled by placing a homogeneously dispersed solution throughout the fuel lattice. The parameter used to represent the maximized difference between hot operating k and cold shutdown k was designated HUCU###. The symbol ### represents the amount of parts-per-million of boron in the solution. HUCU### is calculated by the following equation: ppmtdSolutionaColdBoratengHotOperatikkHUCU###### (2.6) Maximizing these parameters in the lattice development stage will maximize the global parameters that these parameters represent in the 3-dimensional core modeling stage. Fuel Bundle Geometry The fuel bundle utilized in the lattice physics calculations was a typical 10X10 boiling water reactor fuel bundle design with 92 fuel rods and two water rods. Figure 2-1

PAGE 34

22 displays a cross sectional view of the fuel bundle geometry. Since each lattice physics calculations was completed utilizing a 2-dimensional model, the fuel bundle had to be sub-sectioned into 2-dimensional axial zones in order to accurately model the sections of the bundle that experience different void concentrations, decreased average moderator density, variable gadolinium and enrichment placement, and different lattice geometries. The axial zones utilized were designated naturally enriched bottom (NAT), power-shaping zone (PSZ), dominant zone (DOM), plenum zone (PLE), vanished rod location zone (VAN), natural vanished rod zone (N-V) and natural top zone(N-T). The NAT was a naturally enriched zone filled with all 92 fuel rods and no gadolinium. This zone represented the first 6 inches of the bottom of the active core length. Both the PSZ and DOM were enriched zones containing 92 fuel rods with gadolinium present in certain locations. The PSZ zone was located on top of the NAT zone and was 48 inches in length. The DOM zone was located on top of the PSZ and was 30 inches long. Though in 2-D geometry these axial zones were identical, the zones are separated due to the different inherent thermo-hydraulic and neutronic characteristics experienced in each zone. The PLE was a 12 inch zone containing 78 fuel rods and gadolinium rods present in needed locations. This zone was used to model the interface of the part length rods and the vanished rod locations began. On top of the PLE was the VAN. The VAN contained 78 fuel rods and 14 vanished rod locations and ranged between 37 and 48 inches in length. On top of the VAN was the N-V. The N-V contained natural enrichment and has pellets existing in 78 fuel rod locations. The N-T was also naturally enrichment but only had pellets in locations where no gadolinium existed in axial portions of that specific rod.

PAGE 35

23 Figure 2-1. A cross sectional view of the modeled fuel bundle. As displayed in figure 2-2, there existed only 4 possible fuel rod geometries. The DOM and PSZ had the same fuel rod geometry, and the VAN and N-V had the same fuel rod geometry. In the N-T the locations marked E are used to represent empty fuel locations in the lattice of where gadolinium rods exist in the N-V. In the N-V, N-T, and VAN the locations marked V are used to represent the vanished rod locations. In the PLE the locations marked E are used to represent the area of the plenum tip of the part length fuel rods. Though 4 different possible fuel rod geometries exist only 3 different types of geometries were modeled in the lattice physics investigations. The DOM, PLE and VAN region were modeled. The N-T was not investigated because this region contained only

PAGE 36

24 natural enrichment and therefore the low power level experienced in this region would never be most limiting in any cold shutdown condition. Figure 2-2. The geometric setup of the fuel lattice axial zones. Thermal Limit Design Considerations Nuclear reactors are designed so that operation will not induce unnecessary risk to the health and safety of the general public. Therefore thermal limits are imposed on

PAGE 37

25 certain core parameters to ensure that radioactive release during reactor operation or any type of transient event does not exceed the acceptable limits imposed by the NRC. Constraining operation to within the thermal limits of the fuel guarantees that during normal operation and emergency transients the fuel integrity will be maintained. For the applicability of this project the two main thermal limits monitored were MFLPD and MFLCPR. These limits are set to limit boiling around the fuel rod locations and limit fuel rod power density in order to preserve fuel integrity [11]. Linear heat generation rate (LHGR) is the amount of power produced per length of fuel and is defined as LengthRodFuelAssmeblyPerRodsFuelAssembliesFuelofNumberOutputPowerThermalMaximumLHGRAverage____________ (1.6) A maximum average LHGR is specified for the utility in order to limit the plastic strain or deformation of the cladding. A limit of 1% deformation of zicaloy cladding is considered a conservative limit below which fuel damage is not expected to occur. New pellets undergo slight densification during irradiation. This causes the gap between the fuel and the cladding to increase and thus decrease thermal conductance. The pellet densification also has a shrinking axial effect. If one of the pellets gets stuck during this process, a gap is created resulting in more fissions occurring in newly exposed faces of the pellets increasing heat flux in that area [6]. Therefore LHGR is adjusted for the possible elevated heat flux and is defined as LTLPPLHGRLHGRdesignit*1*maxlim (1.7) Where: LHGRdesign = Maximum LHGR allowable to prevent clad damage

PAGE 38

26 LT = Total active core length L = Axial position in feet above the bottom of the core maxPP Maximum power spiking penalty In the core simulator LHGR is calculated for certain axial nodes. MFLPD is the maximum fractional limiting power density for the most limiting node and is defined as itnodeLHGRLHGRMFPLDlimmax_ (1.8) As long as MFLPD is less than one LHGR is not exceeded. However, because these calculations are based off of the assumptions of the maximum power spike penalty, and because the designer needs to be certain that MFLPD will never exceed one, the design basis requirement for MFLPD is 0.909 to ensure enough variation between the actual calculation and the measured data [8]. Critical power is the bundle power required to produce transition boiling in a reactor channel. If transition boiling were to manifest in a channel, it may lead to fuel rod dry out in the channel with the inability of the fuel rod surface to rewet. This phenomenon leads to a decrease in the ability of the clad to reject heat to the water through convection and thus heat up the clad to the point of mechanical failure [6]. CPR is the ratio to determine how close the actual power is to transition boiling and is defined as: APCPCPR (1.9) CP = Critical power for transition boiling AP = Actual power.

PAGE 39

27 CPR must always be below 1.0 for safe operation. MFLCPR is the flow adjusted ratio of the operating limit CPR for a specific fuel type to the CPR of that bundle and is defined as: CPRKLimitCPRMFLCPRf*_ (1.10) Kf = Flow adjustment factor Since MFLCPR should never exceed one in any section of the reactor during operation, and since slight uncertainty exists in knowing the actual power of the reactor and the critical power for a specified bundle, the design basis for MFLCPR is set to 0.930 to accommodate these uncertainties [8].

PAGE 40

CHAPTER 3 MAXIMIZING HOT-COLD BORATED k DIFFERENCE UTILIZING ENRICHMENT TGBLA 6 was utilized to understand SLCS improvement by enhancing lattice behavior characteristics utilizing enrichment perturbations. C and D lattices types were examined at 0%, 40% and 70% void fraction. The four system states inspected were HU, CU0, CU###, and CC. Lattices with a homogeneous enrichment distribution were examined to determine the effects of lattice average enrichment on the enhancement of the HUCU### and HUCC. Next, Local and gross enrichment perturbations were also analyzed to determine the effects of these types of enrichment perturbations on HUCU### and HUCC. Since an enormous amount of combinations of temperature states, lattice axial zones, lattice types and void concentrations could be created, the homogenous enrichment work was utilized to determine which of these temperature states, lattice axial zones, lattice types and void concentration were most limiting in order to limit the amount of cases to investigate therefore only examining the most effective strategies for enhancement. Homogeneous Enrichment Distribution A homogeneously enriched distribution was defined to be a fuel lattice with constant enrichment throughout the lattice. Therefore homogenous enrichment perturbations were defined as a change in enrichment to every fuel pin in the lattice by the exact same amount. 28

PAGE 41

29 Determining the Most Limiting Lattice Axial Zone and Void Concentration A variety of tests were completed to determine which lattice parameters were most limiting to HUCU### and HUCC. Figure 3-1 depicts the effects of lattice type and void fraction on HUCU###. Lattice type did not significantly affect HUCU###; however, as void fraction increased HUCU### decreased. For this case, at 0 GWD/STU the difference in HUCU### was solely related to the effective moderator density difference at increased void fraction. At higher void fractions the average moderator density was decreased. Because the average moderator density was decreased fewer neutrons were thermalized and absorbed by the fuel for fission, and an increased amount of neutrons were parasitically captured by the fuel [18]. Therefore HUCU### was smaller for higher void fractions. 00.020.040.060.080.10.120.140.160.18010203040506070Exposure (GWD/STU)HUCU660 0% Void, C Lattice 40% Void, C Lattice 70% Void, C Lattice 0% Void D lattice 40% Void, D Lattice 70% Void, D lattice Figure 3-1. Exposure dependent HUCU660 for the DOM at 3.95% enrichment. Initially U238 was the main parasitic neutron absorber in the fuel due to increased void concentration. When U238 absorbed a neutron it became Pu239. Because Pu239 had a high thermal absorption cross section (a = 1015b) as well as multiple resonance absorption peaks, it became another main parasitic neutron absorber. The increases in

PAGE 42

30 build up of parasitic neutron absorbers lead to a decrease in the effectiveness of boron to capture thermal neutrons [18]. Therefore as the lattice burned, plutonium was built up thus increasing the content of competing neutrons absorbers and therefore decreasing HUCU###. Furthermore, in the higher void history condition it took longer for plutonium production to reach an equilibrium state; therefore at increased void history conditions HUCU### decreases at a faster rate for a longer amount of time. Figure 3-2 illustrates the effects of the combination of axial zone and void fraction on HUCU###. The DOM was the most limiting axial zone because of the maximum amount of fuel rod inventory present in the lattice and minimum amount of volume to place borated water. A lattice geometry that allows for more moderator space allows for more ability to place borated water in the lattice; therefore since the VAN and PLE both have evacuated regions where more space exists to place a boron volume these axial zones were not the most limiting in terms of HUCU###. In order to maximize improvements in HUCU###, enhancements must be made to the most limiting conditions of HUCU###. HUCU### was most limiting in the 70% void fraction and DOM case; however, in the core, on average, the DOM exhibits a 40% void fraction therefore modeling a DOM at 70% void fraction would not have been an accurate realistic model to examine SLCS. The realistic model utilized which was most limiting was determined to be 40% void fraction in the DOM. Therefore since lattice type did not significantly effect HUCU###, and the DOM 40% void fraction was the most realistic limiting condition state, the C lattice type, DOM, 40% void fraction lattice was chosen as the base lattice in which all other perturbations were compared.

PAGE 43

31 00.050.10.150.20.25010203040506070Exposure (GWD/STU)HUCU660 Dom Zone, 0% Void Dom Zone, 40% Void Dom Zone, 70% Void Ple Zone, 0% Void Ple Zone, 40% Void Ple Zone, 70% Void Van Zone, 0% Void Van Zone, 40% Void Van Zone, 70% Void Figure 3-2. Exposure dependent HUCU660 at varied void fraction and axial zone for the C lattice at an enrichment of 3.95%. Understanding the Exposure Dependent HUCU### Curve Understanding the exposure dependence of the HUCU### curve was paramount to determining the appropriate strategy for enhancing HUCU###. Figure 3-3 depicts the two major portions of the exposure dependent HUCU### curve. Portion A encompasses 0 GWD/STU to roughly 11-15 GWD/STU depending upon geometry of the axial zone and void concentration. Portion B encompasses the rest of the HUCU### curve. When a fissile isotope absorbs a neutron, the isotope may either undergo fission or parasitic capture. The capture-to-fission ratio is defined by: f (3.1) In a thermal reactor the majority of the neutrons cause fissions at thermal energies in U235. Therefore for most thermal reactor applications the capture-to-fission ratio is an

PAGE 44

32 explanation of the fission efficiency of the thermal neutrons [13]. As increases k decreases because more thermal neutrons undergo parasitic capture and are removed from the system instead of undergoing a fission event and creating more neutrons [18]. During portion A of the exposure dependent HUCU### curve, HUCU### is decreasing due to increased plutonium production. Pu239 has a capture-fission-ratio of 0.370 (2200 m/s neutron) while U235 has a capture to fission ratio of 0.175 (2200 m/s neutron) [13]. Therefore with an increased plutonium acts as a competing neutron absorber that decreases boron worth thus limiting the effective absorption ability of the boron. The capture-to-fission ratio is a function of the system temperature. Doppler broadening is a phenomenon in which due to the kinetic motion of the target atoms at elevated temperatures the resonance absorption cross sections broaden while the peak magnitude of the cross section decreases, and in most cases slightly preserving the area under the original resonance [3]. Therefore though the effective peak of the cross section has decreased, the width of the resonance is increased and therefore the resonance affects a greater range of energy of neutrons; therefore causing a greater interaction rate in that energy interval and thus leading to more absorption and decreased flux in that energy interval [15]. At higher temperatures there is more kinetic motion of target particles and thus more Doppler broadening of the resonance cross sections. With increased parasitic capture and decrease thermal-to-fast flux ratio, HU k decreases at a much faster rate than CU### during Portion A of the HUCU curve because the worth of the plutonium produced is progressively worth more in the hot operating condition than in the cold condition.

PAGE 45

33 The thermal-to-fast flux ratio is defined by: fast thermal 1 (3.2) As the temperature of the system increases the average moderator density decreases. Because the average moderator de nsity is decreased the neutron spectrum has a higher density in the fast region. In th e hot operating condition the decreased average moderator density causes an increase in 1; therefore fewer neutrons are available for thermal fission events. Since at elevated temperatures there exists greater Doppler Broadening as well as decreased averag e moderator density, the decrease in 1 leads to a decrease in k of the system. Therefore the increasing and decreasing 1 in the hot condition leads to a decrease in th e HUCU### curve because the hot k is decreasing faster in comparison to the cold k. HUCU### Exposure (GWD/STU) A B Figure 3-3. Exposure dependant HUCU### curve. During portion B, as plutonium production reaches an equilibrium concentration the difference between the hot operating condition and cold condition worth becomes

PAGE 46

34 almost constant and therefore during this portion of the curve HUCU### experiences relatively no exposure dependence no exposure dependence. Enrichment and Boron Concentration Effects Figure 3-4 depicts the effects of increasing enrichment on HUCU### at different boron concentrations. For each 1.0% increase in average enrichment 0.0188 HUCU### was lost. Since the derivatives of HUCU### were equivalent at different boron concentrations, the amount of HUCU### gained from a boron concentration increase was linearly dependent on the boron concentration increase and not also affected by the average enrichment. Equation 3.3 calculated 1.84 x 10-4 HUCU660 gained for each 1 ppm or boron introduced to the lattice. Therefore 99.6 ppm of boron was required to compensate for a 1.0% average enrichment increase. EnrichmentSpecificionConcentratBoronHUCUBoronppmgainedHUCU__###__1_### (3.4) 00.050.10.150.20.250.300.40.81.21.622.42.83.23.644.44.85.2EnrichmentHUC U 660 PPM 726 PPM 742 PPM 792 PPM 935 PPM Figure 3-4. Beginning of cycled HUCU vs. enrichment in the DOM, at 40% void fraction, for a C lattice.

PAGE 47

35 Power Peaking Distribution The lattice power peaking distribution was a function of the relative distance of fissile material from the moderating regions. Moderation capability of certain lattice regions was a function of the water boundaries of that certain lattice region as well as the temperature state, boron concentration and geometry of poison utilized within the lattice. Power Peaking distributions for a homogenous 3.95% enrichment lattice at 5 GWD/STU are displayed in figure 3-5 for HU, CU0, CC and CU660. Each fuel pin location is identified by the horizontal and vertical location in which the pin resides. The water rod locations were marked with a zero in order to distinguish the water rod locations from the fuel pin locations. 123456789101234567891011.43661.22771.12291.07471.0611.0691.09251.1411.24311.4510.5740.56290.570.58890.61580.64960.69430.78260.99541.3971.30 < x21.22771.00670.90690.86970.86980.89090.91020.93911.0281.243320.56290.59380.62410.66020.70620.76050.79990.84670.98281.30141.30 > x > 1.2031.12290.90690.81880.80060.83190.90320.91620.88410.93921.141530.570.62410.67630.7410.83260.9660.99660.94291.01321.29371.20 > x > 1.1041.07470.86970.80060.81480.9034000.91640.91051.093240.58890.66020.7410.85391.0385001.09391.06281.31561.10 > x > 1.0551.0610.86980.83190.90340.9974000.90350.89141.069950.61580.70620.83261.03851.2382001.12971.08781.34031.05 > x > 1.0061.0690.89090.9032000.99760.90370.83230.87041.062160.64960.76050.966001.29821.16161.04211.08491.36291.00 > x > 0.9571.09250.91020.9162000.90370.81530.80130.87051.07670.69430.79990.9966001.16161.03131.00621.09621.39710.95 > x > 0.9081.1410.93910.88410.91640.90350.83230.80130.81960.9081.124580.78260.84670.94291.09391.12971.04211.00621.02851.14541.46370.90 > x > 0.8591.24311.0280.93920.91050.89140.87040.87050.9081.0081.229690.99540.98281.01321.06281.08781.08491.09621.14541.27661.60350.85 > x > 0.80101.451.24331.14151.09321.06991.06211.0761.12451.22961.439101.3971.30141.29371.31561.34031.36291.39711.46371.60351.91640.80 > x123456789101234567891011.45141.21961.12211.08471.07721.08531.10161.13781.23191.462111.38471.18591.10631.07791.07361.08081.09281.11971.19561.392321.21960.97270.87890.8520.85930.8840.89660.91060.99151.232921.18590.96750.88770.86690.87550.89850.90820.91650.98371.196331.12210.87890.79450.78770.83220.92560.93210.86770.91111.139531.10630.88770.81430.81110.85450.94340.94790.88260.91691.120941.08470.8520.78770.82020.9418000.93270.89771.10441.07790.86690.81110.84440.9612000.94840.90911.094651.07720.85930.83220.94181.0713000.92660.88551.088251.07360.87550.85450.96121.085000.94420.89981.083161.08530.8840.9256001.07170.94260.83350.86121.080661.08080.89850.9434001.08530.96190.85560.87711.076271.10160.89660.9321000.94260.82140.78930.85431.088571.09280.90820.9479000.96190.84550.81260.86881.080981.13780.91060.86770.93270.92660.83350.78930.79660.88161.126481.11970.91650.88260.94840.94420.85560.81260.81620.891.109791.23190.99150.91110.89770.88550.86120.85430.88160.9761.224691.19560.98370.91690.90910.89980.87710.86880.890.97021.1898101.46211.23291.13951.1041.08821.08061.08851.12641.22461.4576101.39231.19631.12091.09461.08311.07621.08091.10971.18981.3894Key 5 GWD,HU,3.95 Enrichment, Dom Zone, C Lattice 40% Void5 GWD,CU0,3.95 Enrichment, Dom Zone, C Lattice 40% Void5 GWD,CC,3.95 Enrichment, Dom Zone, C Lattice 40% Void5 GWD,CU660,3.95 Enrichment, Dom Zone, C Lattice 40% Void Figure 3-5. The power peaking distributions at 5 GWD/STU, 3.95% enrichment, DOM, C lattice, and 40% void fraction vs. temperature state and boron concentration.

PAGE 48

36 Figure 3-5 suggests that there were significant differences between the HU and CU0 power peaking distributions. In the HU state the outer borders of the lattice exhibited the greatest amount of power peaking due to the close proximity of large areas of water to that location and therefore displaying the greatest moderation capabilities. Due to the moderation of the internal water rod locations, fuel pins located near the internal water rods exhibited a higher relative power than locations that were located away from the borders of the lattice and away from the internal water rod locations. The lack of moderation for the fuel pins located away from the borders of the lattice and away from the internal water rod locations caused these locations to exhibit the lowest relative power. In the CU0 state, power was raised in the highly moderated areas. With no voids, the outer borders of the lattice and the internal water rod locations exhibit a greater amount of power peaking than the areas of the lattice that were between these locations. Because of this effect, the importance of fuel pins located away from the borders and water rod locations were significantly decreased, and if a perturbation were to be made to a fuel lattice in order to improve inherent HUCU0 characteristics these locations would not play an important role. There were also significant differences in power peaking distribution for different poison types. In the CC state a high anisotropy of power peaking was exhibited due to poison residing at the corners of the lattice. Fuel pins located closest to the control blade exhibit the greatest power suppression; therefore if a poison introduction was necessary for power suppression in the HU state, placing that poison away from the greatest power suppressed pins in the CC condition will achieve the greatest improvement in HUCC.

PAGE 49

37 In the CU660 state the boron caused the power to be suppressed in highly moderated regions thereby flattening out the power distribution of the lattice. Because boron was present in the moderator, regions that had greater power peaking due to increased moderation capability also consequently had greater power suppression from the boron dispersed within the moderator. Because of the flatter power distribution in the CU660 as compared with the HU state, placing power suppressors in peaked locations corresponding to the HU state did not necessarily have as severe an impact on the cold borated state. However, this leads to a distinct design advantage because it may be possible switch locations of a distributed poison and have a miniscule effect on HU but a major effect on CU###. Therefore in order to maximize HUCU###, power suppressors must be placed in areas where the CU### state exhibits a higher power peak than the power peak in the HU state. As enrichment increased the power peaking distribution in the lattice became more skewed. Figure 3-6 displays that as average enrichment was increased in the CU### state the power peaked more in the border regions and internal water rod locations of the lattice. Figure 3-7 displays that as average enrichment was increased in the HU state the power also peaked more in the border regions and internal water rod locations of the lattice. Therefore there exist fewer locations in which moving a distributed poison will not greatly affect the HU state while greatly affecting the CU### state. Unfortunately this demonstrates that in a power up rate or increased exposure design, it will be harder for the designer to create a design that improves SLCS and decreases the power peak in the HU state. Figure 3-6. The power peaking distributions at 5 GWD/STU, CU660, DOM, C lattice, and 40% void fraction vs. enrichment.

PAGE 50

38 123456789101234567891011.19231.0951.05951.04711.04621.05031.05571.0671.09961.192911.45141.21961.12211.08471.07721.08531.10161.13781.23191.462121.0950.97290.93360.92370.92970.94190.9470.9510.98221.098621.21960.97270.87890.8520.85930.8840.89660.91060.99151.232931.05950.93360.89630.89580.92450.97750.98020.94010.95111.066231.12210.87890.79450.78770.83220.92560.93210.86770.91111.139541.04710.92370.89580.91680.9912000.98040.94741.055341.08470.8520.78770.82020.9418000.93270.89771.10451.04620.92970.92450.99121.0681000.97790.94241.050151.07720.85930.83220.94181.0713000.92660.88551.088261.05030.94190.9775001.06830.99160.92510.93041.046161.08530.8840.9256001.07170.94260.83350.86121.080671.05570.9470.9802000.99160.91740.89650.92461.047271.10160.89660.9321000.94260.82140.78930.85431.088581.0670.9510.94010.98040.97790.92510.89650.89720.93461.059781.13780.91060.86770.93270.92660.83350.78930.79660.88161.126491.09960.98220.95110.94740.94240.93040.92460.93460.9741.095391.23190.99150.91110.89770.88550.86120.85430.88160.9761.2246101.19291.09861.06621.05531.05011.04611.04721.05971.09531.1923101.46211.23291.13951.1041.08821.08061.08851.12641.22461.4576123456789101234567891011.34151.1681.09651.07041.06651.07331.08461.10931.17711.34811.43131.2041.11661.08621.08161.08911.10161.13031.21411.439921.1680.9730.89950.87970.88760.90890.91840.9270.98861.177521.2040.960.87470.85340.86270.88730.89690.90430.97661.21531.09650.89950.83120.82770.86790.94860.95330.89550.92731.110131.11660.87470.79690.79430.84090.93880.94290.86870.90481.131941.07040.87970.82770.85790.9645000.95370.91911.085941.08620.85340.79430.83090.9588000.94340.89791.103851.06650.88760.86790.96451.0768000.94930.90991.075151.08160.86270.84090.95881.095000.93970.88871.091961.07330.90890.9486001.07720.96510.86890.8891.068661.08910.88730.9388001.09540.95960.84210.86451.084871.08460.91840.9533000.96510.85890.8290.88131.072871.10160.89690.9429000.95960.83210.79590.85561.089881.10930.9270.89550.95370.94930.86890.8290.83280.90141.099381.13030.90430.86870.94340.93970.84210.79590.7990.87731.120691.17710.98860.92730.91910.90990.8890.88130.90140.97531.171291.21410.97660.90480.89790.88870.86450.85560.87730.96311.2086101.3481.17751.11011.08591.07511.06861.07281.09931.17121.3451101.43991.2151.13191.10381.09191.08481.08981.12061.20861.43725 GWD,CU660,0.71 Enrichment, Dom Zone, C Lattice 40% Void5 GWD,CU660,3.2 Enrichment, Dom Zone, C Lattice 40% Void5 GWD,CU0,3.95 Enrichment, Dom Zone, C Lattice 40% Void5 GWD, CU660, 4.9 Enrichment, Dom Zone, C Lattice, 40% Void Figure 3-6. The power peaking distribution at 5 GWD/STU, CU660, DOM, C lattice, and 40% void fraction versus enrichment. 123456789101234567891011.22971.12191.07021.04431.03651.04181.05651.08361.1341.238711.43661.22771.12291.07471.0611.0691.09251.1411.24311.451.30 < x21.12190.99720.94610.92450.92370.93510.94840.96741.01261.132821.22771.00670.90690.86970.86980.89090.91020.93911.0281.24331.30 > x > 1.2031.07020.94610.89970.88750.90650.95070.96140.94280.96751.082731.12290.90690.81880.80060.83190.90320.91620.88410.93921.14151.20 > x > 1.1041.04430.92450.88750.89430.9499000.96150.94861.055741.07470.86970.80060.81480.9034000.91640.91051.09321.10 > x > 1.0551.03650.92370.90650.94991.0071000.95090.93541.041251.0610.86980.83190.90340.9974000.90350.89141.06991.05 > x > 1.0061.04180.93510.9507001.00720.95010.90680.92411.03661.0690.89090.9032000.99760.90370.83230.87041.06211.00 > x > 0.9571.05650.94840.9614000.95010.89460.88790.9251.043871.09250.91020.9162000.90370.81530.80130.87051.0760.95 > x > 0.9081.08360.96740.94280.96150.95090.90680.88790.90010.94671.069881.1410.93910.88410.91640.90350.83230.80130.81960.9081.12450.90 > x > 0.8591.1341.01260.96750.94860.93540.92410.9250.94670.99781.121591.24311.0280.93920.91050.89140.87040.87050.9081.0081.22960.85 > x > 0.80101.23871.13281.08271.05571.04121.0361.04381.06981.12151.2291101.451.24331.14151.09321.06991.06211.0761.12451.22961.4390.80 > x123456789101234567891011.38911.20631.11161.06681.05371.06141.0841.12951.22171.402211.4881.24931.13461.08371.06951.07781.10171.15271.26451.501721.20631.01020.91850.88280.88210.90170.92080.94951.03131.221821.24931.00040.89340.85550.85660.87930.89820.92621.02161.264931.11160.91850.83670.81830.84620.91060.92410.89810.94971.129831.13460.89340.79980.78260.81750.89650.90870.86880.92641.153341.06680.88280.81830.82960.9089000.92420.92111.084541.08370.85550.78260.80030.8993000.90890.89861.102651.05370.88210.84620.90890.9928000.91090.90211.062151.06950.85660.81750.89931.0045000.89690.87981.078961.06140.90170.9106000.9930.90910.84660.88271.054661.07780.87930.8965001.00470.89970.8180.85731.070971.0840.92080.9241000.90910.830.81890.88351.067871.10170.89820.9087000.89970.80090.78330.85651.085381.12950.94950.89810.92420.91090.84660.81890.83740.91941.112881.15270.92620.86880.90890.89690.8180.78330.80080.89461.136591.22171.03130.94970.92110.90210.88270.88350.91941.01131.207891.26451.02160.92640.89860.87980.85730.85650.89461.0021.2517101.40221.22181.12981.08451.06211.05461.06781.11281.20781.3909101.50171.26491.15331.10261.07891.07091.08531.13651.25171.4913Key 5GWD,HU,0.71 Enrichment, Dom Zone, C Lattice 40% Void5 GWD,HU,3.2 Enrichment, Dom Zone, C Lattice 40% Void5 GWD,HU,3.95 Enrichment, Dom Zone, C Lattice 40% Void5 GWD, HU, 4.9 Enrichment, Dom Zone, C Lattice, 40% Void Figure 3-7. The power peaking distributions at 5 GWD/STU, HU, DOM, C lattice, and 40% void fraction vs. enrichment.

PAGE 51

39 Heterogeneous Enrichment Distribution After determining the effects of average enrichment on the behavior of HUCU###, heterogeneous enrichment perturbations were then examined in order to determine if enrichment changes to individual fuel pins could affect HUCU###. The two major types of enrichment perturbations investigated were localized enrichment perturbations and gross enrichment perturbations. Localized enrichment perturbations were considered to be small sets of fuel pins that were either increased or decreased in enrichment by a certain amount holding the rest of the fuel lattice at constant enrichment. Gross Enrichment perturbations were considered to be a large lump of fuel pins that were either increased or decreased in enrichment by a certain amount holding the average enrichment of the entire lattice constant. Localized Enrichment Perturbation Localized enrichment perturbation patterns were generated based on the power peaking distribution map. The fuel pin locations were set into groups based on locations exhibiting similar power peaking in the homogeneously enriched lattice calculation. Since lattice power peaking was determined to be dependent on enrichment, 3.95% enrichment was chosen as the distribution for which the determination of the pattern type was made. Figure 3-8 displays the distribution of perturbations made to the lattice. Each group of numbers represents a group of fuel pins that were either increased or decreased by 1.0% enrichment as the rest of the lattice was kept at a constant enrichment. Localized enrichment perturbations had no effect on HUCU### as depicted in figure 3-9. The minute difference of 0.00373 HUCU### in figure 3-9 was considered only a function

PAGE 52

40 of the 0.2% average enrichment difference exhibited between each pattern utilized. Therefore localized enrichment perturbation did not greatly affect HUCU### behavior. 12345678910112344443212257888775233799977873448997WW774548976WW7846487WW679847477WW799848378779997392577888752101234444321 Figure 3-8. Localized enrichment perturbation map. 00.020.040.060.080.10.120.14010203040506070Exposure (GWD/STU)HU-CU660 Map 1, Pattern 1 Map 1, Pattern 2 Map 1, Pattern 3 Map 1, Pattern 4 Map 1, Pattern 5 Map 1, Pattern 6 Map 1, Pattern 7 Map 1, Pattern 8 Map 1, Pattern 9 0.074957 0.078689Maximum Change in Hot Uncontolled k-infinity Due To Cold Uncontrolled k-infinity = 0.003732 Which is Soley a Function of Average Enrichment Change (0.2%). Figure 3-9. Exposure dependent HUCU660 for different localized enrichment perturbation patterns.

PAGE 53

41 Gross Enrichment Perturbation Gross enrichment perturbations were next examined in order to determine how these type of lattice perturbations would affect shutdown behavior. Figure 3-10 displays an example pattern of gross enrichment perturbations and table 3-1 lists the enrichment perturbations made to that example pattern. Table 3-1. Gross enrichment perturbation scheme for figure 3-10. Pattern Enrichment Perturbation (1-2) Pattern Enrichment Perturbation (1-2) 1 1.6%-4.9% 7 4.9%-1.6% 2 2.4%-4.9% 8 4.9%-2.4% 3 3.2%-4.9% 9 4.9%-3.2% 4 4.4%-4.9% 10 4.9%-4.4% 5 3.2%-4.4% 11 4.4%-3.2% 6 3.6%-4.4% 12 4.4%-3.6% 12345678910111111111112111111112231111111122411111WW222511111WW2226111WW222227111WW222228111222222291222222222101222222222 Figure 3-10. An example of a gross enrichment perturbation map. Gross enrichment perturbation demonstrated no effect on HUCU###. Though HUCU### was not a function of localized and gross enrichment perturbation, HUCC was highly dependent upon these perturbations. Figure 3-11 and 3-12 display the difference in effect of gross lattice perturbation skewing. Notice in figure 3-11 no effect was noticed on HUCU###; however, in figure 3-12 HUCC was highly dependent upon enrichment distribution.

PAGE 54

42 00.020.040.060.080.10.120.140.16010203040506070Exposure (GWD/STU)HUCU660 Map 6, Pattern 2 Map 6, Pattern 8 Figure 3-11. Exposure dependent HUCU660 at 40% void fraction, in the DOM, with a C lattice. 00.050.10.150.20.25010203040506070Exposure (GWD/STU)HUCC Map 6, Pattern 2 Map 6, Pattern 8 Figure 3-12. Exposure dependent HUCC at 40% void fraction, in the DOM, with a C lattice. Placing a higher enrichment closer to the control blade location allowed for greater power suppression and thus enhanced HUCC due to the increased control the blade exhibited over the maximum power producing section of the lattice. Therefore though

PAGE 55

43 enrichment perturbation was not limiting in HUCU###, distorting the enrichment distribution had an effect on HUCC. Though SLCS does not depend on local or gross enrichment perturbation, SDM is sensitive to this type of perturbation. However, the designer may only enhance HUCU### by perturbing average enrichment of the entire lattice therefore as long as the average of the enrichment of the lattice satisfies SLCS requirements the enrichment may be perturbed to meet SDM without violating SLCS.

PAGE 56

CHAPTER 4 MAXIMIZING HOT-COLD BORATED k DIFFERENCE UTILIZING GADOLINIUM There were four different isolated studies examined for the purpose of determining the optimum strategies for utilizing gadolinium to enhance HUCU###. Gadolinium rods were examined in a variety of clumped geometries in order to determine the lumped spatial self-shielding effects. After the effects of self-shielding were determined, the effects of increasing the amount of gadolinium rods on HUCU### were investigated. Gadolinium concentration was next analyzed. Finally, gadolinium rod placement was examined to determine the optimum gadolinium locations for enhancing HUCU### without diminishing HUCC. Spatial Self-Shielding Effects of Gadolinium Rods on HUCU### Gadolinium rods were clumped in a variety of geometries to determine the effects of lumped spatial self-shielding on HUCU###. Four samples of examined clumped gadolinium rod geometries are displayed in figure 4-1. Clumping the gadolinium rods decreased the BOL gadolinium worth because the gadolinium rods were effectively spatially self-shielding each other from the impinging neutron flux. The self-shielding of the gadolinium decreased the effective surface area utilized for neutron absorption [15]. Because the thermal-to-fast flux ratio was much higher in the cold state than in the hot state more neutrons were likely to be thermally absorbed in the gadolinium in the cold condition; therefore decreasing the effective surface area for neutron absorption decreases 44

PAGE 57

45 the effectiveness of the power suppression from the gadolinium rods and thus decreasing HUCU###. Figure 4-1. Four sample clumped geometries. Figure 4-2 depicts the effects of gadolinium spatial self-shielding on gadolinium worth. Highlighted in red are the patterns corresponding to those displayed in figure 4-1. As gadolinium clumping increased, gadolinium worth decreased. Face adjacent clumping of all four sides of a gadolinium rod resulted in a 38% decrease in gadolinium worth, and face adjacent clumping of two sides resulted in a 19% decrease in gadolinium worth. Diagonal face adjacent clumping lead to a 7% decrease in gadolinium worth.

PAGE 58

46 -0.3-0.25-0.2-0.15-0.1-0.05010111213Pattern Gadolinium Worth (dk/k) HU Gad Worth CU0 Gad Worth CU660 Gad Worth CU 935 Gad Worth CC Gad Worth Figure 4-2. Corresponding 0 GWD/STU gadolinium worth for the patterns displayed in figure 4-1. 00.020.040.060.080.10.12010203040506070Exposure (GWD/STU)HUCU660 Pattern 10 Pattern 11 Pattern 12 Pattern 13 Figure 4-3. Corresponding exposure dependent gadolinium clumping effects on HUCU660 for the patterns displayed in figure 4-1.

PAGE 59

47 Because clumping a group of gadolinium rods decreased the effective surface area for absorption, the exposure time required to burn out the gadolinium increased. In figure 4-3 as clumping increased the exposure point in which gadolinium burns out also increased. Also depicted in figure 4-3 is the decrease in HUCU### as a function of increase clumping. Therefore in order to design an optimum lattice to enhance HUCU### gadolinium rods must be spaced as far apart as reasonably achievable and face adjacent and diagonal adjacent clumping must be eliminated. The Effects of Increasing the Amount of Gadolinium Rods on HUCU### In a power up-rate and an increased exposure cycle, extra positive reactivity must be installed in the fuel bundle. Placing extra positive reactivity will cause a greater skewing of the lattice power peaking as well as violating beginning of cycle critical eigenvalue requirements. In order to decrease the beginning of cycle eigenvalue to the critical requirements and decrease power peaking to improve lattice efficiency and meet thermal margins, gadolinium must be placed in the fuel bundle. As more positive reactivity is installed, more gadolinium rods at higher concentrations are needed. The effects of increasing the amount of gadolinium rods in the lattice on gadolinium worth are demonstrated in figure 4-4. The gadolinium rod placement geometry was held constant while 8 to 18 rods were placed in the lattice. As the amount of gadolinium rods placed in the lattice increased, the degree of gadolinium clumping decreased due to the size limitations of the lattice. In the increase of 15 gadolinium rods to 16 gadolinium rods, a clumped geometry was utilized that resulted in a decrease in gadolinium worth. Each gadolinium rod insertion for the hot condition was worth -0.0103 k/k while each gadolinium rod insertion in the CU660 case was worth -0.0095

PAGE 60

48 k/k leading to 0.5 mk/k difference in gadolinium worth between the hot and cold lattice states. -0.3-0.25-0.2-0.15-0.1-0.05089101112131415161718Number of RodsGadolinium Worth (dk/k) HU Gad Worth CU0 Gad Worth CU660 Gad Worth CU935 Gad Worth CC Gad Worth Figure 4-4. The effects of increased number of gadolinium rods on the gadolinium worth at 0 GWD/STU. Increasing the amount of gadolinium rods decreased hot and cold k by increasing the amount of neutrons removed from the system by absorption. HUCU### also decreased as the number of gadolinium rods increased. Figure 4-5 displays BOL decrease in HUCU660 as a function of increasing the amount of gadolinium rods placed in the lattice. The thermal-to-fast flux ratio is higher in the cold state than in the hot state due to the cold states increased moderator density, and the thermal-to-fast flux ratio is lower in higher boron concentration due to decreased thermal neutron availability after boron capture. Gadolinium is dominantly a thermal neutron absorber therefore in the increased

PAGE 61

49 thermal-to-fast flux ratio gadolinium was a more effective absorber. The decreased thermal-to-fast flux in the hot state as compared to the cold borated states results in a decrease in HUCU### as each gadolinium rod was inserted because the gadolinium was worth more per rod insertion in the cold state than in the hot state. Gadolinium rod worth was also a function of the boron concentration utilized in the cold condition. At 0 GWD/STU HUCU660 changes -0.0017 per rod insertion (10-13 ppm boron equivalence) while HUCU935 changes -0.0025 per rod insertion (16-20 ppm boron equivalence). This demonstrates that when a utility decides to go to a power up-rate or increased exposure cycle, the increased amount of gadolinium needed to offset the increased installed reactivity will result in a decrease in the HUCU### parameter on the lattice level resulting in a decrease in SLCS margin on the core wide level. y = -0.0025x + 0.1197y = -0.0017x + 0.070300.020.040.060.080.10.1202468101214161820Number of Gadolinium RodsHUCU HUCU660 HUCU935 Figure 4-5. The effects of the number of gadolinium rods inserted on HUCU at 0 GWD/STU.

PAGE 62

50 The Effects of Increasing the Gadolinium Concentration on HUCU### The effects of increasing gadolinium concentration of a given gadolinium configuration on HUCU### was next examined to determine if gadolinium concentration was a design constraint for HUCU###. Increasing the gadolinium concentration of the lattice had similar results to increasing the amount of rods in the lattice. Figure 4-6 displays the increase in gadolinium worth as a function of increasing concentration. For CU660 at 0 GWD/STU a 1% increase in gadolinium concentration for 14 gadolinium rods is worth -0.002343 k/k. For HU at 0 GWD/STU a 1% increase in gadolinium concentration for 14 gadolinium rods is worth -0.004587 k/k. -0.3-0.25-0.2-0.15-0.1-0.0500%1%2%3%4%5%6%7%8%9%Gadolinium ConcentrationGadolinium Worth (dk/k) HU Gad Worth CU0 Gad Worth CU660 Gad Worth CU935 Gad Worth CC Gad Worth Figure 4-6. The effect of increasing the gadolinium concentration for 14 gadolinium rods on gadolinium worth at 0 GWD/STU. The HU state exhibited 2 times greater worth in increasing 1% in gadolinium worth than the CU state; therefore increasing the gadolinium concentration will decrease HUCU###. Figure 4-7 exhibits the decrease in HUCU### as the gadolinium

PAGE 63

51 concentration is increased. For a 1% Change In Concentration for 14 Gadolinium Rods at 0 GWD/STU, HU660 changes -0.004504 (33 ppm boron equivalent) and HU935 changes -0.004906 (36 ppm boron equivalent). y = -0.4504x + 0.0795y = -0.4906x + 0.119800.020.040.060.080.10.120%1%2%3%4%5%6%7%8%9%Gadolinium ConcentrationHUCU HUCU660 HUCU935 Figure 4-7. The effect of increasing the gadolinium concentration of 14 gadolinium rods on HUCU at 0 GWD/STU The Importance of Gadolinium Rod Location The lattice power distribution is never uniform. The effectiveness of gadolinium to suppress power while increasing HUCU### was highly dependent upon the location in the lattice in which the gadolinium was placed. Since many parameters contributed to the power distribution within the lattice, determining an optimum location for gadolinium placement resulted from satisfying all the parameters that were most limiting. The power peaking distributions for the HU, CU### and CC states differed therefore determining an optimum location for placing gadolinium involved placement in areas that maximized

PAGE 64

52 improvement to the most limiting state without violating the parameter requirements of the other states. Two gadolinium rods were placed in series of different locations throughout the lattice to determine the areas in which HUCU### and HUCC could be maximized (two gadoliniums rods were used in order to preserve mirror symmetry of the lattice design). Figure 4-8 presents the locations examined and corresponding case numbers of the gadolinium location tests. 1234567891012145113123681012134379WW145469WW1517658WW161820710WW1619218111214151821222391317202310 Figure 4-8. Gadolinium rod placement diagram. The effectiveness of the gadolinium placement was a function of the power distribution. The power distribution was a function of the moderation ability and poison geometry. In the CC state as gadolinium rods were placed further from the edges of the control blade the worth of the gadolinium increased. This was due to the decreased competition for neutrons between the gadolinium and the control blade. If the

PAGE 65

53 gadolinium was placed to close to the control blade then effectively the gadolinium and blade were spatially self-shielding each other and therefore decreased both of the poisons effective worth. In the CU### case, the difference in worth of a certain gadolinium rod location was not a function of boron poison geometry (assuming no clumping) because the boron poison geometry was uniform; however, the difference in worth of certain gadolinium rod locations was related to the moderation capability of the fuel lattice. Areas of the lattice exhibiting more moderation created more thermal neutrons, leading to a higher power peaking. Gadolinium was worth more in these areas of increased moderation capability due to the increased amount of thermal neutrons available for absorption. Figure 4-9 displays the difference in gadolinium worth as a function of gadolinium location corresponding to the patterns in figure 4-8. Certain pattern changes caused opposing worth differences in different temperature and boron geometry states. In the change from pattern 4 to pattern 5 and in the change from pattern 15 to pattern 16, CC gadolinium worth increased while CU660 and HU gadolinium worth decreased. In the change from pattern 10 to pattern 11, CC gadolinium worth greatly decreased while CU660 worth slightly decreased and HU worth slightly increased. Placing a gadolinium rod in a higher power peaked area resulted in up to a 5% increase in gadolinium worth. In the CC case, increasing the distance of the gadolinium rod from the center of the control blade increased gadolinium worth by 0.00525 until the water rods in the center of the lattice were reached. Once the water rods were reached in the CC lattice (on the lower right diagonal half of the lattice), the power distribution and gadolinium rod worth become independent of the effects of the control blade.

PAGE 66

54 Altering a current lattice design to improve SDM and SLCS while maintaining HU must include shifting gadolinium locations where both the CU### and CC states have the most significant worth improvement while HU only has slight gadolinium worth increase. Improving CC gadolinium worth involves placing the gadolinium away from the control blade so that the gadolinium does not compete for neutrons with the boron in the control blade for. Enhancing the CU### worth involves spacing out the gadolinium so that spatial self-shielding does not occur and placing the gadolinium in the areas of highest power peaking exhibited by the cold power shape (areas of greatest moderation capabilities). Enhancing the HU worth also involves spacing out gadolinium and placing them in areas of highest power peaking corresponding to the HU power shape. The optimum gadolinium pattern for any given amount of gadolinium rods is the design that meets all three of these criteria. -0.05-0.045-0.04-0.035-0.03-0.025-0.02-0.015-0.01-0.005001234567891011121314151617181920212223PatternGad Worth (dk/k) HU Gad Worth CU0 Gad Worth CU660 Gad Worth CC Gad Worth Figure 4-9. Gadolinium worth versus location for 0 GWD/STU, 7% gadolinium concentration,

PAGE 67

55 Fuel Lattice Design Conclusions Certain parameters in the 2-dimensional fuel lattice design have a significant contribution to HUCU###. Lattice enrichment may be utilized to enhance HUCU###. While local lattice enrichment perturbations do not contribute to HUCU###, decreasing the lattice average enrichment decreases the power distribution skewing of the lattice and therefore increases HUCU###. However, with the demand for increased cycle lengths at higher powers, unfortunately higher average enrichments are needed to meet these requirements. Therefore with the needed increased average enrichment of the bundles will result in an increase in power skewing of the lattice thus decreasing HUCU###. The addition of competing thermal neutron poisons decreases HUCU###. Fuel designs with a tighter pitch between fuel rods lead to an increased production of plutonium. Plutonium is a competing thermal neutron poison. Therefore creating smaller fuel rods with a tighter pitch may increase the heat transfer of the fuel bundle, but also wa greater amount of plutonium is generated and therefore HUCU### is compromised. Also utilization of mixed oxide fuels (MOX) introduces an increased plutonium inventory in the core therefore further decreasing HUCU###. Gadolinium is also a thermal neutron poison. Enough positive reactivity must be installed into the reactor core at the beginning of cycle in order to meet the cycle length requirements. Gadolinium must installed in each of the fuel bundles in order to make sure that with the installed reactivity the reactor core is critical throughout operation. Therefore though gadolinium competes for thermal neutrons thereby decreasing HUCU###, it is a necessary component of reactor operation. In order to enhance HUCU### while maintaining a cycle operation goal, only certain fuel lattice parameters may be varied. Cycle length and power level is dependent

PAGE 68

56 upon installed reactivity; therefore average enrichment of the fuel is a fixed parameter if the number of fresh bundles utilized in the design is fixed. Plutonium production is related to power level, fuel lattice pitch, and isotope content of the fuel. In most cases all of those are fixed. The only design parameter with room for enhancement is gadolinium. If gadolinium is utilized effectively in certain locations of the fuel bundle, maximized differences between the HU and CU### may be created; therefore HUCU### is improved leading to an improvement in SLCS on the full core level. However, in increased average enrichment cores more gadolinium rods are needed to meet critical eigenvalue requirements; therefore resulting in fewer locations to manipulate gadolinium rod placement for improvement in HUCU###. Therefore if gadolinium has already been placed in the areas of maximized HUCU### enhancement further techniques must be utilized on the full core level to enhance HUCU###.

PAGE 69

CHAPTER 5 FULL CORE SLCS MODELING The reference base reactor core analyzed was a generic BWR/3. The reactor core was quarter core symmetric meaning that only a quarter of the full core had to be modeled to accurately represent characteristics of the full core. Figure 5-1 was the base reference core in which all perturbations were compared. Two different average bundle enrichments of fresh fuel were loaded into the core for the investigated cycle. The high enrichment bundles (fuel type 19) were 4.18% enriched, and the low enriched bundles (fuel type 20) were 3.89% enriched. Three major types of perturbations utilized to enhance SLCS were investigated on the full core level. The perturbations were selected based on the knowledge generated from the lattice physics analysis, and fell into two distinct characteristic types. The first type involved making a perturbation to the entire bundle. Gadolinium rod placement perturbations to the entire bundle were examined in order to determine the maximum achievable enhancement to SLCS. The second type involved perturbing the axial power shape. Based on the fact that average enrichment was also a dominant parameter in enhancing HUCU### in the lattice physics calculations, axial power shaping techniques utilizing enrichment differencing in certain axial zones was next examined to determine the maximum achievable enhancement to SLCS by perturbing the cold axial power shape. Gadolinium insertion in certain axial zones was also examined to determine if this method was also effective in enhancing SLCS by perturbing the axial power shape utilizing a poison. 57

PAGE 70

58 33899 733557 632011 631230 629071 633219 630031 626946 625807 726128 725187 733611 732365 630011 730073 717908 1715550 1615517 1616187 1615726 1633451 628541 629470 727398 727574 717496 160 190 190 200 1933992 633626 625332 725539 618506 1718019 170 190 1918275 160 2016968 1633476 633533 618102 1717534 1615903 1617983 170 190 1918023 170 2018156 170 2034030 728585 625349 717563 1617073 170 200 190 1918657 170 2018564 160 2018368 1632422 629444 725517 615879 160 2018404 160 1918791 170 2017545 170 2018513 160 2029955 727372 718511 1717980 170 190 1918610 170 2018586 170 2017211 160 2018702 1633233 630085 727593 718030 170 190 1918809 170 2018404 160 2018625 170 2018470 170 2033890 730081 617919 1717512 160 190 1918661 170 2018590 170 2017333 170 2018608 170 2017902 1733527 626959 615552 160 190 1918024 170 2017542 170 2018629 170 2017094 170 2018054 170 2031928 625804 715484 160 1918292 160 2018558 160 2017214 160 2018646 170 2017372 170 2018539 1731253 626087 716242 160 200 2018166 170 2018537 160 2018472 170 2018059 170 2018176 170 2029057 625179 715725 160 1916977 160 2018402 160 2018682 160 2017898 170 2018529 170 2018485 17 Fresh BundleOnce Burnded BundleTwice Burned Bundle XXXX ZZZZ Bundle Ex p osureBundle T yp e Figure 5-1. Reference base core fuel bundle loading map. In each perturbation case the critical eigenvalue, thermal limits, and SDM were monitored in order to determine if the enhancement to SLCS would violate the requirements of these margins. Calculated eigenvalue was monitored for each case to determine if calculated eigenvalue varied more than 0.001 k from the base case critical

PAGE 71

59 eigenvalue. At BOC rods patterns may always be adjusted in order to make the reactor critical and have critical eigenvalue deviate less than 0.001 k; however, at EOC when all the rods are pulled out of the core and no other form of positive reactivity may exist in the core to supply reactivity for criticality any decrease in critical eigenvalue as compared from the base case resulted in loss of cycle exposure and decreases of cycle energy. MFLPD was observed to make sure no perturbation resulted in a MFLPD greater than 0.909 as the BWR design basis requires. MFLCPR was also monitored to be certain that no perturbation caused a MFLCPR to become greater than the design basis requirements of 0.930. A SLCS enhancement that leads to decreased cycle energy and results in loss of cycle exposure was unacceptable due to the $ 1,000,000 at day cost involved in shutting the reactor down early. Furthermore, a core that does not meet thermal limits may not be licensed; therefore though SLCS may be improved through a certain modification, if that modification leads to unacceptable thermal margin, the core will not be licensed to operate. The optimum enhancement for SLCS involves an enhancement that meets thermal limits and does not deplete EOC calculated eigenvalue. Enhancing SLCS by Perturbing the Location of Gadolinium Rods A gadolinium placement modification to certain lattice axial zones was made in each fresh fuel type separately. The lattice physics calculations ensured that HUCU### improved with enhanced gadolinium location loading; therefore applying the technique to each fuel type individually determined the limiting effects of core radial and axial power weighting incurred on the enhancement of SLCS. The gadolinium rods that were interchanged were chosen based on the fact that the cold power peaking map displayed an

PAGE 72

60 increased worth for the new rod locations while the hot power peaking displayed a lesser change in worth. Figure 5-2 displays the base DOM gadolinium geometry and the areas circled in red correspond to where the gadolinium pins were interchanged with normal fuel pins in the perturbed cases. These perturbations were made to each axial zone individually and then to the entire bundle for each fresh bundle type. ABCDEFGHIJ11.602.803.203.953.953.953.953.953.952.8022.802.803.203.953.603.958.003.954.406.003.953.9533.203.204.403.004.404.906.004.404.406.004.404.406.004.9043.953.954.404.908.003.95WR-4.904.904.9053.953.604.906.003.954.90--4.904.904.9063.953.958.004.40WR-4.904.904.904.908.004.9073.953.954.406.00--4.904.904.908.004.904.9083.954.406.004.404.904.904.904.908.004.904.908.004.9093.953.954.406.004.904.904.908.004.904.908.004.904.90102.803.954.904.904.904.904.904.904.903.20 #.###.## #.## % U235 Enrichment % Gadolinium Enrichment Figure 5-2. The perturbation diagram for the gadolinium rod perturbation cases. SLCS margin was improved by the greatest amount when every axial zone containing gadolinium was perturbed. Figure 5-3 displays the maximum SLCS enhancement exhibited by each bundle type perturbation. Case 1 and Case 2 represent perturbations made to every axial zone in the bundle containing gadolinium. Case 1 represents when the perturbation was only made to the high enrichment bundles, and Case 2 represents when the perturbation was only made to the low enrichment bundles. Case 1 exhibited a 0.0095 improvement in BOC SLCS margin while Case 2 exhibited a 0.0341 increase in BOC SLCS margin. The low enrichment bundles represented 69% of the total loaded batch fraction and the majority of these bundles

PAGE 73

61 resided in the high power peak locations in the interior core region; therefore any perturbations made to these bundles demonstrated a more pronounced enhancement than perturbations made to the high enrichment bundles. 00.0050.010.0150.020.0250.030.0350.040200040006000800010000120001400016000MWD/STUSLCS Base Case 1 Case 2 Most Limiting Base SLCS Figure 5-3. Exposure dependent SLCS for the reference base case, the case in which the perturbation was made to only all of the fresh low enrichment bundles (case 2), and the case in which the perturbation was made to only all of the fresh high enrichment bundles (case 1). Though SLCS margin was enhanced, other limiting factors were greatly affected. Table 5-1 displays the effects of the enrichment perturbation on eigenvalue, and highlighted in red are the points in which eigenvalue deviated more than 0.001 k from the critical eigenvalue. All exposure points ending in an A represented the exposure step in which the control blade was shifted into the next pattern configuration. Due to the slight increase in gadolinium utilization caused by the perturbation, BOC eigenvalue decreased; and due to the saved positive reactivity from BOC, mid-cycle eigenvalue increased. In order to increase BOC eigenvalue and decrease mid-cycle eigenvalue the

PAGE 74

62 control blade patterns were manipulated to offset this reactivity imbalance. Table 5-2 displays the exposure dependent MFLPD. Case 2 improved most limiting MFLPD below the most limiting base case MFLPD after the rod pattern adjustment. Table 5-3 displays the exposure dependent MFLCPR. The most limiting MFLCPR in case 2 was also improved below the base case after the rod pattern adjustment. Therefore after the control blade adjustments were made both cases could meet critical eigenvalue requirements, but only case 2 could also meet MFLPD requirements as well. Table 5-1. Critical eigenvalue at specified exposure points for the gadolinium rod location perturbation cases that exhibited greatest enhancement in SLCS. Exposure Critical Eigenvalue (MWD/STU) Base Case 1 Case 1 Fix Case 2 Case 2 Fix 0 1.0136 1.0123 1.013 1.0104 1.0129 181 1.0142 1.0129 1.0139 1.011 1.0146 907 1.0141 1.0129 1.0139 1.0111 1.0138 1814 1.0128 1.0117 1.0125 1.0101 1.0124 2722 1.0133 1.0123 1.0131 1.0108 1.0132 2722A 1.0122 1.0112 1.0112 1.0095 1.0126 3629 1.0128 1.0119 1.0119 1.0104 1.0136 4536 1.0118 1.0111 1.0111 1.0098 1.012 5443 1.0126 1.012 1.0121 1.0108 1.0134 5443A 1.0119 1.0113 1.0114 1.0103 1.012 6350 1.013 1.0126 1.0126 1.0116 1.0135 7258 1.012 1.0117 1.0118 1.0108 1.0125 8165 1.0134 1.0133 1.0134 1.0126 1.0135 8165A 1.0123 1.0122 1.0123 1.0115 1.0123 9072 1.0134 1.0133 1.0134 1.0129 1.0137 9979 1.0135 1.0135 1.0136 1.0134 1.0138 10886 1.0148 1.0149 1.0149 1.0153 1.0152 10886A 1.0147 1.0148 1.0148 1.0152 1.0152 11794 1.0149 1.0153 1.0152 1.0163 1.0155 12570 1.0163 1.0168 1.0167 1.0182 1.0169 12701 1.0157 1.0164 1.0162 1.0179 1.0164 13608 1.0159 1.0168 1.0165 1.0186 1.0167 13608A 1.0169 1.0178 1.0175 1.0195 1.0176 14061 1.0159 1.0168 1.0165 1.0188 1.0167 14334 1.0164 1.0174 1.0171 1.0195 1.0171 14570 1.0163 1.0173 1.017 1.0193 1.0169

PAGE 75

63 Table 5-2. Exposure dependent MFLPD for the gadolinium rod location perturbation cases that exhibited greatest enhancement in SLCS. Exposure MFLPD (MWD/STU) Base Case 1 Case 1 Fix Case 2 Case 2 Fix 0 0.846 0.829 0.815 0.866 0.821 181 0.845 0.85 0.832 0.858 0.799 907 0.806 0.811 0.796 0.82 0.779 1814 0.807 0.814 0.803 0.821 0.786 2722 0.781 0.789 0.778 0.795 0.763 2722A 0.742 0.753 0.754 0.753 0.712 3629 0.714 0.725 0.724 0.729 0.712 4536 0.717 0.726 0.726 0.734 0.702 5443 0.703 0.711 0.71 0.72 0.682 5443A 0.838 0.842 0.84 0.858 0.822 6350 0.849 0.857 0.853 0.878 0.824 7258 0.847 0.865 0.859 0.884 0.825 8165 0.889 0.917 0.912 0.923 0.886 8165A 0.847 0.865 0.859 0.892 0.841 9072 0.852 0.863 0.863 0.887 0.878 9979 0.784 0.786 0.791 0.806 0.836 10886 0.683 0.686 0.685 0.699 0.723 10886A 0.72 0.724 0.729 0.717 0.755 11794 0.704 0.713 0.711 0.718 0.706 12570 0.704 0.709 0.706 0.73 0.693 12701 0.704 0.708 0.705 0.736 0.691 13608 0.854 0.855 0.851 0.878 0.852 13608A 0.734 0.742 0.738 0.762 0.737 14061 0.841 0.84 0.834 0.871 0.837 14334 0.746 0.748 0.741 0.789 0.736 14570 0.763 0.766 0.759 0.805 0.753 Utilizing any type of gadolinium insertion will only enhance BOC SLCS. Though BOC SLCS was enhanced in case 2 by gadolinium location improvement, once the gadolinium burned out (~11,000 MWD/STU for this specific case) the perturbed case became limiting again in SLCS. Therefore if SLCS is enhanced utilizing this method, the designer must consider if the gadolinium burn out point is acceptable as well. If at the gadolinium burn out point SLCS is not acceptable in magnitude, another method must be utilized to enhance SLCS.

PAGE 76

64 Table 5-3. Exposure dependent MFLCPR for the gadolinium rod location perturbation cases that exhibited greatest enhancement in SLCS. Exposure MFLCPR (MWD/STU) Base Case 1 Case 1 Fix Case 2 Case 2 Fix 0 0.711 0.723 0.727 0.707 0.714 181 0.721 0.729 0.727 0.713 0.715 907 0.726 0.733 0.733 0.717 0.72 1814 0.737 0.744 0.741 0.731 0.721 2722 0.741 0.748 0.744 0.734 0.727 2722A 0.73 0.737 0.737 0.717 0.744 3629 0.736 0.743 0.743 0.725 0.754 4536 0.729 0.734 0.734 0.72 0.736 5443 0.734 0.738 0.738 0.726 0.744 5443A 0.773 0.77 0.77 0.778 0.767 6350 0.775 0.774 0.774 0.78 0.769 7258 0.731 0.733 0.734 0.734 0.735 8165 0.732 0.732 0.732 0.731 0.737 8165A 0.745 0.744 0.744 0.744 0.75 9072 0.746 0.743 0.743 0.748 0.749 9979 0.754 0.752 0.751 0.758 0.752 10886 0.767 0.766 0.764 0.773 0.763 10886A 0.757 0.756 0.754 0.766 0.755 11794 0.79 0.793 0.792 0.789 0.785 12570 0.824 0.828 0.828 0.838 0.817 12701 0.825 0.83 0.829 0.836 0.818 13608 0.829 0.836 0.834 0.841 0.821 13608A 0.825 0.833 0.831 0.827 0.817 14061 0.822 0.83 0.828 0.836 0.815 14334 0.822 0.818 0.814 0.84 0.816 14570 0.808 0.803 0.8 0.825 0.802 Enhancing SLCS at the cost of SDM was not an acceptable option if SDM was already a limiting constraint from the original design. Figure 5-4 demonstrates that the modifications made to the low enriched fresh bundles did not diminish SDM below the most limiting value of the base case. For this perturbation, BOC SDM was improved 0.0190 at the cost of decreasing EOC SDM; however, the decrease in EOC SDM did not fall below the most limiting SDM value, and therefore the perturbation yielded acceptable SDM consequence.

PAGE 77

65 00.0050.010.0150.020.0250.030.0350.040200040006000800010000120001400016000MWD/STUSDM Base Case 1 Case 2 Most Limiting Base SDM Figure 5-4. Exposure dependent SDM for the gadolinium rod location perturbation cases. Utilizing a gadolinium location perturbation may be utilized to enhance BOC SLCS. However, the magnitude of the improvement is limited by the ability to separate the gadolinium and move it into areas of greater effective worth. As the amount of gadolinium rods in the lattice increases, the ability to move gadolinium rods to more effective locations decreases. As fuel bundle designs move to higher average enrichments more gadolinium rods are needed in the fuel bundles to counteract the increased installed reactivity. More gadolinium rods in the fuel bundle causes this technique to be less effective due to the inability to move the gadolinium to locations of greater effective worth due to the space constraints of the fuel lattice. Axial Power Shape Characteristics The base case most limiting power peak bundle location was bundle (15, 11). Because lattice physics work determined that the DOM was the most limiting geometry for HUCU###, decreasing the cold power peak in the DOM decreases SLCS.

PAGE 78

66 The cold power shape and the hot power shape were not the same. Figure 5-5 is the most limiting radial power peaking base case axial power distribution relative to its radial power peaking. Superimposed in blue over figure 5-5 is an example of the cold power shape. Though not to scale, the superimposition displays the difference in where the power peaking resides in the two conditions. The BOC cold power shape was a cosine shape peaked in the DOM, and the hot power shape was a modified Bessel function peaked in the PSZ. Therefore in the axial power shape perturbations this characteristic was utilized to maximize SLCS. 016324864809611212814416000.20.40.60.811.21.41.61.8Relative Power PeakAxial Location (in.) Base (15,11) (15,10) (14,11) (15,12) Example Cold Power Shape Calculated Hot Power Shape Figure 5-5. The base case hot axial power shape with superimposed cold axial power shape. Enhancing SLCS through Axial Power Shaping Utilizing Enrichment Differencing The position of the cold axial power peak is the axial portion of the fuel bundle exhibiting the least amount of power suppression in the cold condition; therefore the cold axial power peak region is also the most limiting HUCU### region. As previously displayed in figure 3-2, the DOM was the most limiting region for HUCU### due to the decreased availability of borated water locations in the lattice. The VAN exhibited the

PAGE 79

67 greatest HUCU### due to the increased availability to place borated water in the lattice as a result of the vanished rod locations. Since the region of the cold axial power peak was the most limiting in HUCU###, shifting the cold axial power peak out of the DOM and into the VAN should increase SLCS. The cold axial power peak may be decreased utilizing enrichment differencing in the DOM and VAN. Figure 5-6 illustrates the goal of enrichment differencing. By increasing the enrichment in the VAN and decreasing the enrichment in the DOM, the DOM axial power peak is decreased thereby increasing SLCS. N-T N-V VAN PLE DOM PSZ NAT Base Case Power Peak Decreased Power Peak in DOM Zone Base CasePerturbed Case Utilizin g Axial Enrichment Differencin g Figure 5-6. Cold axial power shape perturbation diagram. Axial power shaping, utilizing enrichment differencing, enhanced SLCS at BOC and at the gadolinium burn out exposure point. Figure 5-7 displays the SLCS

PAGE 80

68 enhancement utilizing axial power shape perturbation by enrichment differencing as well as SLCS enhancement utilizing gadolinium placement perturbations. Case 11 was the case that utilized enrichment differencing. Gadolinium perturbations enhanced SLCS only at BOC; however, axial power shape perturbations utilizing enrichment differencing in the DOM and VAN enhanced SLCS at both BOC and the gadolinium burn out exposure point. The BOC SLCS margin enhancement utilizing enrichment differencing was 0.035 and the gadolinium burn out exposure point enhancement was 0.0142. Therefore if improvement in SLCS is necessary in both BOC and gadolinium burn out exposure point the enrichment differencing method is the preferred method. 00.0050.010.0150.020.0250.030.0350.040200040006000800010000120001400016000MWD/STUSLCS Base Case 2 Case 11 Most Limiting Base SLCS Figure 5-7. Exposure dependent SLCS for the gadolinium location perturbation case (case 2) and axial power shape perturbation utilizing enrichment differencing case (case 11) that exhibited the greatest enhancement in SLCS. In the gadolinium perturbation case, the fresh bundles reached a maximum peak power point once the gadolinium burned out. Once the gadolinium had burned out, the main parameters affecting the cold power shape were the enrichment distribution and

PAGE 81

69 axial leakage of the bundle. Since the axial leakage of the fuel bundle was a function of axial height (a fixed parameter) and controlled utilizing top and bottom natural zones, axial enrichment distribution was the main mode for altering the power shape at the gadolinium burn out exposure point. Increasing the enrichment distribution in the VAN and decreasing the enrichment in the DOM resulted in a decreased DOM cold power peak at the gadolinium burn out exposure point due to the decreased availability of enrichment in the DOM. Figure 5-8 presents the SLCS enhancement as a function of enrichment difference between the DOM and VAN. The maximum amount of SLCS margin enhancement for BOC and the gadolinium burn out exposure point occurs at 0.30% enrichment difference between the DOM and VAN. 00.0050.010.0150.020.0250.030.0350.040200040006000800010000120001400016000MWD/STUSLCS Base (0.01) Case 17 (0.35) Case 11 (0.31) Case 18 (0.20) Case 19 (0.10) Case 20 (0.04) Most Limiting Base SLCS Figure 5-8. SLCS enhancement utilizing different magnitudes of enrichment differencing between the DOM and VAN.

PAGE 82

70 An optimum enrichment difference arises from the fact that reactivity worth is a flux weighted. As the enrichment was increased in the VAN, the flux increased in the VAN; and as the enrichment decreases in the DOM, the flux decreases in the DOM. Therefore the 0.30 enrichment difference represented the optimum decrease in flux weighting of the DOM and increase in flux weighting of the VAN that resulted in the greatest average cold borated negative reactivity insertion. Axial power shaping utilizing enrichment differencing alters the hot power shape and mode in which the core burns. The BOC hot axial power profile utilizing enrichment differencing is displayed in Figure 5-9. By increasing the VAN zone enrichment while decreasing the DOM zone enrichment, the DOM and PSZ zones exhibited a decrease in power peak while the VAN zone experiences and increase in power peaking. 016324864809611212814416000.20.40.60.811.21.41.61.8Relative Power PeakAxial Location (in.) Base (15,11) (15,10) (14,11) (15,12) Decreased Power Peak In DOM and PSZ Zones Increased Power Peak In VAN Zone Figure 5-9. The hot axial power shape for maximum SLCS enhancement utilizing enrichment differencing.

PAGE 83

71 The change in axial power shape slightly altered the calculated eigenvalue and thermal margins. Table 5-4 demonstrates that critical eigenvalue of the enrichment perturbations case did not vary more than 0.001 k from the base case critical eigenvalue; therefore utilizing this method did not warrant a rod pattern adjustment. The final calculated eigenvalue for the enrichment differencing case was 0.0007 k less than the critical base case eigenvalue; however, the increased mid cycle energy created could have been suppressed by utilizing a rod pattern adjustment if determined necessary. Table 5-4. Critical eigenvalue at specified exposure points for the gadolinium rod location perturbation case and enrichment differencing case that exhibited greatest enhancement in SLCS. Exposure Critical Eigenvalue (MWD/STU) Base Case 2 Fix Case 11 0 1.0136 1.0129 1.0142 181 1.0142 1.0146 1.0143 907 1.0141 1.0138 1.0143 1814 1.0128 1.0124 1.0128 2722 1.0133 1.0132 1.0133 2722A 1.0122 1.0126 1.013 3629 1.0128 1.0136 1.0136 4536 1.0118 1.012 1.0125 5443 1.0126 1.0134 1.0134 5443A 1.0119 1.012 1.0121 6350 1.013 1.0135 1.0133 7258 1.012 1.0125 1.0127 8165 1.0134 1.0135 1.0142 8165A 1.0123 1.0123 1.013 9072 1.0134 1.0137 1.0141 9979 1.0135 1.0138 1.014 10886 1.0148 1.0152 1.0153 10886A 1.0147 1.0152 1.0152 11794 1.0149 1.0155 1.015 12570 1.0163 1.0169 1.0162 12701 1.0157 1.0164 1.0156 13608 1.0159 1.0167 1.0153 13608A 1.0169 1.0176 1.0163 14061 1.0159 1.0167 1.0151 14334 1.0164 1.0171 1.0157 14570 1.0163 1.0169 1.0156

PAGE 84

72 MFLPD for the axial power shaping utilizing enrichment differencing case also was under the acceptable limit for all exposure points through out the cycle. Table 5-5 displays that most limiting MFLPD decreased by 0.026 from the base case. Therefore utilizing this technique improves the MFLPD of the cycle. Table 5-5. Exposure dependent MFLPD for the gadolinium rod location perturbation case and the enrichment differencing case that exhibited greatest enhancement in SLCS. Exposure MFLPD (MWD/STU) Base Case 2 Fix Case 11 0 0.846 0.821 0.825 181 0.845 0.799 0.834 907 0.806 0.779 0.792 1814 0.807 0.786 0.799 2722 0.781 0.763 0.771 2722A 0.742 0.712 0.718 3629 0.714 0.712 0.7 4536 0.717 0.702 0.699 5443 0.703 0.682 0.681 5443A 0.838 0.822 0.827 6350 0.849 0.824 0.83 7258 0.847 0.825 0.819 8165 0.889 0.886 0.863 8165A 0.847 0.841 0.818 9072 0.852 0.878 0.839 9979 0.784 0.836 0.793 10886 0.683 0.723 0.69 10886A 0.72 0.755 0.735 11794 0.704 0.706 0.707 12570 0.704 0.693 0.692 12701 0.704 0.691 0.691 13608 0.854 0.852 0.829 13608A 0.734 0.737 0.72 14061 0.841 0.837 0.805 14334 0.746 0.736 0.718 14570 0.763 0.753 0.728 Table 5-6 shows no significant difference realized in MFLCPR as compared with the base case. Therefore utilizing this technique does not deplete the cores to meet any thermal margin requirements.

PAGE 85

73 Table 5-6. Exposure dependent MFLCPR for the gadolinium rod location perturbation cases that exhibited greatest enhancement in SLCS. Exposure MFLCPR (MWD/STU) Base Case 2 Fix Case 11 0 0.711 0.714 0.724 181 0.721 0.715 0.719 907 0.726 0.72 0.725 1814 0.737 0.721 0.734 2722 0.741 0.727 0.741 2722A 0.73 0.744 0.742 3629 0.736 0.754 0.75 4536 0.729 0.736 0.737 5443 0.734 0.744 0.744 5443A 0.773 0.767 0.763 6350 0.775 0.769 0.767 7258 0.731 0.735 0.741 8165 0.732 0.737 0.741 8165A 0.745 0.75 0.753 9072 0.746 0.749 0.751 9979 0.754 0.752 0.756 10886 0.767 0.763 0.763 10886A 0.757 0.755 0.753 11794 0.79 0.785 0.787 12570 0.824 0.817 0.821 12701 0.825 0.818 0.821 13608 0.829 0.821 0.825 13608A 0.825 0.817 0.82 14061 0.822 0.815 0.818 14334 0.822 0.816 0.821 14570 0.808 0.802 0.807 The effect of axial enrichment differencing had a similar effect on SDM as the lattice geometric placement perturbation. Figure 5-10 displays the exposure dependence effects of these perturbations on SDM at different exposure points. SDM for both perturbations did not fall below the most limiting base case value; therefore both enhancements may be utilized to enhance SLCS if BOC SDM were to be in a limiting condition. However, only axial power shaping utilizing enrichment differencing also improves the gadolinium burn out exposure point limiting condition.

PAGE 86

74 00.0050.010.0150.020.0250.030.0350.040200040006000800010000120001400016000MWD/STUSDM Base Case 2 Case 11 Most Limiting Base SDM Figure 5-10. Exposure dependent SDM for the gadolinium rod location perturbation case and axial power shaping utilizing enrichment differencing case. Enhancing SLCS by Means of Axial Power Shaping Utilizing Gadolinium Insertion Enrichment differencing was not the only method for perturbing the axial power shape in order to decrease the power peak in the DOM. Axial power shaping from the utilization of an additional gadolinium pellets in certain axial zones was also analyzed in order to determine if the negative reactivity insertion from adding additional gadolinium was more favorable than shifting the axial enrichment distribution to create similar types of perturbations. The concept of utilizing the negative reactivity of a gadolinium rod insertion to decrease the power peak in the most limiting zone was similar to the concept of decreasing enrichment in the most limiting axial zone. In both cases a negative reactivity insertion in the limiting axial zone caused the power to peak to decrease in that zone in which the gadolinium was inserted thus decreasing the worth of that axial zone to SLCS.

PAGE 87

75 As displayed in figure 4-5 increasing the amount of rods in a lattice decreased HUCU###; however, k of the lattice also decreased therefore leading to an improvement of SLCS due to the decreased cold k. Figure 5-11 displays the gain in BOC SLCS utilizing a gadolinium rod insertion as compared with the other types of perturbations examined. Case 26 represented a gadolinium insertion made in the PSZ, and Case 27 represented a gadolinium rod insertion made in the DOM. Because the cold power shape peaks in the DOM, inserting a gadolinium rod into the PSZ does not have as drastic of an effect on SLCS as placing a gadolinium rod in the DOM. 00.0050.010.0150.020.0250.030.0350.040200040006000800010000120001400016000MWD/STUSLCS Base Case 2 Case 11 Case 26 Case 27 Most Limiting Base SLCS Figure 5-11. Exposure dependent SLCS for the gadolinium location perturbation case (case 2), axial power shape perturbation utilizing enrichment differencing case (case 11), inserting a gadolinium rod in the PSZ (case 26) and inserting a gadolinium rod in DOM (case27) that exhibited the greatest enhancement in SLCS. The DOM gadolinium rod insertion yielded the greatest increase in BOC SLCS as compared with the other perturbations. Inserting a gadolinium rod in the DOM enhanced SLCS by 0.422 while inserting a gadolinium in the PSZ only enhanced SLCS by 0.189.

PAGE 88

76 Table 5-7. Critical eigenvalue at specified exposure points for the gadolinium insertion into the DOM (case 27) and gadolinium insertion into the PSZ (case 26) that exhibited greatest enhancement in SLCS. Exposure Critical Eigenvalue (MWD/STU) Base Case 26 Case 26f Case 27 Case 27f 0 1.0136 1.0127 1.0133 1.0116 1.013 181 1.0142 1.0129 1.0136 1.012 1.0139 907 1.0141 1.0131 1.0138 1.0121 1.0141 1814 1.0128 1.012 1.012 1.0111 1.0121 2722 1.0133 1.013 1.013 1.0121 1.0131 2722A 1.0122 1.0121 1.0121 1.0112 1.0119 3629 1.0128 1.0129 1.0129 1.0122 1.013 4536 1.0118 1.0121 1.0121 1.0116 1.0117 5443 1.0126 1.013 1.013 1.0126 1.0128 5443A 1.0119 1.0122 1.0122 1.0118 1.0119 6350 1.013 1.0133 1.0133 1.0129 1.0131 7258 1.012 1.0124 1.0125 1.0119 1.0121 8165 1.0134 1.0139 1.014 1.0133 1.0136 8165A 1.0123 1.0128 1.0128 1.0122 1.0124 9072 1.0134 1.0137 1.0137 1.0132 1.0134 9979 1.0135 1.0135 1.0135 1.0134 1.0135 10886 1.0148 1.0146 1.0145 1.0149 1.0147 10886A 1.0147 1.0145 1.0145 1.0148 1.0147 11794 1.0149 1.0143 1.0142 1.0151 1.0147 12570 1.0163 1.0155 1.0161 1.0165 1.016 12701 1.0157 1.0148 1.0154 1.0159 1.0154 13608 1.0159 1.0147 1.0151 1.016 1.0154 13608A 1.0169 1.0156 1.0162 1.017 1.0164 14061 1.0159 1.0146 1.0149 1.016 1.0153 14334 1.0164 1.0151 1.0148 1.0167 1.016 14570 1.0163 1.015 1.0146 1.0165 1.0158 Placing negative reactivity into one region of the bundle without introducing positive reactivity into some other region will cause a decrease in BOC eigenvalue. Therefore a rod pattern change was utilized in this method in order to achieve acceptable BOC eigenvalue requirements. Table 5-7 displays the calculated eigenvalue as compared with the base case for inserting a gadolinium rod in the DOM zone and in the PSZ before. Inserting a gadolinium rod in the PSZ greatly reduced the BOC reactivity of the bundle; therefore the rod patterns had to be adjusted to meet the BOC condition. The

PAGE 89

77 decrease in integrated power realized in the bundle due to the gadolinium insertion in the PSZ caused the core to fall 0.0017 k short of EOC critical eigenvalue requirements. However, inserting a gadolinium rod in the DOM zone caused only a 0.0005 k decrease in EOC critical eigenvalue. Distorting the hot axial power shape altered the thermal margins of the core. Figure 5-12 and figure 5-13 displays the distorted hot axial power shape caused from inserting a gadolinium rod in the PSZ and in the DOM. 016324864809611212814416000.20.40.60.811.21.41.61.8Relative Power PeakAxial Location (in.) Base (15,11) (15,10) (14,11) (15,12) Figure 5-12. The hot axial power shape of the most power peaked fuel bundle caused by inserting a gadolinium rod into the PSZ. When inserting a gadolinium rod into the PSZ, the decreased power peak in the PSZ causes the hot axial power shape to flatten. When inserting a gadolinium rod into

PAGE 90

78 the DOM, the extreme decreased power peak in the DOM leads to an increased relative power peak in the PSZ. 016324864809611212814416000.20.40.60.811.21.41.61.8Relative Power PeakAxial Location (in.) Base (15,11) (15,10) (14,11) (15,12) Figure 5-13. The hot axial power shape of the most power peaked fuel bundle caused by inserting a gadolinium rod into the DOM. Table 5-8 displays MFLPD for the PSZ and DOM gadolinium insertions as compared to the base case. Inserting a gadolinium rod in the PSZ decreased BOC MFLPD by 0.083, and also decreased most limiting MFLPD by 0.033. However, inserting a gadolinium rod in the DOM yielded no significant enhancement in MFLPD. In both cases there was no significant alteration in MFLCPR as displayed in table 5-9. Therefore inserting an extra gadolinium rod into a certain axial zone of the fuel bundle does not hinder the ability to meet thermal margins.

PAGE 91

79 Table 5-8. MFLPD at specified exposure points for the gadolinium insertion into the DOM (case 27) and gadolinium insertion into the PSZ (case 26) that exhibited greatest enhancement in SLCS. Exposure MFLPD (MWD/STU) Base Case 26 Case 26f Case 27 Case 27f 0 0.846 0.771 0.763 0.873 0.847 181 0.845 0.772 0.762 0.875 0.839 907 0.806 0.748 0.738 0.832 0.795 1814 0.807 0.768 0.768 0.829 0.811 2722 0.781 0.765 0.765 0.790 0.776 2722A 0.742 0.707 0.706 0.746 0.738 3629 0.714 0.710 0.709 0.716 0.707 4536 0.717 0.722 0.722 0.718 0.718 5443 0.703 0.698 0.697 0.703 0.700 5443A 0.838 0.827 0.825 0.840 0.836 6350 0.849 0.827 0.824 0.855 0.845 7258 0.847 0.816 0.813 0.853 0.840 8165 0.889 0.861 0.856 0.894 0.882 8165A 0.847 0.807 0.804 0.854 0.840 9072 0.852 0.841 0.839 0.849 0.850 9979 0.784 0.812 0.815 0.776 0.789 10886 0.683 0.710 0.713 0.687 0.688 10886A 0.72 0.757 0.761 0.715 0.727 11794 0.704 0.716 0.722 0.712 0.711 12570 0.704 0.677 0.684 0.714 0.705 12701 0.704 0.677 0.684 0.709 0.702 13608 0.854 0.838 0.866 0.841 0.831 13608A 0.734 0.703 0.720 0.749 0.741 14061 0.841 0.821 0.859 0.822 0.807 14334 0.746 0.719 0.710 0.744 0.737 14570 0.763 0.736 0.727 0.755 0.749 Therefore when a designer chooses to utilize this method for enhancing SLCS, the designer must decide which parameters are most necessary for achieving the required result. If the designer is experiencing limiting MFLPD and willing to compromise cycle energy to meet this requirement, then placing a gadolinium rod in the PSZ is the better choice. If the designer does not have limiting MFLPD, then inserting a gadolinium rod in the DOM zone is the better choice. Therefore the choice of one method or the other depends on the thermal margins and the critical eigenvalue requirements.

PAGE 92

80 Table 5-9. MFLCPR at specified exposure points for the gadolinium insertion into the DOM (case 27) and gadolinium insertion into the PSZ (case 26) that exhibited greatest enhancement in SLCS. Exposure MFLCPR (MWD/STU) Base Case 26 Case 26f Case 27 Case 27f 0 0.711 0.712 0.715 0.694 0.692 181 0.721 0.708 0.712 0.683 0.683 907 0.726 0.717 0.721 0.692 0.695 1814 0.737 0.728 0.728 0.711 0.709 2722 0.741 0.737 0.737 0.724 0.723 2722A 0.73 0.724 0.724 0.708 0.717 3629 0.736 0.733 0.733 0.723 0.732 4536 0.729 0.729 0.729 0.723 0.724 5443 0.734 0.738 0.738 0.732 0.734 5443A 0.773 0.772 0.772 0.771 0.77 6350 0.775 0.775 0.775 0.774 0.773 7258 0.731 0.741 0.742 0.73 0.733 8165 0.732 0.741 0.742 0.73 0.733 8165A 0.745 0.752 0.752 0.742 0.744 9072 0.746 0.748 0.748 0.745 0.744 9979 0.754 0.751 0.75 0.754 0.751 10886 0.767 0.758 0.757 0.768 0.763 10886A 0.757 0.748 0.747 0.758 0.753 11794 0.79 0.786 0.786 0.79 0.789 12570 0.824 0.819 0.818 0.824 0.823 12701 0.825 0.819 0.818 0.825 0.823 13608 0.829 0.824 0.822 0.829 0.826 13608A 0.825 0.818 0.815 0.825 0.822 14061 0.822 0.817 0.814 0.822 0.819 14334 0.822 0.81 0.805 0.824 0.815 14570 0.808 0.796 0.791 0.809 0.8 SDM was neither greatly enhanced nor greatly decreased utilizing gadolinium insertion. Figure 5-14 displays SDM as a function of exposure for the base case and all three types of perturbations. Therefore if a designer was limited in EOC SDM then inserting a gadolinium rod should be utilized in order to enhance BOC SDM. The decision to enhance SLCS margin by inserting a gadolinium rod into a certain axial zone of a fuel bundle is dependent upon the preexisting limiting conditions of the fuel design. If the fuel designer decides that maximizing BOC SLCS without concern for

PAGE 93

81 SLCS at the gadolinium burn out exposure point is the most limiting design characteristic, then inserting a gadolinium rod into the DOM will suffice as a solution to enhancing BOC SLCS margin. If the designer cannot afford loss in EOC SDM, and only needs a minimal improvement in thermal margins as well as minimally enhanced BOC SLCS, then adding a gadolinium in PSZ at the cost of cycle energy may be an adequate solution to enhancing BOC SLCS. 00.0050.010.0150.020.0250.030.0350.040200040006000800010000120001400016000MWD/STUSDM Base Case 2 Case 11 Case 26 Case 27 Most Limiting Base SDM Figure 5-14. Exposure dependent SDM for the gadolinium rod location perturbation case, axial power shaping utilizing enrichment differencing case and the axial power shaping utilizing gadolinium placement case. Enhancing BOC SLCS margin utilizing gadolinium perturbations may cause the gadolinium burn out exposure point to become the most limiting in SLCS. If SLCS at the gadolinium burn out exposure point is of acceptable magnitude, then the designer has utilized an acceptable technique for enhancing SLCS. If, however, SLCS at the gadolinium burn out exposure point is of unacceptable magnitude, then the gadolinium insertion techniques are not feasible methods for improving SLCS. Therefore the

PAGE 94

82 decision to utilize this method is solely dependent upon the limitations of the gadolinium burn out exposure point.

PAGE 95

CHAPTER 6 CONCLUSIONS SLCS is a core wide phenomenon that is dependent upon the HUCU### characteristics of each fuel bundle. Introducing fresh bundles into the core with inherently enhanced HUCU### characteristics will improve SLCS. HUCU### is improved by manipulating design parameters on the lattice design level as well as in the full core design. Therefore understanding the most limiting design parameters in both design aspects and the capability of those parameters to increase HUCU### is paramount to improving SLCS. The ability of a certain type of fuel lattice design perturbation to enhance SLCS was determined by the limiting characteristics of that lattice perturbation. HUCU### was highly dependent upon average enrichment. As average enrichment of the fuel bundle was increased HUCU### decreased thereby decreasing SLCS on the full core level. Increasing enrichment has a greater impact per percent increase of reactivity in the cold, collapsed void lattice state then in the hot Doppler broadened voided operating state. Localized enrichment perturbations did not affect HUCU### therefore when a designer creates a lattice with SLCS in mind they need only be concerned with the average enrichment of the lattice and not how the local enrichment is schemed. Gadolinium rods also had a significant impact on HUCU### lattice behavior and therefore significantly impacted SLCS. Gadolinium geometries that were clumped and incurred significant spatial self-shielding decreased HUCU### while gadolinium geometries that were spread out limiting the self-shielding exhibited an increased 83

PAGE 96

84 HUCU###. Increasing the amount of gadolinium rods in the fuel lattice decreased relative HUCU###; however, inserting the gadolinium also reduced k thereby actually improving SLCS by decreasing the worth of the bundle to the entire core. Therefore increasing the amount of gadolinium rods in the bundle had a diminishing return. Increasing the gadolinium concentration also decreased the relative HUCU###; however, increasing the gadolinium concentration also reduced k thereby also improving SLCS for the whole core. Optimum locations for gadolinium rod placement exist for certain amounts of gadolinium rods. These optimum placement locations are realized by understanding the difference in power peaking between the hot and cold homogenously enriched power shapes (the power shape realized explicitly from geometry of the fuel bundle and flux level) and placing gadolinium rods in areas where the difference in power peak between the two states is the greatest. After understanding the 2-dimensional lattice physics calculations, perturbations were made to fuel bundles in the full core simulator in order to determine effects on full core criticality and thermal limits. Perturbing the placement of the gadolinium rods in order to maximize gadolinium worth utilized in the cold borated condition improved BOC SLCS at the expense of decreased BOC critical eigenvalue. Therefore after perturbing gadolinium locations to maximize negative reactivity, the control blade patterns must be adjusted in order to introduce enough positive reactivity in the hot condition to meet the critical eigenvalue requirements. Perturbing the axial enrichment distribution in order to decrease the power peaking in the axial zone most limiting to HUCU### decreased that axial zones flux importance to the SLCS calculation and thereby improved both the BOC and the gadolinium burn out exposure point SLCS.

PAGE 97

85 However, utilizing this method causes an increased complexity in manufacturing of the bundle and therefore leading to an increased production cost. Inserting an extra gadolinium rod into a certain axial zone in order to also perturb the axial power shape improved BOC SLCS without decreasing EOC SDM. However, utilizing gadolinium perturbations only helped improve the BOC SLCS and did not enhance the gadolinium burn out exposure point SLCS. SLCS may always be improved by increasing the boron concentration or boron enrichment in the SLCS tank. However, if the utility is limited by time, cost or aggravation then utilizing an acceptable design technique in order to enhance SLCS margin is solely dependent upon the limiting characteristics of the core behavior and the acceptable sacrifice in margin of those parameters. Unfortunately, not all core situations will have a possible remedy for SLCS. The greatest increase in BOC SLCS utilizing any of the mentioned techniques was roughly 0.5% and the gadolinium burnout point maximum improvement was 0.14%. Therefore utilities exhibiting marginal SLCS fuel design difficulties that wish to have power output increases in their following cycles, increasing the average enrichment and gadolinium content in their core, will need to understand the limitations of the inherent fuel design. Utilities must then realize that an increase in boron concentration of their SLCS tank or utilizing enriched boron is needed if they wish to accommodate SLCS while not incurring the extra cost per cycle of loading extra bundles to flatten the power distribution and reduce SLCS.

PAGE 98

CHAPTER 7 FUTURE WORK The purpose of this study was to conduct a sensitivity analysis in order to determine limiting fuel design characteristics for SLCS. The methodology developed by Yasushi Hirano, Kazuki Hida, Koichi Sakurada and Munenari Yamamoto utilized a fixed gadolinium pattern and then generated an optimal enrichment distributions for a 2-dimensional BWR fuel lattice [10]. Since this study proved that radial enrichment distribution was not a factor in SLCS and that SLCS was only limited by average enrichment, the possibility exists to expand on the enrichment distribution tool and develop a tool that determines an optimum SLCS gadolinium placement for a given lattice average enrichment. The tool would basically compare homogenously enriched hot and cold lattice power distributions and determine an optimum gadolinium scheme based on the maximum difference in the two power distributions. Because the placement of the gadolinium for SLCS is basically decoupled from the enrichment distribution, this problem does not become over-constrained, and therefore it is possible to obtain an optimum gadolinium configuration for SLCS while creating an optimum enrichment distribution for thermal limit and fuel efficiency requirements. The optimum enrichment distribution methodology was also a 2-dimensional methodology. This study concluded that axial enrichment and gadolinium perturbations may be utilized to improve SLCS. In modern core design strategy 2-dimensional lattice calculations are completed and then the group constants from the 2-dimensional codes are utilized by the full core simulators because of computational time constraints and 86

PAGE 99

87 memory requirements of the processor. With computers getting faster and distributed parallel computing schemes becoming more optimized, core design may reach a point where full 3-dimensional bundles are modeled assuming an infinite bundle approximation (or a more brilliant scheme) to get group constants for the full core simulator. When this technology is available, utilizing the design criteria from this study for the SLCS portion, a full bundle axial and radial enrichment and gadolinium configuration optimization methodology may be devised that creates the optimum fuel bundle for SLCS, SDM, thermal margin and fuel utilization. This will create an automated core design environment thus freeing the designers time to allow for examination of other pressing issues in the design strategy.

PAGE 100

LIST OF REFERENCES 1. Aoyama, Mooto, Sadao Uchikawa and Renzo Takeda, Reactivity Control Method for Extended Burnup of Boiling Water Reactor Fuel Bundles, Journal of Nuclear Science and Technology, 26, pp.403-410, April 1989. 2. Cochran, Robert and Nicholas Tsoulfanidis, The Nuclear Fuel Cycle: Analysis and Management, American Nuclear Society, La Grange Park, Illinois, 1999. 3. Dresner, Lawerance, Resonance Absorption in Nuclear Reactors, Pergamon Press, New York, New York, 1976. 4. Duderstadt, James and Louis Hamilton, Nuclear Reactor Analysis, John Wiley & Sons, Inc., New York, New York, 1976 5. General Electric Company, TGBLA06A; General Electric Lattice Physics Method, DRF A00-05526, October, 1994. (Proprietary Information) 6. General Physics Corporation, BWR Generic Fundamentals: Chapter 9 Core Thermal Limits, Columbia, Maryland 1993. (Proprietary Information) 7. Glasstone, Samuel and Walter H. Jordan, Nuclear Power and its Environmental Effects, American Nuclear Society, La Grange Park, Illinois, 1980. 8. Global Nuclear Fuels, PANAC11 Users Manual, UM-0021 Rev. 1, February 2001. (Proprietary Information) 9. Hida, Kazuki and Ritsuo Yoshioka, Optimal Axial Enrichment Distribution of the Boiling Water Reactor Fuel Under the Haling Strategy, Nuclear Technology, 80, pp. 423-430, March 1988. 10. Hirano, Yasushi, Kazuki Hida, Koichi Sakurada, and Munenari Yamamoto, Optimization of Fuel Rod Enrichment Distribution to Minimize Rod Power Peaking throughout Life with BWR Fuel Assembly, Journal of Nuclear Science and Technology, 34, pp. 5-12, January 1997. 11. Kazimi, Mujid and Neil Todreas, Nuclear Systems 1: Thermal Hydraulic Fundamentals, Taylor and Francis, Bristol, PA, 1993 12. Lahey, R.T. and F.J. Moody, The Thermal Hydraulics of a Boiling Water Nuclear Reactor, American Nuclear Society, La Grange Park, Illinois, 1979. 88

PAGE 101

89 13. Lamarsh, John R., Introduction to Nuclear Engineering, Addison-Wesley Publishing Company, Inc., Melano Park, California, 1983. 14. Lewis, E.E. and W.F. Miller, Computational Methods of Neutron Transport, Nuclear Society, La Grange Park, Illinois, 1993. 15. Raharjo, R. and Mark Williams, Space-Dependent Resonance Self-Shielding, Nuclear Science and Engineering, 126, pp. 19-34, May 1997. 16. Rust, James H., Nuclear Power Plant Engineering, S.W. Holland Company, Atlanta, GA, 1979. 17. USNRC 10CFR Part 50, Section 50.62, Requirements for Reduction of Risk from Anticipated Transients Without Scram (ATWS) Events for Light-Water-Cooled Nuclear Power Plants, Washington D.C., January 1, 1996. 18. Weinberg, Alvin M. and Eugene P. Wigner, The Physical Theory of Neutron Chain Reactors, The University of Chicago Press, Chicago 1958.

PAGE 102

BIOGRAPHICAL SKETCH Michael Lorne Fensin was born in the city of Miami, Florida, on February 2, 1980. He served as president for the Bnai Brith Youth Organization city of Miami counsel and state of Florida region from May 1997-98. Michael is a member of the American Nuclear Society (ANS) and served as treasurer for the University of Floridas ANS chapter. He further served as president for the American Nuclear Societys honors society, for University of Florida. Michael was a recipient of the bright futures scholarship, dean of the college of engineering scholarship, and the national academy of nuclear training fellowship. During his undergraduate and masters degree work, Michael worked for the University of Florida as well as a variety of businesses in the nuclear industry. He served as a laboratory technician for the University of Floridas neutron activation analysis laboratory. Michael also interned for a summer at Southern Nuclear Companys Alvin W. Vogtle Electric Generating Plant in the area of reactor engineering and reactor operations. In the following summer Michael interned at Global Nuclear Fuels where he collaborated his thesis efforts with work completed at that facility. After completing his masters thesis requirements Michael will continue on for a PhD at the University of Florida in the area of nuclear space power and propulsion. His PhD thesis will be in collaboration with work at Los Alamos National Labs. 90


Permanent Link: http://ufdc.ufl.edu/UFE0005364/00001

Material Information

Title: Optimum Boiling Water Reactor Fuel Design Strategies to Enhance Reactor Shutdown by the Standby Liquid Control System
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0005364:00001

Permanent Link: http://ufdc.ufl.edu/UFE0005364/00001

Material Information

Title: Optimum Boiling Water Reactor Fuel Design Strategies to Enhance Reactor Shutdown by the Standby Liquid Control System
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0005364:00001


This item has the following downloads:


Full Text












OPTIMUM BOILING WATER REACTOR FUEL DESIGN STRATEGIES TO
ENHANCE REACTOR SHUTDOWN BY THE STANDBY LIQUID CONTROL
SYSTEM















By

MICHAEL LORNE FENSIN


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF ENGINEERING

UNIVERSITY OF FLORIDA


2004

































Copyright 2004

by

Michael Lorne Fensin


































This document is dedicated to the memory of my late grandmothers Bernice Anker and
Edna Fensin.















ACKNOWLEDGMENTS

I would like to acknowledge Dr. Samim Anghaie for chairing my committee,

supplying a connection to Global Nuclear Fuels of America, and providing excellent

tutoring and advice as my graduate advisor. I would also like to thank Dr. Bob Coldwell

Dr. Edward Dugan, Dr. Alireza Haghighat, Dr. David Hintenlang, Dr. Travis Knight, Dr.

Alan Jacobs, Dr. Tim Olson, Dr. Benard Mair, Proffessor Jim Tulenko and Dr. William

Vernetson for providing me countless hours of instruction in all areas of nuclear

engineering and mathematical computation during my graduate studies.

I would like to acknowledge Global Nuclear Fuels of America for the sponsorship

of its computer codes, time and efforts. From Global Nuclear Fuels of America I would

specifically like to thank Dr. Mehdi Asgari, Kenneth Gardner, Roland Jackson, J.D.

Kavaal, Thomas Marcille, V.W. Mills, Dr. Brian Moore and Tony Reese for supplying

intriguing knowledge and guidance during the course of the study.

I want to thank my family for being a constant source of support and pushing me to

completion. Without their support none of this would have been possible.
















TABLE OF CONTENTS

page

A C K N O W L E D G M E N T S ................................................................................................. iv

L IS T O F T A B L E S ................. ........................................................................ ... v ii

LIST OF FIGURES ...................................... ........ .......... ............ .. viii

ABSTRACT ........ .............. ............. ...... ...................... xi

CHAPTER

1 IN TR OD U CTION ............................................... .. ......................... ..

The B oiling W ater R eactor System ........................................ ......................... 4
Boiling W ater Reactor History .................................. .....................................8
History of Fuel Bundle Developm ent..................................................................... 10
T he SL C S E vent ............................................................................................ ....... 12
P roje ct S c o p e .....................................................................................13

2 M ODEL AND M ETHODOLOGIES ........................................ ...... ............... 15

Standby Liquid Control System and Shutdown Margin...........................................15
M o d e lin g T o o ls ..................................................................................................... 1 7
T G B L A 6 ............................................................................................................. 1 7
P A N A C 11 ................................................................ ............................18
Utilized Temperature States, Boron Concentrations and Lattice Types...................19
Measurement of SLCS and SDM during the Lattice Development Stage .................20
Fuel Bundle G eom etry .................. ................................. .... ........21
Thermal Limit Design Considerations..................... ..... ......................... 24

3 MAXIMIZING HOT-COLD BORATED k- DIFFERENCE UTILIZING
ENRICHM ENT ................................................ ...................... ........ 28

Hom ogeneous Enrichm ent Distribution ....................... .............. ............... ....28
Determining the Most Limiting Lattice Axial Zone and Void Concentration ....29
Understanding the Exposure Dependent HUCU### Curve..............................31
Enrichment and Boron Concentration Effects.........................................34
Pow er Peaking D istribution........................................... .......................... 35









H heterogeneous Enrichm ent D distribution ........................................ .....................39
Localized Enrichment Perturbation .............. ............................................. 39
G ross Enrichm ent Perturbation ........................................ ........ ............... 41

4 MAXIMIZING HOT-COLD BORATED ko, DIFFERENCE UTILIZING
GADOLINIUM ................................... ..... .. ...... .............. 44

Spatial Self-Shielding Effects of Gadolinium Rods on HUCU###............................44
The Effects of Increasing the Amount of Gadolinium Rods on HUCU### ..............47
The Effects of Increasing the Gadolinium Concentration on HUCU### .................50
The Importance of Gadolinium Rod Location............................................... 51
Fuel Lattice D esign Conclusions ..................................................... ..... .......... 55

5 FULL CORE SLCS M ODELING ....................................... ........................... 57

Enhancing SLCS by Perturbing the Location of Gadolinium Rods...........................59
Axial Power Shape Characteristics................... .............................. 65
Enhancing SLCS through Axial Power Shaping Utilizing Enrichment
D ifferencing ............... .... ............ .................................... ....... 66
Enhancing SLCS by Means of Axial Power Shaping Utilizing Gadolinium
In se rtio n ......................................................................... 7 4

6 C O N C L U SIO N S ....................... .... .......................... ................ ...... ......... 83

7 FUTURE W ORK.......................... ........... .. ........... ... ...... 86

L IST O F R E FE R E N C E S ......................................................................... ....................88

BIO GRAPH ICAL SK ETCH .................................................. ............................... 90















LIST OF TABLES


Table page

3-1 Gross enrichment perturbation scheme for figure 3-10......................................... 41

5-1 Critical eigenvalue at specified exposure points for the gadolinium rod location
perturbation cases that exhibited greatest enhancement in SLCS..........................62

5-2 Exposure dependent MFLPD for the gadolinium rod location perturbation cases
that exhibited greatest enhancement in SLCS...................... ................................. 63

5-3 Exposure dependent MFLCPR for the gadolinium rod location perturbation cases
that exhibited greatest enhancement in SLCS...................... ................................. 64

5-4 Critical eigenvalue at specified exposure points for the gadolinium rod location
perturbation case and enrichment differencing case that exhibited greatest
enhance ent in SL C S. ........................................ ........................ 71

5-5 Exposure dependent MFLPD for the gadolinium rod location perturbation case and
the enrichment differencing case that exhibited greatest enhancement in SLCS. ...72

5-6 Exposure dependent MFLCPR for the gadolinium rod location perturbation cases
that exhibited greatest enhancement in SLCS...................... ................................. 73

5-7 Critical eigenvalue at specified exposure points for the gadolinium insertion into
the DOM (case 27) and gadolinium insertion into the PSZ (case 26) that exhibited
greatest enhancem ent in SLC S.......................................... ........................... 76

5-8 MFLPD at specified exposure points for the gadolinium insertion into the DOM
(case 27) and gadolinium insertion into the PSZ (case 26) that exhibited greatest
enhance ent in SLC S. ........................................ ........................ 79

5-9 MFLCPR at specified exposure points for the gadolinium insertion into the DOM
(case 27) and gadolinium insertion into the PSZ (case 26) that exhibited greatest
enhance ent in SLC S. ........................................ ........................ 80
















LIST OF FIGURES


Figure p

1-1 B W R pressure vessel system ......................................................................... ...... 5

1-2 A typical BW R fuel assem bly and fuel rod..................................... .....................6

1-3 A four fuel assembly group with cruciform control blade.............. ... .................7

2-1 A cross sectional view of the modeled fuel bundle.................... ... ............... 23

2-2 The geometric setup of the fuel lattice axial zones. ...............................................24

3-1 Exposure dependent HUCU660 for the DOM at 3.95% enrichment....................... 29

3-2 Exposure dependent HUCU660 at varied void fraction and axial zone for the C
lattice at an enrichm ent of 3.95% ................................. ........................ ......... 31

3-3 Exposure dependant HUCU### curve. ....................................... ............... 33

3-4 Beginning of cycled HUCU vs. enrichment in the DOM, at 40% void fraction,
for a C lattice. ..........................................................................34

3-5 The power peaking distributions at 5 GWD/STU, 3.95% enrichment, DOM, C
lattice, and 40% void fraction vs. temperature state and boron concentration .........35

3-6 The power peaking distribution at 5 GWD/STU, CU660, DOM, C lattice, and
40% void fraction versus enrichment................ ............................. ............... 38

3-7 The power peaking distributions at 5 GWD/STU, HU, DOM, C lattice, and 40%
void fraction vs. enrichm ent .................................. ............... ............... 38

3-8 Localized enrichment perturbation map............................................ .............40

3-9 Exposure dependent HUCU660 for different localized enrichment perturbation
pattern s. .............................................................................40

3-10 An example of a gross enrichment perturbation map..........................................41

3-11 Exposure dependent HUCU660 at 40% void fraction, in the DOM, with a C
lattice. .....................................................................................4 2









3-12 Exposure dependent HUCC at 40% void fraction, in the DOM, with a C lattice....42

4-1 Four sam ple clum ped geom etries....................................... .......................... 45

4-2 Corresponding 0 GWD/STU gadolinium worth for the patterns displayed in
figure 4-1. .............................................................................46

4-3 Corresponding exposure dependent gadolinium clumping effects on HUCU660
for the patterns displayed in figure 4-1. ...................................... ............... 46

4-4 The effects of increased number of gadolinium rods on the gadolinium worth at
0 G W D /STU ..............................................................................................48

4-5 The effects of the number of gadolinium rods inserted on HUCU at
0 G W D /STU ..............................................................................................49

4-6 The effect of increasing the gadolinium concentration for 14 gadolinium rods on
gadolinium worth at 0 GW D/STU. ............................................... ............... 50

4-7 The effect of increasing the gadolinium concentration of 14 gadolinium rods on
H U CU at 0 G W D /STU ................................................. ............................... 51

4-8 Gadolinium rod place ent diagram .............................................. .....................52

4-9 Gadolinium worth versus location for 0 GWD/STU, 7% gadolinium
concentration, ........................................................................54

5-1 Reference base core fuel bundle loading map .......................................................58

5-2 The perturbation diagram for the gadolinium rod perturbation cases....................60

5-3 Exposure dependent SLCS for the reference base case, the case in which the
perturbation was made to only all of the fresh low enrichment bundles (case 2),
and the case in which the perturbation was made to only all of the fresh high
enrichm ent bundles (case 1). ........................................ ......................................61

5-4 Exposure dependent SDM for the gadolinium rod location perturbation cases.......65

5-5 The base case hot axial power shape with superimposed cold axial power shape...66

5-6 Cold axial power shape perturbation diagram ......................................................67

5-7 Exposure dependent SLCS for the gadolinium location perturbation case
(case 2) and axial power shape perturbation utilizing enrichment differencing
case (case 11) that exhibited the greatest enhancement in SLCS.............................68

5-8 SLCS enhancement utilizing different magnitudes of enrichment differencing
betw een the D OM and VAN .................................. ............... ............... 69









5-9 The hot axial power shape for maximum SLCS enhancement utilizing
enrichm ent differencing. ........................................ ............................................70

5-10 Exposure dependent SDM for the gadolinium rod location perturbation case and
axial power shaping utilizing enrichment differencing case..................................74

5-11 Exposure dependent SLCS for the gadolinium location perturbation case
(case 2), axial power shape perturbation utilizing enrichment differencing case
(case 11), inserting a gadolinium rod in the PSZ (case 26) and inserting a
gadolinium rod in DOM (case27) that exhibited the greatest enhancement in
SL C S ...................................................................................... 7 5

5-12 The hot axial power shape of the most power peaked fuel bundle caused by
inserting a gadolinium rod into the PSZ........................................ ............... 77

5-13 The hot axial power shape of the most power peaked fuel bundle caused by
inserting a gadolinium rod into the DOM .................................... .................78

5-14 Exposure dependent SDM for the gadolinium rod location perturbation case,
axial power shaping utilizing enrichment differencing case and the axial power
shaping utilizing gadolinium place ent case................................ ............... 81















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Engineering

OPTIMUM BOILING WATER REACTOR FUEL DESIGN STRATEGIES TO
ENHANCE REACTOR SHUTDOWN BY THE STANDBY LIQUID CONTROL
SYSTEM

By

Michael Lorne Fensin

August 2004

Chair: Samim Anghaie
Major Department: Nuclear and Radiological Engineering

Licensing a commercial nuclear reactor core involves a stringent amount of

calculations that demonstrate the capability of safe reactor shutdown in the instance of an

emergency transient event. In a boiling water nuclear reactor the control blades and

standby liquid control system are the two independent redundant safety systems utilized

for shutting down the reactor. In past fuel designs lower power cores with smaller cycle

lengths resulting from lower core average enrichment caused shutdown by the control

blades to be the most limiting strategy of the two modes for reactor shutdown. This led

to a lesser focus on fuel design strategies for standby liquid control system margin

(SLCS). Advanced modem core designs involve higher powers and increased cycle

lengths resulting from higher core average enrichments, therefore causing SLCS to now

become a more significant shutdown parameter. This study characterized the most

limiting fuel design parameters for maximizing the margin for safe reactor shutdown

utilizing SLCS while maintaining the demanded cycle energy requirements.









This study examined perturbation effects of certain parameters in the fuel lattice

development stage and the 3-dimesional reactor core simulator modeling. Lattice

enrichment perturbation response was examined first to determine the effects of average

and local enrichment perturbations on SLCS. Lattice gadolinium perturbation response

was next investigated to determine the optimum concentration, number of rods, location

and degree of clump of gadolinium rods necessary for enhancing SLCS. Axial power

shape perturbation utilizing both gadolinium and/or enrichment differencing in certain

axial zones of the fuel bundle was then examined on the full core level to determine the

optimum strategy for maximizing SLCS.

This study concluded that the necessary strategy for maximizing SLCS depended

upon the exposure point at which SLCS was most limiting. Certain perturbations

utilizing gadolinium exhibited maximized beginning of cycle SLCS; however, these

strategies involved a modified operating strategy to meet the beginning of cycle

operational requirements while not maximizing the limiting end of cycle SLCS. Axial

power shaping utilizing enrichment differencing maximized end of cycle SLCS and

increased beginning of cycle SLCS margin but to a lesser magnitude than the gadolinium

perturbation. In all cases the amount of improvement to the margin was limited by a

maximum value. Therefore if the desired magnitude of improvement needed is within

the achievable limits of the examined techniques, the choice of optimum strategy for

enhancing SLCS to a desired value depends upon the magnitude of necessary

improvement at the most limiting exposure points.














CHAPTER 1
INTRODUCTION

Boiling water nuclear reactor cores are major sources of revenue for power

producing utilities. If the utility is able to maximize the amount of energy output from the

nuclear reactor while minimizing the cost of the reactor operation then the utility will

realize an increase in profit. A utility may choose to maximize the energy output from

their nuclear reactors in one of three ways. Either the utility may increase the operating

cycle length of the reactor thereby increasing the amount of energy per cycle and

increasing the amount of time between refueling outages, or the utility may choose to

increase the power level of operation thereby increasing the amount of available

distributable energy at any given time, or the utility may choose to utilize a combination

of both practices [2]. In either of the operational techniques the utility must increase the

installed reactivity in the reactor core in order to meet the desired goal.

Increasing the amount of installed reactivity in a given cycle as compared with a

previous cycle in order to aggressively improve reactor power output is termed

"aggressive core loading." Aggressive core loading strategies involve higher fuel batch

fractions with fuel bundles of higher average enrichment in order to increase the installed

positive reactivity in the reactor core [2]. Greatly increasing the core power output in the

internal core locations greatly increases the neutron flux and thus greatly increases the

exposures of the interior bundles. A twice-burned fuel bundle in the reactor core is at its

least reactive state in bundle life and therefore in ordinary core loadings twice-burned

fuel bundles can be an excellent power suppressor utilized to flatten the power









distribution in the internal core locations; however, in aggressive core loadings the high

neutron flux in the interior of the core may causes twice-burned fuel bundles to exceed

thermo-mechanically limited peak exposure. Therefore in aggressive core loadings after

bundles have burned two cycles they must be moved to the core periphery in order to

inhibit surpassing peak exposure [4]. This leads to only fresh and once burned

assemblies loaded in the interior core locations.

Most of the gadolinium in a once burned fuel bundle is completely burnt up at the

end of the previous cycle therefore these bundles are at the most reactive state. Inability

to suppress this energy output decreases the available margin to shutdown the core in an

emergency situation. Due to the aggressive core loading geometry, the only available

power suppression comes from the fresh fuel bundles that are loaded into the core.

However, with increased energy placed in the fresh bundles by increasing average

enrichment in order to meet the increased power demand, these fresh bundles will have

decreased power suppression capabilities. Therefore with decreased power suppression

capabilities, the reactor core becomes more limiting in emergency shutdown capabilities.

One of the shutdown systems is the standby liquid control system and the margin in

which the reactor core is shutdown utilizing this system is the standby liquid control

system margin (SLCS). If the reactor core becomes more limiting in SLCS due to the

decreased power suppression capabilities of the core loading strategy, it becomes

paramount to then determine the optimum bundle design utilized in order to improve

SLCS in an aggressive core loading environment.

A reactor core is never licensed without being able to meet all the necessary

shutdown criteria, thermal limit characteristics, and cycle length requirements. Therefore









operating reactor cores do not encounter a failure to meet SLCS because the reactor

would not be allowed to operate if the reactor could not meet the SLCS requirements.

Inability to meet SLCS with a certain reactor core fuel bundle configuration is realized

and mitigated in the design phase of the reactor fuel cycle.

The designer has many options to improve SLCS but any one option may endure a

list of consequences some of which may result in extreme economic concern. The

designer may request that the reactor cycle length be decreased; obviously if the utility

wishes to increase profit by increasing power output this option is not acceptable. The

designer may request the utility to increase the boron concentration or enrichment of B10

in the boron solution utilized by the standby liquid control system. However, this course

of action is limited by increased aggravation caused from Nuclear Regulatory

Commission (NRC) licensing, availability for the utility to plan for the change

economically, ample time to complete the concentration increase in time for the next

cycle loading, capabilities of the installed accumulator tank to support the concentration

increase and ability to keep the boron soluble in solution. The designer may choose to

increase the amount of fuel bundles loaded in the cycle and load more fuel bundles with a

smaller enrichment; however, this may cost the utility more than what was budgeted and

therefore is not a viable option.

The action that is demanded by the utility is for the designer to create a core design

that meets the utilities budget and does not increase the amount of bundles that are loaded

into the reactor core. Therefore the designer must design a fuel bundle with inherently

better SLCS characteristics. In order to accomplish this task efficiently the designer must









know the set of limiting design parameters that may be utilized to enhance SLCS, and

have a list of effective techniques that utilize the advantages of those parameters.

The purpose of this study was to determine the fuel bundle design parameters that

were most limiting in achieving the maximum possible enhancement for SLCS, and to

determine the maximum amount of available improvement to SLCS by utilizing certain

enhancement techniques that take advantage of those design parameters. This will

demonstrate the feasibility of designing a fuel bundle and core operating strategy that has

the ability to meet SLCS without incurring the costs of adding extra fuel bundles in the

design or decreasing cycle power output requirements.

The Boiling Water Reactor System

The boiling water reactor (BWR) system is a nuclear system that boils water

creating steam that is converted into power. The entire BWR system is composed of a

reactor pressure vessel system, a turbine system, a generator system, a condenser system

and the auxiliary control and heat removal systems. Steam is created by boiling water in

the reactor pressure vessel system. The high quality steam then passes through a turbine,

and causes the turbine shaft to rotate. The turbine shaft is connected to a generator and as

the turbine shaft rotates the generator converts the mechanical energy of the rotating

turbine shaft into electrical energy. Once the steam leaves the turbine system, it is sent to

the condenser to be condensed into a sub-cooled fluid and pumped back into the reactor

pressure vessel system.

The reactor pressure vessel system is of primary concern to the nuclear reactor core

designer. Figure 1-1 is an illustration of a typical BWR reactor pressure vessel system.

The reactor pressure vessel system consists of the control drive mechanisms, the active








5



fuel, the jet pumps, the moisture separators and steam driers as well as other inlets for


emergency core cooling [16].




STEAM DRYER LIFTING LUG

VENT AND HEAD SPRAY





S-+ STEAM DRYER
C ASSEMBLY

STEAM OUTLET A S B


STEAM SEPARATOR
ASSEMBLY



FEEDWATER INLET
CORE SPRAY INLET
i j FEEDWATER SPARGER


LOW-PRESSURE COOLANT I .
INJECTION INLET CORE SPRAY LINE

CORE SPRAY SPARGER --
TOP GUIDE


JET PUMP ASSEMBLY CORE SHROUD


S1 CONTROL BLADE
FUEL ASSEMBLIES


CORE PLATE
JET PUMP/IECICULATION RECCULA
WATER OUTLET

CONTROL ROD GUIDE TUBE i


-.. I SHIELD WALL


CONTROL ROD DRIVE
HYDRAULIC LINES


IN.COE FLUX MONITOR



Figure 1-1. BWR pressure vessel system [16].











The active reactor fuel length is approximately 12 feet though actual fuel length


may vary according to different types of fuel assembly product lines. The fission power


of the reactor converts the sub-cooled coolant into steam. The steam then travels through


the steam separators and driers to create a high quality steam that is then send to the


turbine. Each fuel assembly is composed of the fuel and water rods, intermediate spacer


grids, upper and lower tie plates, and flow nozzle. Figure 1-2 displays a typical BWR


fuel assembly as well as a typical fuel rod. Each fuel assembly is encased in a zircaloy


fuel box in order to limit flow between adjacent fuel assemblies. This allows the flow to


any given fuel assembly to be orificed to maintain a constant exit steam quality as well as


limit instability in core thermal performance [16].














TIgE PLTE
FUEL CbLAHNG
BUNDLE

----- ~ ^^'(P1NS QN


F', ,, *.: ----- --.
FU*I "AN-1L
PLENUM




TYPICAL OP 4)







Figure 1-2. A typical BWR fuel assembly and fuel rod [16].






Fuel assemblies are loaded into the reactor in groups of four with a cruciform B4C
control blade loaded in the center of the grouped bundles. Displayed in figure 1-3 is a
typical layout of four fuel bundles with a cruciform control rod loaded in the center of the
grouped bundles. The fuel assemblies are diagonally symmetric with themselves and are
loaded so that there exists 1/8 bundle symmetry with the four grouped bundles.


o000o0000 00000000
00000000 00000000
00000000 000.0000
ooooooo oooooooo
OOOOOOO OOOOOOOO
0oo000000 o0000000o


OOOOOO'O OOOOQOO
00000000 00000000
00000000 00000000


00000000 OOOOOOO
OOOOOOO 00000000
0000000O 0000000
00000000 00000000
00000000 00000000
00000000 00000000


FOUR-BUNDLE FUEL MODULE
O FUEL ROD
O WATER RODS
0 TIE RODS


Figure 1-3. A four fuel assembly group with cruciform control blade [16].









By applying this loading scheme, symmetry may be utilized in modeling the fuel

bundle thereby easing the computation time of the fuel assembly parameters [14]. Each

BWR fuel assembly will contain fuel rods at certain enrichments that may vary radially

and axially as well as gadolinium rods which may vary in placement and concentration

radially and axially. The modeling of SLCS will first involve modeling a 2-dimensional

slice of a single fuel assembly at certain axial heights and then modeling the entire 3-

dimensional reactor utilizing the information from the 2-dimensional model.

Boiling Water Reactor History

The first two light water cooled nuclear reactor systems commercially available for

power production were the boiling water reactor and the pressurized water reactor

(PWR). The concept of the commercial PWR was created from the technology

developed for submarines by the navy nuclear program [7]. BWR development occurred

at Argonne National Laboratory and the Nuclear Energy Division of General Electric

(GE) [9]. The PWR concept is generally characterized as a system in which the bulk

coolant is sub-cooled and contains boron. The system utilizes an indirect dual-cycle that

uses a steam generator. The BWR concept is generally characterized as a system that has

boiling in the reactor core, with the bulk fluid containing no boron, utilizing a direct cycle

for power conversion (the demonstration BWR/1 plants utilized a dual cycle).

The first BWR experiments conducted at Argonne National Laboratory utilized the

BORAX in 1953. BORAX-III produced steam-generated electricity for the town of

ARCO, ID in 1955. The experimental boiling water reactor (EBWR) was developed in

1957 and ran until 1967. This reactor produced 100 MWt and was utilized to

demonstrate the BWR concept for electricity generation utilizing a variety of fuel

enrichments. The GE Valecitos boiling water reactor (VBWR) was the first commercial









nuclear power plant to be licensed by the United States Atomic Energy Commission

(USAEC). Utilized as an experimental reactor, VBWR examined BWR fuel cycle

technology and determined the stable modes of operation. In 1955 Dresden-1 became the

first commercial BWR specifically constructed for commercial power [12].

Dresden-1 was a dual cycle plant and fell under the category ofBWR/1. BWR/1

designs were basically prototype designs of both dual and direct cycle utilized as

demonstration plants that were custom made to meet individual utility specifications.

Dual cycle BWR plants eventually fell out of favor because of the enormous capital cost

involved in utilizing a steam generator. Ouster creak was the first attempt at

standardizing the BWR and marked the beginning of the BWR/2. In 1963 BWR/2 plants

were developed incorporating a direct steam cycle as the chosen method of power

conversion. The reactor concept utilized internal steam separators and forced flow

circulation that pumped core flow through 5 variable speed recirculation pumps. In 1965

GE introduced the BWR/3, the Dresden-2 design, which incorporated the use of internal

jet pumps eliminating the need for external flow circulation loops. In 1966 the BWR/4

or Browns Ferry design was introduced. This design was similar to previous designs but

incorporated a 20% increase in the core power density improving power producing

capability of the reactor and thereby increasing its economic value. The year of 1969

marked the introduction of the Zimmer class of plants better known as the BWR/5.

These plants utilized an improved emergency core cooling and recirculation system.

Flow control in these reactors was accomplished through use of valve control rather than

pump speed control allowing the plants to follow more rapid load change and decrease

the capital cost of the control system [12]. The BWR/6 incorporated the used of higher









efficiency steam separators and multi-hole jet pumps as well as improved power

flattening through enhanced coolant distribution and burnable Gadolinia zone loading.

The original BWR/6 fuel design incorporated an 8X8 fuel assembly rather than the

previously utilized 7X7 [12]. The current BWR technologies include the Advanced

Boiling Water Reactor (ABWR) and the European Simplified Boiling Water Reactor

(ESBWR) both of these concepts utilized passive safety features in order to alleviate the

need for complicated control systems. The history of the BWR is one that is based off of

evolutionary concepts in order to increase core power and eliminate external moving

parts that may fail during reactor operation.

History of Fuel Bundle Development

Over the years fuel bundle designs have undergone evolutionary changes in order

to improve the thermal performance of the fuel and the reactivity features. Each fuel

bundle design incorporated a key feature that allowed for increased margin in controlled

conditions, transients, and thermal limits. The original fuel bundle concept utilized by

the General Electric Company was the 7X7 fuel lattice design. These were fat fuel rods

with decreased surface area due to the large size of the fuel rods. The decreased surface

as compared to today's designs lead to an increase in the maximum linear heat generation

rate (kW/ft) in the fuel bundle leading to an increase in fuel duty [12].

With the creation of the BWR/6 came the inclusion of the 8X8 fuel lattice

assembly. Increasing the surface area of the fuel rods by decreasing there width and

increasing the amount of fuel rods in the assembly decreased the maximum linear heat

generation rate of the fuel rods. In 1988 a fuel design study by Motoo Aoyama, Sadao

Uchikawa and Renzon Takeda suggested that extended exposure of fuel assemblies was

possible if 9X9 fuel assemblies were utilized with and optimized internal water rod width









thereby increasing the non boiling area inside the fuel lattice to increase moderation

capability of the internal portions of the fuel lattice [1]. This design change increased

fuel lattice efficiency. Going to a larger amount of fuel rods in the lattice at smaller fuel

diameter decreased the linear heat generation of the fuel rod by increasing the surface

area of the fuel.

The current design utilized today by BWR vendors is the standard 10X10 fuel

lattice design. Though the water rod locations vary from vendor to vendor the idea is the

same; increase the moderation capabilities of the internal locations of the fuel lattice to

boost reactivity in the areas that are most suppressed in power.

Because the moderator density varies axially in the fuel assembly, the BWR has a

distinct axial power shape. Kazuki Hida and Ritsuo Yoshioka determined that there were

optimum axial enrichment distributions that minimized enrichment requirements subject

to thermal margins [9]. They proved that increasing enrichment in the top half of the

core actually decreases the uranium utilization. Therefore the interpretation of that study

determined that fuel utilization was a key design constraint in creating optimum fuel

bundles. In order to mainstream fuel designs industry moved away from axial

enrichment shaping and fabricated fuel rods of a single enrichment and utilized part

length control rods that increased the moderation capability in the top half of the fuel

assembly leading to an increase in fuel efficiency.

In 1997 Yasushi Hirano, Kazuki Hida, Koichi Sakurada and Munenari Yamamoto

created an algorithm for determining optimum enrichment loading schemes for fuel

lattices [10]. Holding the position and concentration of the gadolinium rods as the

constant, the algorithm optimized the enrichments in the fuel lattice in order to meet









certain thermal limit and local peaking factor criteria. The gadolinium configuration

utilized for the study was based off of a configuration that was supposedly optimized

only for shutdown margin (SDM) and certain thermal limit criteria based off of previous

fuel design experience. However, this method lacked the ability to place the gadolinium

and enrichment into the fuel lattice in such an optimum configuration such that all

controls were satisfied. If the chosen gadolinium configuration was only optimum for

SDM yet not also optimum for SLCS then this method was to only be successful in

designing a lattice to meet SDM. What this method was lacking was the rules for

understanding how the gadolinium needed to be configured to meet the SLCS, SDM and

thermal limit configuration for a given average enrichment.

The SLCS Event

The standby liquid control system is initiated during anticipated transient without

scram (ATWS). The following is a list of the events that occur in the SLCS event:

1. A transient even occurs in which it is necessary to SCRAM the reactor.

2. The reactor control blades fail to insert.

3. A calculated amount of steam is relieved from the reactor to the suppression pool at
a rate that will not violate containment.

4. The boron solution is injected into the core at a specified rate and concentration in
accordance with 10CFR50.62.

5. The reactor reaches an equilibrium shutdown condition.

In 1984 the Nuclear Regulatory Commission (NRC) issued 10CFR50.62,

"Requirements for reduction of risk from anticipated transients without scam events for

light water-cooled nuclear power plants" (ATWS rule). The law states:

Each boiling water reactor must have a standby liquid control system (SLCS) with
the capability of injecting into the reactor pressure vessel a borated water solution
at such a flow rate, level of boron concentration and boron-10 isotope enrichment,









and accounting for reactor pressure vessel volume, that the resulting reactivity
control is at least equivalent to that resulting from injection of 86 gallons per
minute of 13 weight percent sodium pentaborate decahydrate solution at the natural
boron-10 isotope abundance into a 251-inch inside diameter reactor pressure vessel
for a given core design. [17]

This is equivalent 660 ppm boron concentration in current reactor designs. The

model utilized for determining if SLCS will satisfy the criteria mentioned in 10CFR50.62

is a steady state point after the transient event has occurred. The purpose of utilizing this

method is to demonstrate that the reactor may be safely shutdown after the transient event

has occurred. Therefore the event modeled is a cold core (160C), borated to an

acceptable concentration that causes the reactor to be sub-critical by a specified amount.

Project Scope

This study was conducted at Global Nuclear Fuels in Wilimington, NC. The study

included both lattice physics analysis and full core modeling in the 3-d core simulator.

The lattice physics work was further subdivided into the enrichment phase and the

gadolinium phase. For a reference BWR/3 the following projects were undertaken:

1. Enrichment Phase

a. Analyze the effects of homogenous average enrichment perturbation on the
ability to maximize k, difference between the hot operating condition and cold
borated condition.

b. Determine the effect of localized heterogeneous enrichment perturbations on the
ability to maximize k- difference between the hot operating condition and cold
borated condition.

2. Gadolinium Phase

a. Ascertain the effects of gadolinium clumping on maximizing k- difference
between the hot operating condition and cold borated condition.
b. Resolve the effects of increasing the amount of gadolinium rods on maximizing
k- difference between the hot operating condition and cold borated condition.

c. Analyze the effects of gadolinium concentration on increasing k- difference









between the hot operating condition and cold borated condition.

d. Determine a methodology for placing gadolinium rods in order to improve k-
difference between the hot operating condition and cold borated condition.

3. Full Core Modeling Phase

a. Establish the maximum SLCS improvement utilizing an altered geometric
gadolinium placement within freshly loaded fuel bundles.

b. Determine the SLCS attainable from axial power shape perturbations utilizing
enrichment differencing in certain axial zones of the fresh fuel bundles.

c. Resolve the maximum SLCS gained from inserting extra gadolinium rods into
the freshly loaded fuel bundles.

d. Conclude the optimum design strategy for maximizing SLCS.














CHAPTER 2
MODEL AND METHODOLOGIES

In order to determine the necessary strategies for enhancing a margin of shutdown

it is necessary to have a clear definition of that margin. A model and tools to analyze that

model must then be selected that depict the physics of the problem as accurately as

possible. After the designation of a model and utilized tools, the design parameters that

are to be perturbed within the model must be determined. Finally, all other limiting

parameters must be clearly defined so that it may be determined if the improvement to

SLCS is feasible and will not cause the nuclear reactor to violate the thermo mechanical

limits of the fuel.

Standby Liquid Control System and Shutdown Margin

The two shutdown parameters utilized for reactor core licensing are SLCS and

SDM. SDM is a measure of the amount in which the reactor core is shutdown utilizing

all of the control blades excluding the highest reactivity worth control blade.

S kif kCHBWE
SDM = k k
keff (2.1)

CHBWE = controlled case highest worth blade excluded

If keff = 1 then

SDM = 1 k (2.2)


Therefore SDM is the reactivity needed to make the system critical or conversely viewed

as the amount of reactivity in which the system is shutdown utilizing all of the control

blades except for the highest worth control blade.









SLCS is a measure of the amount that the reactor core is shutdown utilizing a

homogenously dispersed boron poison solution.


SLCS= keff -kB.3)
keLC= ff (2.3)
keff

B = borated keff

If keff = 1 then

SDM = 1- k (2.4)

Similar to SDM, SLCS is the reactivity needed to make the system critical or conversely

viewed as the amount of reactivity in which the system is shutdown utilizing a

homogenously dispersed boron poison solution.

Both parameters depict the amount in which the reactor is safely shutdown;

however, the difference in geometry of the poison causes the physics involved in each

shutdown process to be significantly different. Because shutdown margin calculations

utilize a control blade, a heterogeneous poison located on the boundary of two sides of

the fuel bundle, the power distribution of the SDM case is expected to be skewed radially

across the fuel lattice with power peaking occurring in areas furthest from the control

blade. SLCS calculations utilize an evenly dispersed boron poison solution; therefore the

power distribution in the lattice is expected to follow the power distribution dictated by

the actual geometry of the fuel lattice.

The two different modes of control have two separate types of lattice reactivity

responses. Due to this significant difference in reactivity response, it is possible that the

ability to meet specified margin may be satisfied in one mode but not in the other.

Understanding the reactivity response to each mode's shutdown independently and then









utilizing the commonalities in maximized shutdown in each of the two modes ultimately

leads to a fuel design that has maximized margin in both cases.

Modeling Tools

TGBLA 6

TGBLA 6 is a static, multi-group, 2-dimensional, diffusion theory code with

transport corrections factors that assumes infinite lattice behaviors. The steady state

multi-group diffusion equation that is solved is [14]:


-VD (r). V+ o-g (r) (r)= o-g, (r),) () + -Xg vo-,g, (r)g, ((r) + q (r) (1.5)


Because of the major differences in fuel bundle design, void fraction history,

control blade history, enrichment distribution, gadolinium content and accumulated

exposure, the fuel bundle's nuclear characteristics in the core are very different both

radially and axially. Neighboring fuel bundles also have an influence on the

characteristics of the modeled fuel bundle; however, modeling the effects of these

neighboring fuel bundles may be a daunting task because each neighboring fuel bundle in

the core incurs nuclear characteristics that are unique from every other bundle. Therefore

assumptions have to be made in order to be able to achieve an effective and timely

approximation of the fuel bundle's nuclear behavior [5].

TGBLA 6 makes key assumptions in order to accurately approximate a fuel

bundle's nuclear characteristics. Because fuel bundle designs may be varied axially in

bundle geometry, gadolinium content, enrichment, and void concentration, the influence

of axial conditions are considered of primary influence to the fuel bundle's nuclear

behavior. TGLBA 6 completes 2-dimensional lattice physics calculations at different

exposure points for certain axial sections where there exists a known major variation in









fuel bundle geometry. Because in certain defined axial zones the void concentration

changes drastically and because the fuel bundle characteristics are also needed for certain

temperature states, each fuel axial zone is modeled at 0%, 40%, and 70% void

concentration. Though potentially any parameter may be varied by TGBLA 6, the main

variables manipulated in a lattice design are the pellet enrichment, number of gadolinium

rods and gadolinium concentration in each gadolinium rod. As a result of utilizing 2-

dimensional calculations in certain axial zones of the fuel bundle, enrichment distribution

and gadolinium content are only varied in the axial zones represented by the 2-

dimensional lattice physics calculations [5].

Because the influence of neighboring fuel bundle was assumed a secondary

influence on the bundle behavior, TGBLA 6 assumes infinite lattice behavior as a

boundary condition. Assuming infinite lattice behavior results in a good approximation

of the lattice power peaking distribution as well as an accurate generation of group

constants to be later utilized in PANAC11.

Utilizing these design constraints and boundary conditions, TGBLA 6 uses the

solution of the multi-group diffusion theory equation to generate group averaged cross-

sections for 3 energy ranges. Group constants are generated for the fast, epithermal and

thermal energy range to be later used by 3-dimensional core simulator PANAC 11.

PANAC11

After the multi-group cross sections were collapsed and generated by TGBLA6,

Panacl 1 was utilized as the 3-dimensional full core simulator. Panacl 1 is a static, three-

dimensional coupled nuclear-thermal-hydraulic computer program utilized to represent a

BWR core by a coarse-mesh nodal, 1-1/2 group (quasi-two group), static diffusion theory

approximation. The program was utilized explicitly for detailed three-dimensional









calculations of neutron flux, power distributions, and thermal limits at different exposure

steps during reactor core life. The main variable parameters in PANAC 11 were the

control rod positions, refueling patterns, coolant flows, reactor pressures, reactor power

level as well as other operational and design variables [8].

The diffusion equations are solved using the fast energy group. Resonance energy

neutronic effects are included in the model by relating the resonance fluxes to the fast

energy flux. The thermal flux is represented by an asymptotic expansion using a slowing

down source from the epithermal region. A pin power reconstruction model is also

implemented to account for the effect of flux gradients across the nodes on the local

peaking distribution.

Utilized Temperature States, Boron Concentrations and Lattice Types

There was a combination of 4 main types of temperature states and boron

concentrations investigated in the study. These states included the hot uncontrolled state

(HU), cold uncontrolled state (CUO), cold controlled state (CC) and a cold state

containing soluble boron (CU###). The HU state was defined to be the operating

temperature state with no control blade placed next to the fuel lattice. All cold states

were to be defined at a moderator temperature of 160C, and all the cold uncontrolled

states also had no control bladed placed next to the fuel lattice. The CU### condition

was designated as a cold lattice containing a homogenously dispersed soluble boron

solution at a specified boron concentration. The CC condition represented a cold fuel

lattice with a control blade placed in the upper and left side of the lattice.

There were two fuel lattice types examined in the enrichment perturbation portion

of this study. A "C" lattice was defined to be a fuel lattice that exhibited the same

amount of moderator spacing on all four sides of the lattice while a "D" lattice exhibited









slightly more moderator spacing in the vicinity of a control blade location. Therefore the

radial power distributions of the two different lattices are slightly different in lattice

peaking characteristics.

Measurement of SLCS and SDM during the Lattice Development Stage

SLCS and SDM are both global parameters that describe a margin experienced by

the entire nuclear reactor core. Therefore the calculation of these parameters involves

utilizing a 3-dimensional core simulation tool. Fuel bundles are generally designed by

first utilizing a 2-dimensional fuel lattice physics tool to create average collapsed group

cross sections to then be utilized by the 3-dimensional reactor core simulator. An

abundant amount of energy groups are utilized in the lattice physics calculation in order

to properly model the physics of the lattice. Many bundles within the reactor core will

exhibit similar characteristics due to the similar enrichment or gadolinium concentration

within the fuel bundle. Therefore by generating these average group cross sections for

similar fuel bundles, the 3-dimensional core calculation is significantly faster because the

calculation does not involve solving equations at an abundant amount of energies for

many different points within the reactor core [14].

The 3-dimensional simulator only utilizes few averaged group cross sections

(usually 3 averaged groups). The 3-dimensional core simulation tool utilized for this

study, PANAC 11 separated the reactor core into a series of 6 in. cubic nodes. A flux was

then solved in each individual node.

Enhancement to the fuel bundle design therefore involvements modifications to the

fuel design in both the lattice physics development stage and the 3-dimensional core

simulation stage. Since SDM and SLCS global parameters defined for the entire system,









a separate set of parameters must be utilized for characterizing how fuel improvements in

the lattice development stage will affect the full core global parameters.

Maximizing SDM and SLCS involves increasing the difference between the hot

operating condition and the cold shutdown condition. Therefore in the lattice

development stage an enhancement in SLCS and SDM meant and improvement in the

difference between the hot operating k- and cold shutdown k-.

The cold shutdown condition related to SDM is defined to be when the lattice is

controlled by the placing a control blade next to it. The parameter used to represent the

maximized difference between hot operating k- and cold shutdown k- was designated

HUCC, and calculated by the equation:

HUCC = k HotOperahng_ k ColdControlled (2.5)

The cold shutdown condition related to SLCS is when the lattice is controlled by

placing a homogeneously dispersed solution throughout the fuel lattice. The parameter

used to represent the maximized difference between hot operating k- and cold shutdown

k- was designated HUCU###. The symbol ### represents the amount of parts-per-

million of boron in the solution. HUCU### is calculated by the following equation:

HUCU# # #= kHotOperathng kColdBoratedSoluhonat ###ppm (2.6)

Maximizing these parameters in the lattice development stage will maximize the

global parameters that these parameters represent in the 3-dimensional core modeling

stage.

Fuel Bundle Geometry

The fuel bundle utilized in the lattice physics calculations was a typical 10X10

boiling water reactor fuel bundle design with 92 fuel rods and two water rods. Figure 2-1









displays a cross sectional view of the fuel bundle geometry. Since each lattice physics

calculations was completed utilizing a 2-dimensional model, the fuel bundle had to be

sub-sectioned into 2-dimensional axial zones in order to accurately model the sections of

the bundle that experience different void concentrations, decreased average moderator

density, variable gadolinium and enrichment placement, and different lattice geometries.

The axial zones utilized were designated naturally enriched bottom (NAT), power-

shaping zone (PSZ), dominant zone (DOM), plenum zone (PLE), vanished rod location

zone (VAN), natural vanished rod zone (N-V) and natural top zone(N-T). The NAT was

a naturally enriched zone filled with all 92 fuel rods and no gadolinium. This zone

represented the first 6 inches of the bottom of the active core length. Both the PSZ and

DOM were enriched zones containing 92 fuel rods with gadolinium present in certain

locations. The PSZ zone was located on top of the NAT zone and was 48 inches in

length. The DOM zone was located on top of the PSZ and was 30 inches long. Though in

2-D geometry these axial zones were identical, the zones are separated due to the

different inherent thermo-hydraulic and neutronic characteristics experienced in each

zone.

The PLE was a 12 inch zone containing 78 fuel rods and gadolinium rods present in

needed locations. This zone was used to model the interface of the part length rods and

the vanished rod locations began. On top of the PLE was the VAN. The VAN contained

78 fuel rods and 14 vanished rod locations and ranged between 37 and 48 inches in

length. On top of the VAN was the N-V. The N-V contained natural enrichment and has

pellets existing in 78 fuel rod locations. The N-T was also naturally enrichment but only

had pellets in locations where no gadolinium existed in axial portions of that specific rod.












0000000000
OOOOOOOOOO
FOo oor
00000 0000
00 0000
000 0000
00 00000 J
S Co~t~ir Blad


KK


F Full Length Ful
) Part Lengh F I
Tie Feul Rod

w Large Water Rod
TopGe Beanm Getertkne


cI


I9


Oq0 ooo0 oo
O^ o_ o oo 7Po
00 0 ow

0100000 000
0000000000

oo000000000
-4--


1I


I(f
HW-" i


Figure 2-1. A cross sectional view of the modeled fuel bundle.


T-


HA


As displayed in figure 2-2, there existed only 4 possible fuel rod geometries. The

DOM and PSZ had the same fuel rod geometry, and the VAN and N-V had the same fuel

rod geometry. In the N-T the locations marked "E" are used to represent empty fuel

locations in the lattice of where gadolinium rods exist in the N-V. In the N-V, N-T, and

VAN the locations marked "V" are used to represent the vanished rod locations. In the

PLE the locations marked "E" are used to represent the area of the plenum tip of the part

length fuel rods.

Though 4 different possible fuel rod geometries exist only 3 different types of

geometries were modeled in the lattice physics investigations. The DOM, PLE and VAN

region were modeled. The N-T was not investigated because this region contained only


0000000000
0000000000

00000 w000
( 0 00000
000 00000
0000000000
0000000000
o0o0OOOO
00 D00 0 0


- ^


Rod


I


L


c


















natural enrichment and therefore the low power level experienced in this region would




never be most limiting in any cold shutdown condition.


N-T
A 8 0 D E


0,71 071 071 71 071 71 071 071 071 0.71 071

0,71 V 071 V 0.71 E V E V 0,71

0 71 071 E 071 E 071 E 071 E 071

0.71 V 0.71 E 071 WR 0.71 V 0.71

0.71 0.71 E 71 V 0.71 0.71 0.71

0.71 E 071 WR V E 07-1 E 0.71

0.71 V E E 0.71 E V 0 71

0o.1 E 0o71 071 0.71 0.71 E 071 0.71

0.71 V E V 0.71 E V E V 0.71

0.71 071 071 07.7.71 0.71 0.71 071 0.71 071


M-V
A I 0 D E F O H I ,J
071 071 071 071 071 071 071 071 071 071

0.71 V 0.71 V 071071V 0 71 V 071

071 0.71 071 071 071 0071 071 0771 071 071

071 V 0.71 0.71 0.71 'R 071 V 0,71

071 0.71 071 0.71 V 0.71 071 071

0,71 071 071 R V o.71 0.71 0,71 071

071 V 0.701 07.071 0.71 V 071

071 071 0.71 0.71 071 071 0.7 071 071071

071 V 071 V 071 0.71 V 071 V 071

071 0.71 071 0.71 071 0.71 0,71 071 071071


PLE
A B D E F a H I J
1,6I W 3 3.20 3Z9 395 Z9 5 3.L35s 3..9 3.95 2S

30o E .0 E 34O 3.i5 E E ,5
7I ~ 777 4-90 ..40 ^^

3.9S E 3 4 .4 3.95 'R 4-90 E 490

39 380 35 E -90 490 l90

3,95 3 o5 4,3 *A IR E 4- 4

3.gS E g 490 &M E 14,90













, = 4. J a o a J 4

4 4 4 "
*. 40 490 W4 90 4 -' 1 4,90
"E i0E 4S E
220- 3.95 4.90 4.909 490 4 9: 490 4,


PSZ


1W&0 20 3.20 Z.96 3Z953,95 3.951 35 3.95 Z80



*-, ;..40 a


S,9- 30 3.95 4.9 490 4.90 490
S 2a 440 WR L 90 4.9 4.0 44.9



--..- I 0 Sk5



2SO 3.95 4.90 4.90 9 49 4. M 4.90 4.90 J30


Figure 2-2. The geometric setup of the fuel lattice axial zones.


Thermal Limit Design Considerations




Nuclear reactors are designed so that operation will not induce unnecessary risk to




the health and safety of the general public. Therefore thermal limits are imposed on


Hear
I 4.2

tie::'


6.00


V. I 3724


%60- 1


RLE


1

-i
2


4

6
1200 a

7


IS







-I
1

2



4
6



7


VAN
A U O D E


395 V 4.40 3.9 R -V 4.0 V 4.90-
3.B 3.60, 3 j V -A-. 4 90- 4,90 4390

-5 S- 40 W R V M,1 W 4 _So

395 V 0,7 -1 4.90 V 1 4.90

39 4 4043 4 4.90 0 1 401 0
[EV4 -90 B v

23 4.90 490490490490 9040 3


DOA
A a 0 D E F O H I J








3031 0316 071 .5 90 0- 4.930 4,90 4-90

07S710" 071 0710-











07 07 07 071 071 071 0.71 07A 1
S95&04.0 4- -.90 4.9003770











01 071 0710.71 07071071071071 .71 071 071 0.71 071


0,71 071 0.71 071 071 071 071 071 071 071

071 071 071 071071 071 0.71 071 0.71 071


PSZ 4AM00

2

3

4

5
e


7


a
NAT 6.00J
1S


F 0 H 1 J


F O H I j









certain core parameters to ensure that radioactive release during reactor operation or any

type of transient event does not exceed the acceptable limits imposed by the NRC.

Constraining operation to within the thermal limits of the fuel guarantees that during

normal operation and emergency transients the fuel integrity will be maintained. For the

applicability of this project the two main thermal limits monitored were MFLPD and

MFLCPR. These limits are set to limit boiling around the fuel rod locations and limit

fuel rod power density in order to preserve fuel integrity [11].

Linear heat generation rate (LHGR) is the amount of power produced per length of

fuel and is defined as

Average LHGR = Maximum Thermal Power Output (1.6)
S (Number _of _Fuel _Assemblies XFuel Rods _Per _Assmebly XFuel Rod Length )

A maximum average LHGR is specified for the utility in order to limit the plastic

strain or deformation of the cladding. A limit of 1% deformation of zicaloy cladding is

considered a conservative limit below which fuel damage is not expected to occur.

New pellets undergo slight densification during irradiation. This causes the gap

between the fuel and the cladding to increase and thus decrease thermal conductance.

The pellet densification also has a shrinking axial effect. If one of the pellets gets stuck

during this process, a gap is created resulting in more fissions occurring in newly exposed

faces of the pellets increasing heat flux in that area [6]. Therefore LHGR is adjusted for

the possible elevated heat flux and is defined as


LHGRh1int = LHGRdegn 1[- m (1.7)
1718X LT

Where:

LHGRdesign = Maximum LHGR allowable to prevent clad damage









LT = Total active core length

L = Axial position in feet above the bottom of the core


I ax= Maximum power spiking penalty
P max

In the core simulator LHGR is calculated for certain axial nodes. MFLPD is the

maximum fractional limiting power density for the most limiting node and is defined as

LHGR
MFPLD = maxnode (1.8)
LHGRhm ,t

As long as MFLPD is less than one LHGR is not exceeded. However, because

these calculations are based off of the assumptions of the maximum power spike penalty,

and because the designer needs to be certain that MFLPD will never exceed one, the

design basis requirement for MFLPD is 0.909 to ensure enough variation between the

actual calculation and the measured data [8].

Critical power is the bundle power required to produce transition boiling in a

reactor channel. If transition boiling were to manifest in a channel, it may lead to fuel

rod dry out in the channel with the inability of the fuel rod surface to rewet. This

phenomenon leads to a decrease in the ability of the clad to reject heat to the water

through convection and thus heat up the clad to the point of mechanical failure [6]. CPR

is the ratio to determine how close the actual power is to transition boiling and is defined

as:

CP
CPR =- (1.9)
AP

CP = Critical power for transition boiling

AP = Actual power.









CPR must always be below 1.0 for safe operation. MFLCPR is the flow adjusted

ratio of the operating limit CPR for a specific fuel type to the CPR of that bundle and is

defined as:

CPR Limit K
MFLCPR = -(1.10)
CPR

Kf = Flow adjustment factor

Since MFLCPR should never exceed one in any section of the reactor during

operation, and since slight uncertainty exists in knowing the actual power of the reactor

and the critical power for a specified bundle, the design basis for MFLCPR is set to 0.930

to accommodate these uncertainties [8].















CHAPTER 3
MAXIMIZING HOT-COLD BORATED k- DIFFERENCE UTILIZING
ENRICHMENT

TGBLA 6 was utilized to understand SLCS improvement by enhancing lattice

behavior characteristics utilizing enrichment perturbations. C and D lattices types were

examined at 0%, 40% and 70% void fraction. The four system states inspected were HU,

CUO, CU###, and CC. Lattices with a homogeneous enrichment distribution were

examined to determine the effects of lattice average enrichment on the enhancement of

the HUCU### and HUCC. Next, Local and gross enrichment perturbations were also

analyzed to determine the effects of these types of enrichment perturbations on

HUCU### and HUCC.

Since an enormous amount of combinations of temperature states, lattice axial

zones, lattice types and void concentrations could be created, the homogenous

enrichment work was utilized to determine which of these temperature states, lattice axial

zones, lattice types and void concentration were most limiting in order to limit the

amount of cases to investigate therefore only examining the most effective strategies for

enhancement.

Homogeneous Enrichment Distribution

A homogeneously enriched distribution was defined to be a fuel lattice with

constant enrichment throughout the lattice. Therefore homogenous enrichment

perturbations were defined as a change in enrichment to every fuel pin in the lattice by

the exact same amount.












Determining the Most Limiting Lattice Axial Zone and Void Concentration


A variety of tests were completed to determine which lattice parameters were most


limiting to HUCU### and HUCC. Figure 3-1 depicts the effects of lattice type and void


fraction on HUCU###. Lattice type did not significantly affect HUCU###; however, as


void fraction increased HUCU### decreased.


For this case, at 0 GWD/STU the difference in HUCU### was solely related to the


effective moderator density difference at increased void fraction. At higher void


fractions the average moderator density was decreased. Because the average moderator


density was decreased fewer neutrons were thermalized and absorbed by the fuel for


fission, and an increased amount of neutrons were parasitically captured by the fuel [18].


Therefore HUCU### was smaller for higher void fractions.




0 18

0 16

0 14 -

0 12
S--- 0% Void, C Lattice
0 1 --40% Void, C Lattice
70% Void, C Lattice
0% Void D lattice
0 08 --40% Void, D Lattice
70% Void, D lattice
006

004

0 02


0 10 20 30 40 50 60 70
Exposure (GWDISTU)

Figure 3-1. Exposure dependent HUCU660 for the DOM at 3.95% enrichment.


Initially U238 was the main parasitic neutron absorber in the fuel due to increased


void concentration. When U238 absorbed a neutron it became Pu239. Because Pu239 had a


high thermal absorption cross section (oa = 1015b) as well as multiple resonance


absorption peaks, it became another main parasitic neutron absorber. The increases in









build up of parasitic neutron absorbers lead to a decrease in the effectiveness of boron to

capture thermal neutrons [18]. Therefore as the lattice burned, plutonium was built up

thus increasing the content of competing neutrons absorbers and therefore decreasing

HUCU###. Furthermore, in the higher void history condition it took longer for

plutonium production to reach an equilibrium state; therefore at increased void history

conditions HUCU### decreases at a faster rate for a longer amount of time.

Figure 3-2 illustrates the effects of the combination of axial zone and void fraction

on HUCU###. The DOM was the most limiting axial zone because of the maximum

amount of fuel rod inventory present in the lattice and minimum amount of volume to

place borated water. A lattice geometry that allows for more moderator space allows for

more ability to place borated water in the lattice; therefore since the VAN and PLE both

have evacuated regions where more space exists to place a boron volume these axial

zones were not the most limiting in terms of HUCU###.

In order to maximize improvements in HUCU###, enhancements must be made to

the most limiting conditions ofHUCU###. HUCU### was most limiting in the 70%

void fraction and DOM case; however, in the core, on average, the DOM exhibits a 40%

void fraction therefore modeling a DOM at 70% void fraction would not have been an

accurate realistic model to examine SLCS. The realistic model utilized which was most

limiting was determined to be 40% void fraction in the DOM. Therefore since lattice

type did not significantly effect HUCU###, and the DOM 40% void fraction was the

most realistic limiting condition state, the C lattice type, DOM, 40% void fraction lattice

was chosen as the base lattice in which all other perturbations were compared.











025




02



--Dom Zone, 0% Void
0 15 -Dom Zone, 40% Void
-Dom Zone, 70% Void
SPie Zone, 0% Void
Pie Zone, 40% Void
Sc --Pie Zone, 70% Void
-Van Zone, 0% Void
0 1 --Van Zone, 40% Void
Van Zone, 70% Void



005





0 10 20 30 40 50 60 70
Exposure (GWDISTU)

Figure 3-2. Exposure dependent HUCU660 at varied void fraction and axial zone for the
C lattice at an enrichment of 3.95%.

Understanding the Exposure Dependent HUCU### Curve

Understanding the exposure dependence of the HUCU### curve was paramount to


determining the appropriate strategy for enhancing HUCU###. Figure 3-3 depicts the


two major portions of the exposure dependent HUCU### curve. Portion A encompasses


0 GWD/STU to roughly 11-15 GWD/STU depending upon geometry of the axial zone


and void concentration. Portion B encompasses the rest of the HUCU### curve.


When a fissile isotope absorbs a neutron, the isotope may either undergo fission or


parasitic capture. The capture-to-fission ratio is defined by:


O
a' (3.1)
(7f


In a thermal reactor the majority of the neutrons cause fissions at thermal energies in


U235. Therefore for most thermal reactor applications the capture-to-fission ratio is an









explanation of the fission efficiency of the thermal neutrons [13]. As ac increases k-

decreases because more thermal neutrons undergo parasitic capture and are removed

from the system instead of undergoing a fission event and creating more neutrons [18].

During portion A of the exposure dependent HUCU### curve, HUCU### is

decreasing due to increased plutonium production. Pu239 has a capture-fission-ratio of

0.370 (2200 m/s neutron) while U235 has a capture to fission ratio of 0.175 (2200 m/s

neutron) [13]. Therefore with an increased a plutonium acts as a competing neutron

absorber that decreases boron worth thus limiting the effective absorption ability of the

boron.

The capture-to-fission ratio is a function of the system temperature. Doppler

broadening is a phenomenon in which due to the kinetic motion of the target atoms at

elevated temperatures the resonance absorption cross sections broaden while the peak

magnitude of the cross section decreases, and in most cases slightly preserving the area

under the original resonance [3]. Therefore though the effective peak of the cross section

has decreased, the width of the resonance is increased and therefore the resonance affects

a greater range of energy of neutrons; therefore causing a greater interaction rate in that

energy interval and thus leading to more absorption and decreased flux in that energy

interval [15]. At higher temperatures there is more kinetic motion of target particles and

thus more Doppler broadening of the resonance cross sections. With increased parasitic

capture and decrease thermal-to-fast flux ratio, HU k- decreases at a much faster rate

than CU### during Portion A of the HUCU curve because the worth of the plutonium

produced is progressively worth more in the hot operating condition than in the cold

condition.









The thermal-to-fast flux ratio is defined by:


a, = thermal (3.2)
1 fast

As the temperature of the system increases the average moderator density

decreases. Because the average moderator density is decreased the neutron spectrum has

a higher density in the fast region. In the hot operating condition the decreased average

moderator density causes an increase in ai; therefore fewer neutrons are available for

thermal fission events. Since at elevated temperatures there exists greater Doppler

Broadening as well as decreased average moderator density, the decrease in al leads to a

decrease in k- of the system. Therefore the increasing a and decreasing aL in the hot

condition leads to a decrease in the HUCU### curve because the hot k- is decreasing

faster in comparison to the cold k-.

















Exposure (GWD/STU)

Figure 3-3. Exposure dependant HUCU### curve.

During portion B, as plutonium production reaches an equilibrium concentration

the difference between the hot operating condition and cold condition worth becomes











almost constant and therefore during this portion of the curve HUCU### experiences


relatively no exposure dependence no exposure dependence.


Enrichment and Boron Concentration Effects

Figure 3-4 depicts the effects of increasing enrichment on HUCU### at different


boron concentrations. For each 1.0% increase in average enrichment 0.0188 HUCU###


was lost. Since the derivatives of HUCU### were equivalent at different boron


concentrations, the amount of HUCU### gained from a boron concentration increase was


linearly dependent on the boron concentration increase and not also affected by the


average enrichment. Equation 3.3 calculated 1.84 x 10-4 HUCU660 gained for each 1


ppm or boron introduced to the lattice. Therefore 99.6 ppm of boron was required to


compensate for a 1.0% average enrichment increase.


HUCU### gained AHUCU### (3.4)
1 ppm Boron ABoron Concentration pec Encmnt



03


0 25





0 15- 742 PPM
792 PPM
-I-935 PPM
01


0 05



0 04 08 12 16 2 24 28 32 36 4 44 48 52
Enrichment

Figure 3-4. Beginning of cycled HUCU vs. enrichment in the DOM, at 40% void
fraction, for a C lattice.











Power Peaking Distribution

The lattice power peaking distribution was a function of the relative distance of


fissile material from the moderating regions. Moderation capability of certain lattice


regions was a function of the water boundaries of that certain lattice region as well as the


temperature state, boron concentration and geometry of poison utilized within the lattice.


Power Peaking distributions for a homogenous 3.95% enrichment lattice at 5 GWD/STU


are displayed in figure 3-5 for HU, CUO, CC and CU660. Each fuel pin location is


identified by the horizontal and vertical location in which the pin resides. The water rod


locations were marked with a zero in order to distinguish the water rod locations from the


fuel pin locations.

5 ACHJ395Enndcrert, DmZore, CLatbce4MP/oVi d 5 GACQ3 95 Ennchmr t DmZxe, CLattce 4/obVad
1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
1 1122 10747 11 1 9 1 251141 1 057402 057 8 0618 0646 43 8Q 113 2 10067 1l B 2 0520538 06241 02t762 Q7 07~ 9 130>x> 12
3 11229 11415 3 Q57 06241 06763 0741 10321 12>x>110
4 10747 0 1022 4 0588902 0741 10385 0 0 1 C919 28 110>x>10
5 1061 0 01069 5 0615807062 1035 0 0 1129710878 105>x> 100
6 10 0 0 10621 6 06496 07605 0 0 11616 10421 1019 100>x>0
7 125 0 0 1076 7 06943079 0 0 116616 103131021 12 095>x> 090
8 1141 11245 8 07099 19129710421 11 2151 1454 0> x-> 085
9 10 1 9 10132 1 OE2 10B78 149 1 1454 1085>x 0
10 11415 1 1 10621 10711245 10 080>x

5 GCL,395Ennchrr DmeZe, CLatoeD/oVad 5 GWoC ,3 9 BEndirr [hmZae, CL atoe 4C/oVd


1 11221 1 OB47 107713 11016 1 1378 1 11859 113 1079 10736 1 0 1 0 11197 11956
2 2 11859 11963
3 11221 07945 07877 11395 3 11033 1 12D9
4 1047 07877 0 0 1104 4 10779 0 0 1C46
5 1072 10713 0 0 1 02 5 10736 15 0 0 1 B31




9 9 11~6 1189
10 11395 11041 s 10 6 1B 11284 10 113 1129 10946 1 0831 10762 1 B09 11097 118981
Figure 3-5. The power peaking distributions at 5 GWD/STU, 3.95% enrichment,
DOM, C lattice, and 40% void fraction vs. temperature state and boron
concentration.









Figure 3-5 suggests that there were significant differences between the HU and

CUO power peaking distributions. In the HU state the outer borders of the lattice

exhibited the greatest amount of power peaking due to the close proximity of large areas

of water to that location and therefore displaying the greatest moderation capabilities.

Due to the moderation of the internal water rod locations, fuel pins located near the

internal water rods exhibited a higher relative power than locations that were located

away from the borders of the lattice and away from the internal water rod locations. The

lack of moderation for the fuel pins located away from the borders of the lattice and away

from the internal water rod locations caused these locations to exhibit the lowest relative

power.

In the CUO state, power was raised in the highly moderated areas. With no voids,

the outer borders of the lattice and the internal water rod locations exhibit a greater

amount of power peaking than the areas of the lattice that were between these locations.

Because of this effect, the importance of fuel pins located away from the borders and

water rod locations were significantly decreased, and if a perturbation were to be made to

a fuel lattice in order to improve inherent HUCUO characteristics these locations would

not play an important role.

There were also significant differences in power peaking distribution for different

poison types. In the CC state a high anisotropy of power peaking was exhibited due to

poison residing at the covers of the lattice. Fuel pins located closest to the control blade

exhibit the greatest power suppression; therefore if a poison introduction was necessary

for power suppression in the HU state, placing that poison away from the greatest power

suppressed pins in the CC condition will achieve the greatest improvement in HUCC.









In the CU660 state the boron caused the power to be suppressed in highly

moderated regions thereby flattening out the power distribution of the lattice. Because

boron was present in the moderator, regions that had greater power peaking due to

increased moderation capability also consequently had greater power suppression from

the boron dispersed within the moderator. Because of the flatter power distribution in the

CU660 as compared with the HU state, placing power suppressors in peaked locations

corresponding to the HU state did not necessarily have as severe an impact on the cold

borated state. However, this leads to a distinct design advantage because it may be

possible switch locations of a distributed poison and have a miniscule effect on HU but a

major effect on CU###. Therefore in order to maximize HUCU###, power suppressors

must be placed in areas where the CU### state exhibits a higher power peak than the

power peak in the HU state.

As enrichment increased the power peaking distribution in the lattice became more

skewed. Figure 3-6 displays that as average enrichment was increased in the CU### state

the power peaked more in the border regions and internal water rod locations of the

lattice. Figure 3-7 displays that as average enrichment was increased in the HU state the

power also peaked more in the border regions and internal water rod locations of the

lattice. Therefore there exist fewer locations in which moving a distributed poison will

not greatly affect the HU state while greatly affecting the CU### state.

Unfortunately this demonstrates that in a power up rate or increased exposure

design, it will be harder for the designer to create a design that improves SLCS and

decreases the power peak in the HU state. Figure 3-6. The power peaking distributions at

5 GWD/STU, CU660, DOM, C lattice, and 40% void fraction vs. enrichment.














5 GWD,CU660,0 71 Enrichment, Dom Zone, C Lattice 40% Vad 5 GWD,CU0,3 95 Ennchment, Dm Zone, C Lattice 40% Vad
1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
1 1 1923 1095 10595 10471 1 0462 10503 10557 1067 10996 1 1929 1 1 1221 10847 10772 1 0853 1 1016 1 1378
2 1 095 1 0986 2
3 10595 1 0662 3 1 1221 07945 07877 11395
4 10471 0 0 10553 4 1 0847 07877 0 0 104
5 10462 1 0681 0 0 10501 5 1 0772 10713 0 0 10882
6 10503 0 0 10683 10461 6 1 0853 0 0 10717 10806
7 10557 0 0 10472 7 1 1016 0 0 07893 1 0885
8 1 067 10597 8 1 1378 07893 07966 1 1264
9 10996 1 0953 9
10 1 1929 10986 10662 10553 1 0501 10461 10472 10597 10953 1 1923 10 1 1395 1 104 10882 1 0806 10885 1 1264

5 GWD CU660,3 2 Ennchment, Dom Zone, C Lattice 40%Vad 5 GWD, CU660, 4 9 Enrichment, Dom Zone, C Lattice, 40% Vad
1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
1 1168 10965 10704 1 0665 10733 10846 1 1 1166 10862 10816 1 0891 1 1016 11303
2 1 168 1 1775 2
3 10965 11101 3 1 1166 07969 07943 11319
4 1 0704 0 0 10859 4 1 0862 07943 0 01038
5 10665 1 0768 0 0 10751 5 1 0816 1095 0 0 10919
6 10733 0 0 10772 1 0686 6 1 0891 0 0 1 09541 0848
7 10846 0 0 10728 7 1 1016 0 0 07959 10898
8 1 1093 1 0993 8 11303 07959 0799 1 1206
9 11771 11712 9
10 1 1775 1 1101 10859 1 0751 10686 1 0728 10993 1 1712 10 1 1319 1 1038 10919 1 0848 10898 1 1206

Figure 3-6. The power peaking distribution at 5 GWD/STU, CU660, DOM, C lattice,

and 40% void fraction versus enrichment.


5 HU,0 71 Enchment, Dcm Zone, C Lathce 40% 0 d 5 GVOHU,395 Ennchmet, Dom Zne, C Lattice 40%oVad
1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 K
11219 10702 10443 10365 10418 10565 10836 1134 W 1 11229 10747 1061 1069 10925 1141 1130 < x

2 11219 10126 11328 2 10067 102 130 > x > 12C

3 10703 10827 3 11229 11415 120 > x > 1 1

4 10443 0 0 10557 4 10747 0 0 1932 110 > x > 1 0

5 10365 10071 0 0 10412 5 1061 0 0 1699 105 > x > 1 OC

6 10418 0 0 172 1036 6 1069 0 0 1 621 100 > x > 0 9
7 10565 0 0 10438 7 10925 0 0 1076 0 95 > x > 0 9C

8 108336 8 1141 11245 0 90 > x > 0

9 1134 10126 11215 9 1028 1008 0 85 > x > 0 8C

10 11328 10827 10557 10412 1036 10438 10698 11215 10 11415 10932 10699 10621 1076 11245 080 x


5 GDHU,32 Enndimet, DomZcne, C Lathce 40/ Vad 5 GAC HU, 49 Erndmmet, DomZcne, C Lance, 40%/Vad

1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
1 11116 10668 10537 10614 1 120 9 1 11346 10837 10695 10778 11017 11527

2 1i 1 1013 2 1 004 1 16
3 1 1116 1 128 3 1 1346 0798 1 1533

4 10668 0 0 10845 4 10837 07826 0 0 11026

5 10537 0 0 10621 5 10 5 10045 0 0 10789
6 1 0614 0 0 1 0546 6 10778 0 0 1 00471 0709




9 1 013 1013 9 1 6 1002
10 112 10845 10621 10546 107811 10 11533 11026 10789 107 10853 11365

Figure 3-7. The power peaking distributions at 5 GWD/STU, HU, DOM, C lattice, and

40% void fraction vs. enrichment.









Heterogeneous Enrichment Distribution

After determining the effects of average enrichment on the behavior of HUCU###,

heterogeneous enrichment perturbations were then examined in order to determine if

enrichment changes to individual fuel pins could affect HUCU###. The two major types

of enrichment perturbations investigated were localized enrichment perturbations and

gross enrichment perturbations. Localized enrichment perturbations were considered to

be small sets of fuel pins that were either increased or decreased in enrichment by a

certain amount holding the rest of the fuel lattice at constant enrichment. Gross

Enrichment perturbations were considered to be a large lump of fuel pins that were either

increased or decreased in enrichment by a certain amount holding the average enrichment

of the entire lattice constant.

Localized Enrichment Perturbation

Localized enrichment perturbation patterns were generated based on the power

peaking distribution map. The fuel pin locations were set into groups based on locations

exhibiting similar power peaking in the homogeneously enriched lattice calculation.

Since lattice power peaking was determined to be dependent on enrichment, 3.95%

enrichment was chosen as the distribution for which the determination of the pattern type

was made.

Figure 3-8 displays the distribution of perturbations made to the lattice. Each

group of numbers represents a group of fuel pins that were either increased or decreased

by 1.0% enrichment as the rest of the lattice was kept at a constant enrichment.

Localized enrichment perturbations had no effect on HUCU### as depicted in figure 3-9.

The minute difference of 0.00373 HUCU### in figure 3-9 was considered only a function








40



of the 0.2% average enrichment difference exhibited between each pattern utilized.


Therefore localized enrichment perturbation did not greatly affect HUCU### behavior.



1 2 3 4 5 6 7 8 9 10


Figure 3-8. Localized enrichment perturbation map.
Figure 3-8. Localized enrichment perturbation map.


0.078689


0.074957


- Map 1, Pattem 1
- Map 1, Pattem 2
Map 1, Pattem 3
Map 1, Pattem 4
- Map 1, Pattem 5
- Map 1, Pattem 6
- Map 1, Pattem 7
- Map 1, Pattem 8
Map 1, Pattem 9


Maximum Change in Hot Uncontolled k-infinity Due To Cold Uncontrolled k-infinity =
002 0.003732 Wiich is Soley a Function of Average Enrichment Change (0.2%).



0 10 20 30 40 50 60 70
Exposure (GWDISTU)



Figure 3-9. Exposure dependent HUCU660 for different localized enrichment
perturbation patterns.


01


008


' 006











Gross Enrichment Perturbation

Gross enrichment perturbations were next examined in order to determine how

these type of lattice perturbations would affect shutdown behavior. Figure 3-10 displays

an example pattern of gross enrichment perturbations and table 3-1 lists the enrichment

perturbations made to that example pattern.

Table 3-1. Gross enrichment perturbation scheme for figure 3-10.

Enrichment Enrichment
Pattern Perturbation (1-2) Pattern Perturbation (1-2)
1 1.6%-4.9% 7 4.9%-1.6%
2 2.4%-4.9% 8 4.9%-2.4%
3 3.2%-4.9% 9 4.9%-3.2%
4 4.4%-4.9% 10 4.9%-4.4%
5 3.2%-4.4% 11 4.4%-3.2%
6 3.6%-4.4% 12 4.4%-3.6%


1 2 3 4 5 6 7 8 9 10
1
2
3
4 W W
5 W W
6 W W
7W W
8
9
10
Figure 3-10. An example of a gross enrichment perturbation map.

Gross enrichment perturbation demonstrated no effect on HUCU###. Though

HUCU### was not a function of localized and gross enrichment perturbation, HUCC was

highly dependent upon these perturbations. Figure 3-11 and 3-12 display the difference

in effect of gross lattice perturbation skewing. Notice in figure 3-11 no effect was

noticed on HUCU###; however, in figure 3-12 HUCC was highly dependent upon

enrichment distribution.
























- Map 6, Pattern 2
Map 6, Pattern 8


0 10 20 30 40 50 60 70
Exposure (GWDISTU)

Figure 3-11. Exposure dependent HUCU660 at 40% void fraction, in the DOM, with a C
lattice.


025




02-


-Map 6, Pattern 2
-Map 6, Pattern 8


005


0 10 20 30 40 50 60 70
Exposure (GWDISTU)

Figure 3-12. Exposure dependent HUCC at 40% void fraction, in the DOM, with a C
lattice.


Placing a higher enrichment closer to the control blade location allowed for greater


power suppression and thus enhanced HUCC due to the increased control the blade


exhibited over the maximum power producing section of the lattice. Therefore though






43


enrichment perturbation was not limiting in HUCU###, distorting the enrichment

distribution had an effect on HUCC. Though SLCS does not depend on local or gross

enrichment perturbation, SDM is sensitive to this type of perturbation. However, the

designer may only enhance HUCU### by perturbing average enrichment of the entire

lattice therefore as long as the average of the enrichment of the lattice satisfies SLCS

requirements the enrichment may be perturbed to meet SDM without violating SLCS.














CHAPTER 4
MAXIMIZING HOT-COLD BORATED ko, DIFFERENCE UTILIZING
GADOLINIUM

There were four different isolated studies examined for the purpose of determining

the optimum strategies for utilizing gadolinium to enhance HUCU###. Gadolinium rods

were examined in a variety of clumped geometries in order to determine the lumped

spatial self-shielding effects. After the effects of self-shielding were determined, the

effects of increasing the amount of gadolinium rods on HUCU### were investigated.

Gadolinium concentration was next analyzed. Finally, gadolinium rod placement was

examined to determine the optimum gadolinium locations for enhancing HUCU###

without diminishing HUCC.

Spatial Self-Shielding Effects of Gadolinium Rods on HUCU###

Gadolinium rods were clumped in a variety of geometries to determine the effects

of lumped spatial self-shielding on HUCU###. Four samples of examined clumped

gadolinium rod geometries are displayed in figure 4-1. Clumping the gadolinium rods

decreased the BOL gadolinium worth because the gadolinium rods were effectively

spatially self-shielding each other from the impinging neutron flux. The self-shielding of

the gadolinium decreased the effective surface area utilized for neutron absorption [15].

Because the thermal-to-fast flux ratio was much higher in the cold state than in the hot

state more neutrons were likely to be thermally absorbed in the gadolinium in the cold

condition; therefore decreasing the effective surface area for neutron absorption decreases









the effectiveness of the power suppression from the gadolinium rods and thus decreasing

HUCU###.

Pattern 10 Pattern 11
12345678910 12345678910




6 WW ~ WW
7 W_ 7 wWW
8 _8 I--

10 9 10


Pattern 12 Pattern 13
1 2 34 5 6 7 8 910 1 2 3 45 67 8 910
1 1
2 -2
3 3 -- m-
4 WW 4 WW
5 WW 5 ww
6 WW V 6 vW w
7 WW 7 WW
8-- 8-m m
3 9
10 10


Figure 4-1. Four sample clumped geometries.

Figure 4-2 depicts the effects of gadolinium spatial self-shielding on gadolinium

worth. Highlighted in red are the patterns corresponding to those displayed in figure 4-1.

As gadolinium clumping increased, gadolinium worth decreased. Face adjacent

clumping of all four sides of a gadolinium rod resulted in a 38% decrease in gadolinium

worth, and face adjacent clumping of two sides resulted in a 19% decrease in gadolinium

worth. Diagonal face adjacent clumping lead to a 7% decrease in gadolinium worth.






















-0 05


| -0 15
E



S-0 2


Pattern

--HU Gad Worth -U-CUO Gad Worth CU660 Gad Worth CU 935 Gad Worth -*-CC Gad Worth

Figure 4-2. Corresponding 0 GWD/STU gadolinium worth for the patterns displayed in

figure 4-1.






0 12



01



008



S006
U


0 10 20 30 40 50 60 70
Exposure (GWDISTU)
-Pattern 10 -Pattern 11 Pattern 12 Pattern 13

Figure 4-3. Corresponding exposure dependent gadolinium clumping effects on

HUCU660 for the patterns displayed in figure 4-1.









Because clumping a group of gadolinium rods decreased the effective surface area

for absorption, the exposure time required to bum out the gadolinium increased. In figure

4-3 as clumping increased the exposure point in which gadolinium burns out also

increased. Also depicted in figure 4-3 is the decrease in HUCU### as a function of

increase clumping. Therefore in order to design an optimum lattice to enhance

HUCU### gadolinium rods must be spaced as far apart as reasonably achievable and face

adjacent and diagonal adjacent clumping must be eliminated.

The Effects of Increasing the Amount of Gadolinium Rods on HUCU###

In a power up-rate and an increased exposure cycle, extra positive reactivity must

be installed in the fuel bundle. Placing extra positive reactivity will cause a greater

skewing of the lattice power peaking as well as violating beginning of cycle critical

eigenvalue requirements. In order to decrease the beginning of cycle eigenvalue to the

critical requirements and decrease power peaking to improve lattice efficiency and meet

thermal margins, gadolinium must be placed in the fuel bundle. As more positive

reactivity is installed, more gadolinium rods at higher concentrations are needed.

The effects of increasing the amount of gadolinium rods in the lattice on

gadolinium worth are demonstrated in figure 4-4. The gadolinium rod placement

geometry was held constant while 8 to 18 rods were placed in the lattice. As the amount

of gadolinium rods placed in the lattice increased, the degree of gadolinium clumping

decreased due to the size limitations of the lattice. In the increase of 15 gadolinium rods

to 16 gadolinium rods, a clumped geometry was utilized that resulted in a decrease in

gadolinium worth. Each gadolinium rod insertion for the hot condition was worth -

0.0103 Ak/k while each gadolinium rod insertion in the CU660 case was worth -0.0095











Ak/k leading to 0.5 mAk/k difference in gadolinium worth between the hot and cold


lattice states.





0-


-0 05


2 -0 1


0
5 -0 15


o -02 -


-0 25


-0 3
8 9 10 11 12 13 14 15 16 17 18
Number of Rods

-4-HU Gad Worth -U-CUO Gad Worth CU660 Gad Worth CU935 Gad Worth -*-CC Gad Worth

Figure 4-4. The effects of increased number of gadolinium rods on the gadolinium worth
at 0 GWD/STU.

Increasing the amount of gadolinium rods decreased hot and cold k.o by increasing

the amount of neutrons removed from the system by absorption. HUCU### also

decreased as the number of gadolinium rods increased. Figure 4-5 displays BOL

decrease in HUCU660 as a function of increasing the amount of gadolinium rods placed

in the lattice.


The thermal-to-fast flux ratio is higher in the cold state than in the hot state due to


the cold states increased moderator density, and the thermal-to-fast flux ratio is lower in

higher boron concentration due to decreased thermal neutron availability after boron


capture. Gadolinium is dominantly a thermal neutron absorber therefore in the increased











thermal-to-fast flux ratio gadolinium was a more effective absorber. The decreased

thermal-to-fast flux in the hot state as compared to the cold borated states results in a

decrease in HUCU### as each gadolinium rod was inserted because the gadolinium was

worth more per rod insertion in the cold state than in the hot state.

Gadolinium rod worth was also a function of the boron concentration utilized in the

cold condition. At 0 GWD/STU HUCU660 changes -0.0017 per rod insertion (10-13

ppm boron equivalence) while HUCU935 changes -0.0025 per rod insertion (16-20 ppm

boron equivalence). This demonstrates that when a utility decides to go to a power up-

rate or increased exposure cycle, the increased amount of gadolinium needed to offset the

increased installed reactivity will result in a decrease in the HUCU### parameter on the

lattice level resulting in a decrease in SLCS margin on the core wide level.




012



01



0 08 -

y= -0.0025x+ 0.1197
S-- HUCU660
0 06 -


0 04 -
y = -0.0017x + 0.0703


002



0 2 4 6 8 10 12 14 16 18 20
Number of Gadolinium Rods

Figure 4-5. The effects of the number of gadolinium rods inserted on HUCU at 0
GWD/STU.











The Effects of Increasing the Gadolinium Concentration on HUCU###

The effects of increasing gadolinium concentration of a given gadolinium


configuration on HUCU### was next examined to determine if gadolinium concentration


was a design constraint for HUCU###. Increasing the gadolinium concentration of the


lattice had similar results to increasing the amount of rods in the lattice. Figure 4-6


displays the increase in gadolinium worth as a function of increasing concentration. For


CU660 at 0 GWD/STU a 1% increase in gadolinium concentration for 14 gadolinium


rods is worth -0.002343 Ak/k. For HU at 0 GWD/STU a 1% increase in gadolinium


concentration for 14 gadolinium rods is worth -0.004587 Ak/k.




0 -


-005 -


-0 1 -


-015-


-0 2 -


-0 25


-0 3
0% 1% 2% 3% 4% 5% 6% 7% 8% 9%
Gadolinium Concentration
-*-HU Gad Worth ---CUO Gad Worth CU660 Gad Worth CU935 Gad Worth -*-CC Gad Worth

Figure 4-6. The effect of increasing the gadolinium concentration for 14 gadolinium rods
on gadolinium worth at 0 GWD/STU.

The HU state exhibited 2 times greater worth in increasing 1% in gadolinium worth


than the CU state; therefore increasing the gadolinium concentration will decrease


HUCU###. Figure 4-7 exhibits the decrease in HUCU### as the gadolinium







51


concentration is increased. For a 1% Change In Concentration for 14 Gadolinium Rods


at 0 GWD/STU, HU660 changes -0.004504 (33 ppm boron equivalent) and HU935


changes -0.004906 (36 ppm boron equivalent).





0 12


01


0 08 -
y = -0.4906x + 0.1198

HUCU660
( 0 6 -
I--- HUCU935

0 04 -
y = -0.4504x + 0.0795

002


0
0% 1% 2% 3% 4% 5% 6% 7% 8% 9%
Gadolinium Concentration

Figure 4-7. The effect of increasing the gadolinium concentration of 14 gadolinium rods
on HUCU at 0 GWD/STU

The Importance of Gadolinium Rod Location

The lattice power distribution is never uniform. The effectiveness of gadolinium to


suppress power while increasing HUCU### was highly dependent upon the location in


the lattice in which the gadolinium was placed. Since many parameters contributed to the


power distribution within the lattice, determining an optimum location for gadolinium

placement resulted from satisfying all the parameters that were most limiting. The power


peaking distributions for the HU, CU### and CC states differed therefore determining an


optimum location for placing gadolinium involved placement in areas that maximized










improvement to the most limiting state without violating the parameter requirements of

the other states.

Two gadolinium rods were placed in series of different locations throughout the

lattice to determine the areas in which HUCU### and HUCC could be maximized (two

gadoliniums rods were used in order to preserve mirror symmetry of the lattice design).

Figure 4-8 presents the locations examined and corresponding case numbers of the

gadolinium location tests.


1 2 3 4 5 6 7 8 9 10

1

2 11

3 13

4 W W

5 W W

6 W W 18 20

7 W W19

8 11 18 21 23

9 13 20 23

10

Figure 4-8. Gadolinium rod placement diagram.

The effectiveness of the gadolinium placement was a function of the power

distribution. The power distribution was a function of the moderation ability and poison

geometry. In the CC state as gadolinium rods were placed further from the edges of the

control blade the worth of the gadolinium increased. This was due to the decreased

competition for neutrons between the gadolinium and the control blade. If the









gadolinium was placed to close to the control blade then effectively the gadolinium and

blade were spatially self-shielding each other and therefore decreased both of the

poisons' effective worth. In the CU### case, the difference in worth of a certain

gadolinium rod location was not a function of boron poison geometry (assuming no

clumping) because the boron poison geometry was uniform; however, the difference in

worth of certain gadolinium rod locations was related to the moderation capability of the

fuel lattice. Areas of the lattice exhibiting more moderation created more thermal

neutrons, leading to a higher power peaking. Gadolinium was worth more in these areas

of increased moderation capability due to the increased amount of thermal neutrons

available for absorption.

Figure 4-9 displays the difference in gadolinium worth as a function of gadolinium

location corresponding to the patterns in figure 4-8. Certain pattern changes caused

opposing worth differences in different temperature and boron geometry states. In the

change from pattern 4 to pattern 5 and in the change from pattern 15 to pattern 16, CC

gadolinium worth increased while CU660 and HU gadolinium worth decreased. In the

change from pattern 10 to pattern 11, CC gadolinium worth greatly decreased while

CU660 worth slightly decreased and HU worth slightly increased.

Placing a gadolinium rod in a higher power peaked area resulted in up to a 5%

increase in gadolinium worth. In the CC case, increasing the distance of the gadolinium

rod from the center of the control blade increased gadolinium worth by 0.00525 until the

water rods in the center of the lattice were reached. Once the water rods were reached in

the CC lattice (on the lower right diagonal half of the lattice), the power distribution and

gadolinium rod worth become independent of the effects of the control blade.







54



Altering a current lattice design to improve SDM and SLCS while maintaining HU


must include shifting gadolinium locations where both the CU### and CC states have the


most significant worth improvement while HU only has slight gadolinium worth increase.


Improving CC gadolinium worth involves placing the gadolinium away from the control


blade so that the gadolinium does not compete for neutrons with the boron in the control


blade for. Enhancing the CU### worth involves spacing out the gadolinium so that


spatial self-shielding does not occur and placing the gadolinium in the areas of highest


power peaking exhibited by the cold power shape (areas of greatest moderation


capabilities). Enhancing the HU worth also involves spacing out gadolinium and placing


them in areas of highest power peaking corresponding to the HU power shape. The


optimum gadolinium pattern for any given amount of gadolinium rods is the design that


meets all three of these criteria.





0

-0 005

-0 01

-0 015

S-002

-0 025

3 -003

-0 035

-0 04

-0 045

-0 05
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Pattern

-*-HU Gad Worth ---CUO Gad Worth CU660 Gad Worth CC Gad Worth

Figure 4-9. Gadolinium worth versus location for 0 GWD/STU, 7% gadolinium
concentration,









Fuel Lattice Design Conclusions

Certain parameters in the 2-dimensional fuel lattice design have a significant

contribution to HUCU###. Lattice enrichment may be utilized to enhance HUCU###.

While local lattice enrichment perturbations do not contribute to HUCU###, decreasing

the lattice average enrichment decreases the power distribution skewing of the lattice and

therefore increases HUCU###. However, with the demand for increased cycle lengths at

higher powers, unfortunately higher average enrichments are needed to meet these

requirements. Therefore with the needed increased average enrichment of the bundles

will result in an increase in power skewing of the lattice thus decreasing HUCU###.

The addition of competing thermal neutron poisons decreases HUCU###. Fuel

designs with a tighter pitch between fuel rods lead to an increased production of

plutonium. Plutonium is a competing thermal neutron poison. Therefore creating smaller

fuel rods with a tighter pitch may increase the heat transfer of the fuel bundle, but also wa

greater amount of plutonium is generated and therefore HUCU### is compromised. Also

utilization of mixed oxide fuels (MOX) introduces an increased plutonium inventory in

the core therefore further decreasing HUCU###.

Gadolinium is also a thermal neutron poison. Enough positive reactivity must be

installed into the reactor core at the beginning of cycle in order to meet the cycle length

requirements. Gadolinium must installed in each of the fuel bundles in order to make

sure that with the installed reactivity the reactor core is critical throughout operation.

Therefore though gadolinium competes for thermal neutrons thereby decreasing

HUCU###, it is a necessary component of reactor operation.

In order to enhance HUCU### while maintaining a cycle operation goal, only

certain fuel lattice parameters may be varied. Cycle length and power level is dependent









upon installed reactivity; therefore average enrichment of the fuel is a fixed parameter if

the number of fresh bundles utilized in the design is fixed. Plutonium production is

related to power level, fuel lattice pitch, and isotope content of the fuel. In most cases all

of those are fixed.

The only design parameter with room for enhancement is gadolinium. If

gadolinium is utilized effectively in certain locations of the fuel bundle, maximized

differences between the HU and CU### may be created; therefore HUCU### is

improved leading to an improvement in SLCS on the full core level. However, in

increased average enrichment cores more gadolinium rods are needed to meet critical

eigenvalue requirements; therefore resulting in fewer locations to manipulate gadolinium

rod placement for improvement in HUCU###. Therefore if gadolinium has already been

placed in the areas of maximized HUCU### enhancement further techniques must be

utilized on the full core level to enhance HUCU###.














CHAPTER 5
FULL CORE SLCS MODELING

The reference base reactor core analyzed was a generic BWR/3. The reactor core

was quarter core symmetric meaning that only a quarter of the full core had to be

modeled to accurately represent characteristics of the full core. Figure 5-1 was the base

reference core in which all perturbations were compared. Two different average bundle

enrichments of fresh fuel were loaded into the core for the investigated cycle. The high

enrichment bundles (fuel type 19) were 4.18% enriched, and the low enriched bundles

(fuel type 20) were 3.89% enriched.

Three major types of perturbations utilized to enhance SLC S were investigated on

the full core level. The perturbations were selected based on the knowledge generated

from the lattice physics analysis, and fell into two distinct characteristic types. The first

type involved making a perturbation to the entire bundle. Gadolinium rod placement

perturbations to the entire bundle were examined in order to determine the maximum

achievable enhancement to SLCS. The second type involved perturbing the axial power

shape. Based on the fact that average enrichment was also a dominant parameter in

enhancing HUCU### in the lattice physics calculations, axial power shaping techniques

utilizing enrichment differencing in certain axial zones was next examined to determine

the maximum achievable enhancement to SLCS by perturbing the cold axial power

shape. Gadolinium insertion in certain axial zones was also examined to determine if this

method was also effective in enhancing SLCS by perturbing the axial power shape

utilizing a poison.







58





33899 33557 32011 31230 29071
















7 Bundle Exposure6 6 6 6
33219 30031 26946 25807 26128 25187
6 6 6 7 7 7
33611 32365 30011 30073

33451 28541 29470 27398 27574

33992 33626 25332 25539

33476 33533
6 6Twice
34030 28585 25349

32422 29444 25517
6 7 6
29955 27372
7 7
33233 30085 27593

33890 30081
7 6
33527 26959
6 6
31928 25804
6 7
31253 26087
6 7
29057 25179
6 7






Bundle Exposure



Bundle Type Twice
Burned
Bundle


Figure 5-1. Reference base core fuel bundle loading map.

In each perturbation case the critical eigenvalue, thermal limits, and SDM were

monitored in order to determine if the enhancement to SLCS would violate the

requirements of these margins. Calculated eigenvalue was monitored for each case to


determine if calculated eigenvalue varied more than 0.001 Ak from the base case critical









eigenvalue. At BOC rods patterns may always be adjusted in order to make the reactor

critical and have critical eigenvalue deviate less than 0.001 Ak; however, at EOC when

all the rods are pulled out of the core and no other form of positive reactivity may exist in

the core to supply reactivity for criticality any decrease in critical eigenvalue as compared

from the base case resulted in loss of cycle exposure and decreases of cycle energy.

MFLPD was observed to make sure no perturbation resulted in a MFLPD greater than

0.909 as the BWR design basis requires. MFLCPR was also monitored to be certain that

no perturbation caused a MFLCPR to become greater than the design basis requirements

of 0.930.

A SLCS enhancement that leads to decreased cycle energy and results in loss of

cycle exposure was unacceptable due to the $ 1,000,000 at day cost involved in shutting

the reactor down early. Furthermore, a core that does not meet thermal limits may not be

licensed; therefore though SLCS may be improved through a certain modification, if that

modification leads to unacceptable thermal margin, the core will not be licensed to

operate. The optimum enhancement for SLCS involves an enhancement that meets

thermal limits and does not deplete EOC calculated eigenvalue.

Enhancing SLCS by Perturbing the Location of Gadolinium Rods

A gadolinium placement modification to certain lattice axial zones was made in

each fresh fuel type separately. The lattice physics calculations ensured that HUCU###

improved with enhanced gadolinium location loading; therefore applying the technique to

each fuel type individually determined the limiting effects of core radial and axial power

weighting incurred on the enhancement of SLCS. The gadolinium rods that were

interchanged were chosen based on the fact that the cold power peaking map displayed an










increased worth for the new rod locations while the hot power peaking displayed a lesser

change in worth. Figure 5-2 displays the base DOM gadolinium geometry and the areas

circled in red correspond to where the gadolinium pins were interchanged with normal

fuel pins in the perturbed cases. These perturbations were made to each axial zone

individually and then to the entire bundle for each fresh bundle type.

A B C D E F G H I J
1 1.60 2.80 3.20 3.95 3.95 3.95 3.95 3.95 3.95 2.80

2 2.80 2.80 3.20 3.95 3.60 3.95 3.95 3.95
S 0 -10
3 3.20 3.20 4 4.40 .0 4.40 0, 4.40 4.90
SOu __ IO uu IF. CI0 00
4 3.95 3.95 4.40 '3.95 WR 4.90 4.90 4.90 %U235
4 90 Enrichment
5 3.95 3.60 6 0 3.95 4.90 4.90 4.90 4.90

6 3.95 5 4.40 WR 4.9 4.90 4.90 0 4.90
800 -00 .
7 3.95 3.95 0 4.90 4.90 4.90 4.90 % Gadolinium
":'04
8 3.95 4.40 4.90 4.90 4.90 4.90 4.90
4 ------40 --40 0--40
9 3.95 3.95 4.90 4.90 : 4.90 c 4.90 4.90
3 8.0oo --oo
10 2.80 3.95 4.90 4.90 4.90 4.90 4.90 4.90 4.90 3.20


Figure 5-2. The perturbation diagram for the gadolinium rod perturbation cases.

SLCS margin was improved by the greatest amount when every axial zone

containing gadolinium was perturbed. Figure 5-3 displays the maximum SLCS

enhancement exhibited by each bundle type perturbation. Case 1 and Case 2 represent

perturbations made to every axial zone in the bundle containing gadolinium. Case 1

represents when the perturbation was only made to the high enrichment bundles, and

Case 2 represents when the perturbation was only made to the low enrichment bundles.

Case 1 exhibited a 0.0095 improvement in BOC SLCS margin while Case 2

exhibited a 0.0341 increase in BOC SLCS margin. The low enrichment bundles

represented 69% of the total loaded batch fraction and the majority of these bundles











resided in the high power peak locations in the interior core region; therefore any


perturbations made to these bundles demonstrated a more pronounced enhancement than


perturbations made to the high enrichment bundles.




004

0 035

0 03

0 025

002,

0015

001

0005

0
0 2000 4000 6000 8000 10000 12000 14000 16000
MWDISTU
-*-Base ----Case 1 -- Case 2 -*-Most Limiting Base SLCS


Figure 5-3. Exposure dependent SLCS for the reference base case, the case in which the
perturbation was made to only all of the fresh low enrichment bundles (case
2), and the case in which the perturbation was made to only all of the fresh
high enrichment bundles (case 1).

Though SLCS margin was enhanced, other limiting factors were greatly affected.


Table 5-1 displays the effects of the enrichment perturbation on eigenvalue, and


highlighted in red are the points in which eigenvalue deviated more than 0.001 Ak from


the critical eigenvalue. All exposure points ending in an A represented the exposure step


in which the control blade was shifted into the next pattern configuration. Due to the


slight increase in gadolinium utilization caused by the perturbation, BOC eigenvalue


decreased; and due to the saved positive reactivity from BOC, mid-cycle eigenvalue


increased. In order to increase BOC eigenvalue and decrease mid-cycle eigenvalue the










control blade patterns were manipulated to offset this reactivity imbalance. Table 5-2

displays the exposure dependent MFLPD. Case 2 improved most limiting MFLPD below

the most limiting base case MFLPD after the rod pattern adjustment. Table 5-3 displays

the exposure dependent MFLCPR. The most limiting MFLCPR in case 2 was also

improved below the base case after the rod pattern adjustment. Therefore after the

control blade adjustments were made both cases could meet critical eigenvalue

requirements, but only case 2 could also meet MFLPD requirements as well.

Table 5-1. Critical eigenvalue at specified exposure points for the gadolinium rod
location perturbation cases that exhibited greatest enhancement in SLCS.


Exposure
(MWD/STU)
0
181
907
1814
2722
2722A
3629
4536
5443
5443A
6350
7258
8165
8165A
9072
9979
10886
10886A
11794
12570
12701
13608
13608A
14061
14334
14570


Critical Eigenvalue


Base
1.0136
1.0142
1.0141
1.0128
1.0133
1.0122
1.0128
1.0118
1.0126
1.0119
1.013
1.012
1.0134
1.0123
1.0134
1.0135
1.0148
1.0147
1.0149
1.0163
1.0157
1.0159
1.0169
1.0159
1.0164
1.0163


Case 1
1.0123
1.0129
1.0129
1.0117
1.0123
1.0112
1.0119
1.0111
1.012
1.0113
1.0126
1.0117
1.0133
1.0122
1.0133
1.0135
1.0149
1.0148
1.0153
1.0168
1.0164
1.0168
1.0178
1.0168
1.0174
1.0173


Case 1 Fix
1.013
1.0139
1.0139
1.0125
1.0131
1.0112
1.0119
1.0111
1.0121
1.0114
1.0126
1.0118
1.0134
1.0123
1.0134
1.0136
1.0149
1.0148
1.0152
1.0167
1.0162
1.0165
1.0175
1.0165
1.0171
1.017


Case 2
1.0104
1.011
1.0111
1.0101
1.0108
1.0095
1.0104
1.0098
1.0108
1.0103
1.0116
1.0108
1.0126
1.0115
1.0129
1.0134
1.0153
1.0152
1.0163
1.0182
1.0179
1.0186
1.0195
1.0188
1.0195
1.0193


Case 2 Fix
1.0129
1.0146
1.0138
1.0124
1.0132
1.0126
1.0136
1.012
1.0134
1.012
1.0135
1.0125
1.0135
1.0123
1.0137
1.0138
1.0152
1.0152
1.0155
1.0169
1.0164
1.0167
1.0176
1.0167
1.0171
1.0169










Table 5-2. Exposure dependent MFLPD for the gadolinium rod location perturbation
cases that exhibited greatest enhancement in SLCS.


Exposure
(MWD/STU)
0
181
907
1814
2722
2722A
3629
4536
5443
5443A
6350
7258
8165
8165A
9072
9979
10886
10886A
11794
12570
12701
13608
13608A
14061
14334
14570


Base
0.846
0.845
0.806
0.807
0.781
0.742
0.714
0.717
0.703
0.838
0.849
0.847
0.889
0.847
0.852
0.784
0.683
0.72
0.704
0.704
0.704
0.854
0.734
0.841
0.746
0.763


Case 1
0.829
0.85
0.811
0.814
0.789
0.753
0.725
0.726
0.711
0.842
0.857
0.865
0.917
0.865
0.863
0.786
0.686
0.724
0.713
0.709
0.708
0.855
0.742
0.84
0.748
0.766


MFLPD
Case 1 Fix
0.815
0.832
0.796
0.803
0.778
0.754
0.724
0.726
0.71
0.84
0.853
0.859
0.912
0.859
0.863
0.791
0.685
0.729
0.711
0.706
0.705
0.851
0.738
0.834
0.741
0.759


Utilizing any type of gadolinium insertion will only enhance BOC SLCS. Though

BOC SLCS was enhanced in case 2 by gadolinium location improvement, once the

gadolinium burned out (-11,000 MWD/STU for this specific case) the perturbed case

became limiting again in SLCS. Therefore if SLCS is enhanced utilizing this method, the

designer must consider if the gadolinium burn out point is acceptable as well. If at the

gadolinium burn out point SLCS is not acceptable in magnitude, another method must be


utilized to enhance SLCS.


Case 2
0.866
0.858
0.82
0.821
0.795
0.753
0.729
0.734
0.72
0.858
0.878
0.884
0.923
0.892
0.887
0.806
0.699
0.717
0.718
0.73
0.736
0.878
0.762
0.871
0.789
0.805


Case 2 Fix
0.821
0.799
0.779
0.786
0.763
0.712
0.712
0.702
0.682
0.822
0.824
0.825
0.886
0.841
0.878
0.836
0.723
0.755
0.706
0.693
0.691
0.852
0.737
0.837
0.736
0.753










Table 5-3. Exposure dependent MFLCPR for the gadolinium rod
cases that exhibited greatest enhancement in SLCS.


location perturbation


Exposure
(MWD/STU)
0
181
907
1814
2722
2722A
3629
4536
5443
5443A
6350
7258
8165
8165A
9072
9979
10886
10886A
11794
12570
12701
13608
13608A
14061
14334
14570


MFLCPR


Base
0.711
0.721
0.726
0.737
0.741
0.73
0.736
0.729
0.734
0.773
0.775
0.731
0.732
0.745
0.746
0.754
0.767
0.757
0.79
0.824
0.825
0.829
0.825
0.822
0.822
0.808


Case 1
0.723
0.729
0.733
0.744
0.748
0.737
0.743
0.734
0.738
0.77
0.774
0.733
0.732
0.744
0.743
0.752
0.766
0.756
0.793
0.828
0.83
0.836
0.833
0.83
0.818
0.803


Case 1 Fix
0.727
0.727
0.733
0.741
0.744
0.737
0.743
0.734
0.738
0.77
0.774
0.734
0.732
0.744
0.743
0.751
0.764
0.754
0.792
0.828
0.829
0.834
0.831
0.828
0.814
0.8


Case 2
0.707
0.713
0.717
0.731
0.734
0.717
0.725
0.72
0.726
0.778
0.78
0.734
0.731
0.744
0.748
0.758
0.773
0.766
0.789
0.838
0.836
0.841
0.827
0.836
0.84
0.825


Case 2 Fix
0.714
0.715
0.72
0.721
0.727
0.744
0.754
0.736
0.744
0.767
0.769
0.735
0.737
0.75
0.749
0.752
0.763
0.755
0.785
0.817
0.818
0.821
0.817
0.815
0.816
0.802


Enhancing SLCS at the cost of SDM was not an acceptable option if SDM was

already a limiting constraint from the original design. Figure 5-4 demonstrates that the

modifications made to the low enriched fresh bundles did not diminish SDM below the

most limiting value of the base case. For this perturbation, BOC SDM was improved

0.0190 at the cost of decreasing EOC SDM; however, the decrease in EOC SDM did not

fall below the most limiting SDM value, and therefore the perturbation yielded


acceptable SDM consequence.














0 04

0 035

0 03

0 025

002

0015

001

0 005

0
0 2000 4000 6000 8000 10000 12000 14000 16000
MWDISTU
-*-Base --Case 1 -- Case 2 ---Most Limiting Base SDM

Figure 5-4. Exposure dependent SDM for the gadolinium rod location perturbation cases.

Utilizing a gadolinium location perturbation may be utilized to enhance BOC


SLCS. However, the magnitude of the improvement is limited by the ability to separate


the gadolinium and move it into areas of greater effective worth. As the amount of


gadolinium rods in the lattice increases, the ability to move gadolinium rods to more


effective locations decreases. As fuel bundle designs move to higher average


enrichments more gadolinium rods are needed in the fuel bundles to counteract the


increased installed reactivity. More gadolinium rods in the fuel bundle causes this


technique to be less effective due to the inability to move the gadolinium to locations of


greater effective worth due to the space constraints of the fuel lattice.


Axial Power Shape Characteristics

The base case most limiting power peak bundle location was bundle (15, 11).


Because lattice physics work determined that the DOM was the most limiting geometry


for HUCU###, decreasing the cold power peak in the DOM decreases SLCS.











The cold power shape and the hot power shape were not the same. Figure 5-5 is

the most limiting radial power peaking base case axial power distribution relative to its

radial power peaking. Superimposed in blue over figure 5-5 is an example of the cold

power shape. Though not to scale, the superimposition displays the difference in where

the power peaking resides in the two conditions. The BOC cold power shape was a

cosine shape peaked in the DOM, and the hot power shape was a modified Bessel

function peaked in the PSZ. Therefore in the axial power shape perturbations this

characteristic was utilized to maximize SLCS.


160 o,---






112 2 04 0 0 1 1 1 1
96
-4-Base (15,11)
0 ___________________ _______ -(15,10)
o -(14411)
(15, 12)
Calculated Hot Power Shape







0 02 04 06 08 1 12 14 16 18
Relative Power Peak

Figure 5-5. The base case hot axial power shape with superimposed cold axial power
shape.

Enhancing SLCS through Axial Power Shaping Utilizing Enrichment Differencing

The position of the cold axial power peak is the axial portion of the fuel bundle

exhibiting the least amount of power suppression in the cold condition; therefore the cold

axial power peak region is also the most limiting HUCU### region. As previously

displayed in figure 3-2, the DOM was the most limiting region for HUCU### due to the

decreased availability of borated water locations in the lattice. The VAN exhibited the










greatest HUCU### due to the increased availability to place borated water in the lattice

as a result of the vanished rod locations. Since the region of the cold axial power peak

was the most limiting in HUCU###, shifting the cold axial power peak out of the DOM

and into the VAN should increase SLCS.

The cold axial power peak may be decreased utilizing enrichment differencing in

the DOM and VAN. Figure 5-6 illustrates the goal of enrichment differencing. By

increasing the enrichment in the VAN and decreasing the enrichment in the DOM, the

DOM axial power peak is decreased thereby increasing SLCS.




N-T
N-V








PLE
--Decreased Power Peak in DOM Zone

Base Case Power Peak








Base Case

Perturbed Case Utilizing Axial Enrichment Differencing
NAT
Figure 5-6. Cold axial power shape perturbation diagram.

Axial power shaping, utilizing enrichment differencing, enhanced SLCS at BOC

and at the gadolinium burn out exposure point. Figure 5-7 displays the SLCS











enhancement utilizing axial power shape perturbation by enrichment differencing as well


as SLCS enhancement utilizing gadolinium placement perturbations. Case 11 was the


case that utilized enrichment differencing. Gadolinium perturbations enhanced SLCS


only at BOC; however, axial power shape perturbations utilizing enrichment differencing


in the DOM and VAN enhanced SLCS at both BOC and the gadolinium burn out


exposure point. The BOC SLCS margin enhancement utilizing enrichment differencing


was 0.035 and the gadolinium bum out exposure point enhancement was 0.0142.


Therefore if improvement in SLCS is necessary in both BOC and gadolinium burn out


exposure point the enrichment differencing method is the preferred method.




004

0 035

003

0025

0 02

0015

001

0005

0
0 2000 4000 6000 8000 10000 12000 14000 16000
MWDISTU
-*-Base ---Case 2 -A-Case 11 -*-Most Limiting Base SLCS

Figure 5-7. Exposure dependent SLCS for the gadolinium location perturbation case
(case 2) and axial power shape perturbation utilizing enrichment differencing
case (case 11) that exhibited the greatest enhancement in SLCS.

In the gadolinium perturbation case, the fresh bundles reached a maximum peak


power point once the gadolinium burned out. Once the gadolinium had burned out, the


main parameters affecting the cold power shape were the enrichment distribution and











axial leakage of the bundle. Since the axial leakage of the fuel bundle was a function of

axial height (a fixed parameter) and controlled utilizing top and bottom natural zones,

axial enrichment distribution was the main mode for altering the power shape at the

gadolinium burn out exposure point. Increasing the enrichment distribution in the VAN

and decreasing the enrichment in the DOM resulted in a decreased DOM cold power

peak at the gadolinium burn out exposure point due to the decreased availability of

enrichment in the DOM.

Figure 5-8 presents the SLCS enhancement as a function of enrichment difference

between the DOM and VAN. The maximum amount of SLCS margin enhancement for

BOC and the gadolinium burn out exposure point occurs at 0.30% enrichment difference

between the DOM and VAN.




004


0 035


003


0025


L 002


0015


001


0005 --Base (001) ---Case 17 (0 35) Case 11 (0 31) Case 18 (0 20)
---Case 19 (0 10) -- Case 20 (0 04) --Most Limiting Base SLCS

0 2000 4000 6000 8000 10000 12000 14000 16000
MWDISTU
Figure 5-8. SLCS enhancement utilizing different magnitudes of enrichment differencing
between the DOM and VAN.







70


An optimum enrichment difference arises from the fact that reactivity worth is a


flux weighted. As the enrichment was increased in the VAN, the flux increased in the


VAN; and as the enrichment decreases in the DOM, the flux decreases in the DOM.


Therefore the 0.30 enrichment difference represented the optimum decrease in flux


weighting of the DOM and increase in flux weighting of the VAN that resulted in the


greatest average cold borated negative reactivity insertion.


Axial power shaping utilizing enrichment differencing alters the hot power shape


and mode in which the core burns. The BOC hot axial power profile utilizing enrichment


differencing is displayed in Figure 5-9. By increasing the VAN zone enrichment while


decreasing the DOM zone enrichment, the DOM and PSZ zones exhibited a decrease in


power peak while the VAN zone experiences and increase in power peaking.


144 'r- Increased Ftw Peak In VAN Zone

128- -

112 ------




80^-- -------------------------------









16
64-


Decreaeed RFtwer Feak In DOMand PSZZones



32-

oI


Figure


-- se (15,11)
-U--(15,10)
(14,11)
(15,12)


0 02 04 06 08 1 12 14 16 18
Relative PaerPeak

-e 5-9. The hot axial power shape for maximum SLCS enhancement utilizing
enrichment differencing.









The change in axial power shape slightly altered the calculated eigenvalue and

thermal margins. Table 5-4 demonstrates that critical eigenvalue of the enrichment

perturbations case did not vary more than 0.001 k from the base case critical eigenvalue;

therefore utilizing this method did not warrant a rod pattern adjustment. The final

calculated eigenvalue for the enrichment differencing case was 0.0007 k less than the

critical base case eigenvalue; however, the increased mid cycle energy created could have

been suppressed by utilizing a rod pattern adjustment if determined necessary.

Table 5-4. Critical eigenvalue at specified exposure points for the gadolinium rod
location perturbation case and enrichment differencing case that exhibited
greatest enhancement in SLCS.
Exposure Critical Eigenvalue
(MWD/STU) Base Case 2 Fix Case 11
0 1.0136 1.0129 1.0142
181 1.0142 1.0146 1.0143
907 1.0141 1.0138 1.0143
1814 1.0128 1.0124 1.0128
2722 1.0133 1.0132 1.0133
2722A 1.0122 1.0126 1.013
3629 1.0128 1.0136 1.0136
4536 1.0118 1.012 1.0125
5443 1.0126 1.0134 1.0134
5443A 1.0119 1.012 1.0121
6350 1.013 1.0135 1.0133
7258 1.012 1.0125 1.0127
8165 1.0134 1.0135 1.0142
8165A 1.0123 1.0123 1.013
9072 1.0134 1.0137 1.0141
9979 1.0135 1.0138 1.014
10886 1.0148 1.0152 1.0153
10886A 1.0147 1.0152 1.0152
11794 1.0149 1.0155 1.015
12570 1.0163 1.0169 1.0162
12701 1.0157 1.0164 1.0156
13608 1.0159 1.0167 1.0153
13608A 1.0169 1.0176 1.0163
14061 1.0159 1.0167 1.0151
14334 1.0164 1.0171 1.0157
14570 1.0163 1.0169 1.0156









MFLPD for the axial power shaping utilizing enrichment differencing case also

was under the acceptable limit for all exposure points through out the cycle. Table 5-5

displays that most limiting MFLPD decreased by 0.026 from the base case. Therefore

utilizing this technique improves the MFLPD of the cycle.

Table 5-5. Exposure dependent MFLPD for the gadolinium rod location perturbation
case and the enrichment differencing case that exhibited greatest enhancement
in SLCS.


Exposure
(MWD/STU)
0
181
907
1814
2722
2722A
3629
4536
5443
5443A
6350
7258
8165
8165A
9072
9979
10886
10886A
11794
12570
12701
13608
13608A
14061
14334
14570


Base
0.846
0.845
0.806
0.807
0.781
0.742
0.714
0.717
0.703
0.838
0.849
0.847
0.889
0.847
0.852
0.784
0.683
0.72
0.704
0.704
0.704
0.854
0.734
0.841
0.746
0.763


MFLPD
Case 2 Fix
0.821
0.799
0.779
0.786
0.763
0.712
0.712
0.702
0.682
0.822
0.824
0.825
0.886
0.841
0.878
0.836
0.723
0.755
0.706
0.693
0.691
0.852
0.737
0.837
0.736
0.753


Case 11
0.825
0.834
0.792
0.799
0.771
0.718
0.7
0.699
0.681
0.827
0.83
0.819
0.863
0.818
0.839
0.793
0.69
0.735
0.707
0.692
0.691
0.829
0.72
0.805
0.718
0.728


Table 5-6 shows no significant difference realized in MFLCPR as compared with

the base case. Therefore utilizing this technique does not deplete the cores to meet any


thermal margin requirements.










Table 5-6. Exposure dependent MFLCPR for the gadolinium rod location perturbation
cases that exhibited greatest enhancement in SLCS.


Exposl
(MWD/5


ure MFLCPR
STU) Base Case 2 Fix Case 11
0.711 0.714 0.724


0
181
907
1814
2722
2722A
3629
4536
5443
5443A
6350
7258
8165
8165A
9072
9979
10886
10886A
11794
12570
12701
13608
13608A
14061
14334
14570


0.721
0.726
0.737
0.741
0.73
0.736
0.729
0.734
0.773
0.775
0.731
0.732
0.745
0.746
0.754
0.767
0.757
0.79
0.824
0.825
0.829
0.825
0.822
0.822
0.808


0.715
0.72
0.721
0.727
0.744
0.754
0.736
0.744
0.767
0.769
0.735
0.737
0.75
0.749
0.752
0.763
0.755
0.785
0.817
0.818
0.821
0.817
0.815
0.816
0.802


The effect of axial enrichment differencing had a similar effect on SDM as the

lattice geometric placement perturbation. Figure 5-10 displays the exposure dependence

effects of these perturbations on SDM at different exposure points. SDM for both

perturbations did not fall below the most limiting base case value; therefore both

enhancements may be utilized to enhance SLCS ifBOC SDM were to be in a limiting

condition. However, only axial power shaping utilizing enrichment differencing also

improves the gadolinium burn out exposure point limiting condition.


0.719
0.725
0.734
0.741
0.742
0.75
0.737
0.744
0.763
0.767
0.741
0.741
0.753
0.751
0.756
0.763
0.753
0.787
0.821
0.821
0.825
0.82
0.818
0.821
0.807














004

0 035

0 03

0 025

S002

0015

001

0005

0
0 2000 4000 6000 8000 10000 12000 14000 16000
MWDISTU
--Base ---Case 2 -A-Case 11 -+-Most Limiting Base SDM

Figure 5-10. Exposure dependent SDM for the gadolinium rod location perturbation case
and axial power shaping utilizing enrichment differencing case.

Enhancing SLCS by Means of Axial Power Shaping Utilizing Gadolinium Insertion

Enrichment differencing was not the only method for perturbing the axial power


shape in order to decrease the power peak in the DOM. Axial power shaping from the


utilization of an additional gadolinium pellets in certain axial zones was also analyzed in


order to determine if the negative reactivity insertion from adding additional gadolinium


was more favorable than shifting the axial enrichment distribution to create similar types


of perturbations. The concept of utilizing the negative reactivity of a gadolinium rod


insertion to decrease the power peak in the most limiting zone was similar to the concept


of decreasing enrichment in the most limiting axial zone. In both cases a negative


reactivity insertion in the limiting axial zone caused the power to peak to decrease in that


zone in which the gadolinium was inserted thus decreasing the worth of that axial zone to


SLCS.











As displayed in figure 4-5 increasing the amount of rods in a lattice decreased

HUCU###; however, ko of the lattice also decreased therefore leading to an improvement

of SLCS due to the decreased cold ko. Figure 5-11 displays the gain in BOC SLCS

utilizing a gadolinium rod insertion as compared with the other types of perturbations

examined. Case 26 represented a gadolinium insertion made in the PSZ, and Case 27

represented a gadolinium rod insertion made in the DOM. Because the cold power shape

peaks in the DOM, inserting a gadolinium rod into the PSZ does not have as drastic of an

effect on SLCS as placing a gadolinium rod in the DOM.




004

0 035

0 03

0025



0015

001

0005


0 2000 4000 6000 8000 10000 12000 14000 16000
MWDISTU
--Base ----Case 2 -A-Case 11 --Case 26 Case 27 --- Most Limiting Base SLCS

Figure 5-11. Exposure dependent SLCS for the gadolinium location perturbation case
(case 2), axial power shape perturbation utilizing enrichment differencing case
(case 11), inserting a gadolinium rod in the PSZ (case 26) and inserting a
gadolinium rod in DOM (case27) that exhibited the greatest enhancement in
SLCS.

The DOM gadolinium rod insertion yielded the greatest increase in BOC SLCS as

compared with the other perturbations. Inserting a gadolinium rod in the DOM enhanced

SLCS by 0.422 while inserting a gadolinium in the PSZ only enhanced SLCS by 0.189.










Table 5-7. Critical eigenvalue at specified exposure points for the gadolinium insertion
into the DOM (case 27) and gadolinium insertion into the PSZ (case 26) that
exhibited greatest enhancement in SLCS.


Exposure
(MWD/STU)
0
181
907
1814
2722
2722A
3629
4536
5443
5443A
6350
7258
8165
8165A
9072
9979
10886
10886A
11794
12570
12701
13608
13608A
14061
14334
14570


Critical Eigenvalue


Base
1.0136
1.0142
1.0141
1.0128
1.0133
1.0122
1.0128
1.0118
1.0126
1.0119
1.013
1.012
1.0134
1.0123
1.0134
1.0135
1.0148
1.0147
1.0149
1.0163
1.0157
1.0159
1.0169
1.0159
1.0164
1.0163


Case 26
1.0127
1.0129
1.0131
1.012
1.013
1.0121
1.0129
1.0121
1.013
1.0122
1.0133
1.0124
1.0139
1.0128
1.0137
1.0135
1.0146
1.0145
1.0143
1.0155
1.0148
1.0147
1.0156
1.0146
1.0151
1.015


Case 26f
1.0133
1.0136
1.0138
1.012
1.013
1.0121
1.0129
1.0121
1.013
1.0122
1.0133
1.0125
1.014
1.0128
1.0137
1.0135
1.0145
1.0145
1.0142
1.0161
1.0154
1.0151
1.0162
1.0149
1.0148
1.0146


Case 27
1.0116
1.012
1.0121
1.0111
1.0121
1.0112
1.0122
1.0116
1.0126
1.0118
1.0129
1.0119
1.0133
1.0122
1.0132
1.0134
1.0149
1.0148
1.0151
1.0165
1.0159
1.016
1.017
1.016
1.0167
1.0165


Placing negative reactivity into one region of the bundle without introducing

positive reactivity into some other region will cause a decrease in BOC eigenvalue.

Therefore a rod pattern change was utilized in this method in order to achieve acceptable

BOC eigenvalue requirements. Table 5-7 displays the calculated eigenvalue as compared

with the base case for inserting a gadolinium rod in the DOM zone and in the PSZ before.

Inserting a gadolinium rod in the PSZ greatly reduced the BOC reactivity of the

bundle; therefore the rod patterns had to be adjusted to meet the BOC condition. The


Case 27f
1.013
1.0139
1.0141
1.0121
1.0131
1.0119
1.013
1.0117
1.0128
1.0119
1.0131
1.0121
1.0136
1.0124
1.0134
1.0135
1.0147
1.0147
1.0147
1.016
1.0154
1.0154
1.0164
1.0153
1.016
1.0158











decrease in integrated power realized in the bundle due to the gadolinium insertion in the

PSZ caused the core to fall 0.0017 k short of EOC critical eigenvalue requirements.

However, inserting a gadolinium rod in the DOM zone caused only a 0.0005 k decrease

in EOC critical eigenvalue.

Distorting the hot axial power shape altered the thermal margins of the core.

Figure 5-12 and figure 5-13 displays the distorted hot axial power shape caused from

inserting a gadolinium rod in the PSZ and in the DOM.


160





128 "


112

S96 __
-+-Base (15,11)
0
S8_ --(15,10)
o (14,11)
1, (15,12)
S64


48


32----


16 -_



0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Relative Power Peak

Figure 5-12. The hot axial power shape of the most power peaked fuel bundle caused by
inserting a gadolinium rod into the PSZ.

When inserting a gadolinium rod into the PSZ, the decreased power peak in the

PSZ causes the hot axial power shape to flatten. When inserting a gadolinium rod into







78


the DOM, the extreme decreased power peak in the DOM leads to an increased relative

power peak in the PSZ.


160 ---


14 4 -------


128 "


112


---96 /
o= --Base (15,11)
S80Y --(15,10)
0o (14,11)
(15,12)
64 ---


4 8 ----------------_-----


3 2 ----------------------_





0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Relative Power Peak

Figure 5-13. The hot axial power shape of the most power peaked fuel bundle caused by
inserting a gadolinium rod into the DOM.

Table 5-8 displays MFLPD for the PSZ and DOM gadolinium insertions as

compared to the base case. Inserting a gadolinium rod in the PSZ decreased BOC

MFLPD by 0.083, and also decreased most limiting MFLPD by 0.033. However,

inserting a gadolinium rod in the DOM yielded no significant enhancement in MFLPD.

In both cases there was no significant alteration in MFLCPR as displayed in table 5-9.

Therefore inserting an extra gadolinium rod into a certain axial zone of the fuel bundle

does not hinder the ability to meet thermal margins.









Table 5-8. MFLPD at specified exposure points for the gadolinium insertion into the
DOM (case 27) and gadolinium insertion into the PSZ (case 26) that exhibited
greatest enhancement in SLCS.


Exposure
(MWD/STU)
0
181
907
1814
2722
2722A
3629
4536
5443
5443A
6350
7258
8165
8165A
9072
9979
10886
10886A
11794
12570
12701
13608
13608A
14061
14334
14570


Base
0.846
0.845
0.806
0.807
0.781
0.742
0.714
0.717
0.703
0.838
0.849
0.847
0.889
0.847
0.852
0.784
0.683
0.72
0.704
0.704
0.704
0.854
0.734
0.841
0.746
0.763


Case 26
0.771
0.772
0.748
0.768
0.765
0.707
0.710
0.722
0.698
0.827
0.827
0.816
0.861
0.807
0.841
0.812
0.710
0.757
0.716
0.677
0.677
0.838
0.703
0.821
0.719
0.736


MFLPD
Case 26f
0.763
0.762
0.738
0.768
0.765
0.706
0.709
0.722
0.697
0.825
0.824
0.813
0.856
0.804
0.839
0.815
0.713
0.761
0.722
0.684
0.684
0.866
0.720
0.859
0.710
0.727


Case 27
0.873
0.875
0.832
0.829
0.790
0.746
0.716
0.718
0.703
0.840
0.855
0.853
0.894
0.854
0.849
0.776
0.687
0.715
0.712
0.714
0.709
0.841
0.749
0.822
0.744
0.755


Case 27f
0.847
0.839
0.795
0.811
0.776
0.738
0.707
0.718
0.700
0.836
0.845
0.840
0.882
0.840
0.850
0.789
0.688
0.727
0.711
0.705
0.702
0.831
0.741
0.807
0.737
0.749


Therefore when a


designer chooses to utilize this method for enhancing SLCS, the


designer must decide which parameters are most necessary for achieving the required

result. If the designer is experiencing limiting MFLPD and willing to compromise cycle

energy to meet this requirement, then placing a gadolinium rod in the PSZ is the better

choice. If the designer does not have limiting MFLPD, then inserting a gadolinium rod in

the DOM zone is the better choice. Therefore the choice of one method or the other

depends on the thermal margins and the critical eigenvalue requirements.










Table 5-9. MFLCPR at specified exposure points for the gadolinium insertion into the
DOM (case 27) and gadolinium insertion into the PSZ (case 26) that exhibited
greatest enhancement in SLCS.


Exposure
(MWD/STU)
0
181
907
1814
2722
2722A
3629
4536
5443
5443A
6350
7258
8165
8165A
9072
9979
10886
10886A
11794
12570
12701
13608
13608A
14061
14334
14570


Base
0.711
0.721
0.726
0.737
0.741
0.73
0.736
0.729
0.734
0.773
0.775
0.731
0.732
0.745
0.746
0.754
0.767
0.757
0.79
0.824
0.825
0.829
0.825
0.822
0.822
0.808


Case 26
0.712
0.708
0.717
0.728
0.737
0.724
0.733
0.729
0.738
0.772
0.775
0.741
0.741
0.752
0.748
0.751
0.758
0.748
0.786
0.819
0.819
0.824
0.818
0.817
0.81
0.796


MFLCPR
Case 26f
0.715
0.712
0.721
0.728
0.737
0.724
0.733
0.729
0.738
0.772
0.775
0.742
0.742
0.752
0.748
0.75
0.757
0.747
0.786
0.818
0.818
0.822
0.815
0.814
0.805
0.791


SDM was neither greatly enhanced nor greatly decreased utilizing gadolinium

insertion. Figure 5-14 displays SDM as a function of exposure for the base case and all

three types of perturbations. Therefore if a designer was limited in EOC SDM then

inserting a gadolinium rod should be utilized in order to enhance BOC SDM.

The decision to enhance SLCS margin by inserting a gadolinium rod into a certain

axial zone of a fuel bundle is dependent upon the preexisting limiting conditions of the

fuel design. If the fuel designer decides that maximizing BOC SLCS without concern for


Case 27
0.694
0.683
0.692
0.711
0.724
0.708
0.723
0.723
0.732
0.771
0.774
0.73
0.73
0.742
0.745
0.754
0.768
0.758
0.79
0.824
0.825
0.829
0.825
0.822
0.824
0.809


Case 27f
0.692
0.683
0.695
0.709
0.723
0.717
0.732
0.724
0.734
0.77
0.773
0.733
0.733
0.744
0.744
0.751
0.763
0.753
0.789
0.823
0.823
0.826
0.822
0.819
0.815
0.8











SLCS at the gadolinium bum out exposure point is the most limiting design


characteristic, then inserting a gadolinium rod into the DOM will suffice as a solution to


enhancing BOC SLCS margin. If the designer cannot afford loss in EOC SDM, and only


needs a minimal improvement in thermal margins as well as minimally enhanced BOC


SLCS, then adding a gadolinium in PSZ at the cost of cycle energy may be an adequate


solution to enhancing BOC SLCS.




004

0 035

003

0 025

002

0015

001 -

0005

0
0 2000 4000 6000 8000 10000 12000 14000 16000
MWDISTU
--Base -E-Case 2 --&Case 11 ---Case 26 -- Case 27 -I-Most Limiting Base SDM

Figure 5-14. Exposure dependent SDM for the gadolinium rod location perturbation
case, axial power shaping utilizing enrichment differencing case and the axial
power shaping utilizing gadolinium placement case.

Enhancing BOC SLCS margin utilizing gadolinium perturbations may cause the


gadolinium burn out exposure point to become the most limiting in SLCS. If SLCS at the


gadolinium burn out exposure point is of acceptable magnitude, then the designer has


utilized an acceptable technique for enhancing SLCS. If, however, SLCS at the


gadolinium burn out exposure point is of unacceptable magnitude, then the gadolinium


insertion techniques are not feasible methods for improving SLCS. Therefore the






82


decision to utilize this method is solely dependent upon the limitations of the gadolinium

burn out exposure point.














CHAPTER 6
CONCLUSIONS

SLCS is a core wide phenomenon that is dependent upon the HUCU###

characteristics of each fuel bundle. Introducing fresh bundles into the core with

inherently enhanced HUCU### characteristics will improve SLCS. HUCU### is

improved by manipulating design parameters on the lattice design level as well as in the

full core design. Therefore understanding the most limiting design parameters in both

design aspects and the capability of those parameters to increase HUCU### is paramount

to improving SLCS.

The ability of a certain type of fuel lattice design perturbation to enhance SLCS

was determined by the limiting characteristics of that lattice perturbation. HUCU###

was highly dependent upon average enrichment. As average enrichment of the fuel

bundle was increased HUCU### decreased thereby decreasing SLCS on the full core

level. Increasing enrichment has a greater impact per percent increase of reactivity in the

cold, collapsed void lattice state then in the hot Doppler broadened voided operating

state. Localized enrichment perturbations did not affect HUCU### therefore when a

designer creates a lattice with SLCS in mind they need only be concerned with the

average enrichment of the lattice and not how the local enrichment is schemed.

Gadolinium rods also had a significant impact on HUCU### lattice behavior and

therefore significantly impacted SLCS. Gadolinium geometries that were clumped and

incurred significant spatial self-shielding decreased HUCU### while gadolinium

geometries that were spread out limiting the self-shielding exhibited an increased









HUCU###. Increasing the amount of gadolinium rods in the fuel lattice decreased

relative HUCU###; however, inserting the gadolinium also reduced k- thereby actually

improving SLCS by decreasing the worth of the bundle to the entire core. Therefore

increasing the amount of gadolinium rods in the bundle had a diminishing return.

Increasing the gadolinium concentration also decreased the relative HUCU###; however,

increasing the gadolinium concentration also reduced k- thereby also improving SLCS

for the whole core. Optimum locations for gadolinium rod placement exist for certain

amounts of gadolinium rods. These optimum placement locations are realized by

understanding the difference in power peaking between the hot and cold homogenously

enriched power shapes (the power shape realized explicitly from geometry of the fuel

bundle and flux level) and placing gadolinium rods in areas where the difference in

power peak between the two states is the greatest.

After understanding the 2-dimensional lattice physics calculations, perturbations

were made to fuel bundles in the full core simulator in order to determine effects on full

core criticality and thermal limits. Perturbing the placement of the gadolinium rods in

order to maximize gadolinium worth utilized in the cold borated condition improved

BOC SLCS at the expense of decreased BOC critical eigenvalue. Therefore after

perturbing gadolinium locations to maximize negative reactivity, the control blade

patterns must be adjusted in order to introduce enough positive reactivity in the hot

condition to meet the critical eigenvalue requirements. Perturbing the axial enrichment

distribution in order to decrease the power peaking in the axial zone most limiting to

HUCU### decreased that axial zones flux importance to the SLCS calculation and

thereby improved both the BOC and the gadolinium burn out exposure point SLCS.









However, utilizing this method causes an increased complexity in manufacturing of the

bundle and therefore leading to an increased production cost. Inserting an extra

gadolinium rod into a certain axial zone in order to also perturb the axial power shape

improved BOC SLCS without decreasing EOC SDM. However, utilizing gadolinium

perturbations only helped improve the BOC SLCS and did not enhance the gadolinium

burn out exposure point SLCS.

SLCS may always be improved by increasing the boron concentration or boron

enrichment in the SLCS tank. However, if the utility is limited by time, cost or

aggravation then utilizing an acceptable design technique in order to enhance SLCS

margin is solely dependent upon the limiting characteristics of the core behavior and the

acceptable sacrifice in margin of those parameters.

Unfortunately, not all core situations will have a possible remedy for SLCS. The

greatest increase in BOC SLCS utilizing any of the mentioned techniques was roughly

0.5% and the gadolinium burnout point maximum improvement was 0.14%. Therefore

utilities exhibiting marginal SLCS fuel design difficulties that wish to have power output

increases in their following cycles, increasing the average enrichment and gadolinium

content in their core, will need to understand the limitations of the inherent fuel design.

Utilities must then realize that an increase in boron concentration of their SLCS tank or

utilizing enriched boron is needed if they wish to accommodate SLCS while not incurring

the extra cost per cycle of loading extra bundles to flatten the power distribution and

reduce SLCS.














CHAPTER 7
FUTURE WORK

The purpose of this study was to conduct a sensitivity analysis in order to

determine limiting fuel design characteristics for SLCS. The methodology developed by

Yasushi Hirano, Kazuki Hida, Koichi Sakurada and Munenari Yamamoto utilized a fixed

gadolinium pattern and then generated an optimal enrichment distributions for a 2-

dimensional BWR fuel lattice [10]. Since this study proved that radial enrichment

distribution was not a factor in SLCS and that SLCS was only limited by average

enrichment, the possibility exists to expand on the enrichment distribution tool and

develop a tool that determines an optimum SLCS gadolinium placement for a given

lattice average enrichment. The tool would basically compare homogenously enriched

hot and cold lattice power distributions and determine an optimum gadolinium scheme

based on the maximum difference in the two power distributions. Because the placement

of the gadolinium for SLCS is basically decoupled from the enrichment distribution, this

problem does not become over-constrained, and therefore it is possible to obtain an

optimum gadolinium configuration for SLCS while creating an optimum enrichment

distribution for thermal limit and fuel efficiency requirements.

The optimum enrichment distribution methodology was also a 2-dimensional

methodology. This study concluded that axial enrichment and gadolinium perturbations

may be utilized to improve SLCS. In modem core design strategy 2-dimensional lattice

calculations are completed and then the group constants from the 2-dimensional codes are

utilized by the full core simulators because of computational time constraints and









memory requirements of the processor. With computers getting faster and distributed

parallel computing schemes becoming more optimized, core design may reach a point

where full 3-dimensional bundles are modeled assuming an infinite bundle approximation

(or a more brilliant scheme) to get group constants for the full core simulator. When this

technology is available, utilizing the design criteria from this study for the SLCS portion,

a full bundle axial and radial enrichment and gadolinium configuration optimization

methodology may be devised that creates the optimum fuel bundle for SLCS, SDM,

thermal margin and fuel utilization. This will create an automated core design

environment thus freeing the designer's time to allow for examination of other pressing

issues in the design strategy.
















LIST OF REFERENCES


1. Aoyama, Mooto, Sadao Uchikawa and Renzo Takeda, "Reactivity Control Method
for Extended Burnup of Boiling Water Reactor Fuel Bundles," Journal of Nuclear
Science and Technology, 26, pp.403-410, April 1989.

2. Cochran, Robert and Nicholas Tsoulfanidis, The Nuclear Fuel Cycle: Analysis and
Management, American Nuclear Society, La Grange Park, Illinois, 1999.

3. Dresner, Lawerance, Resonance Absorption in Nuclear Reactors, Pergamon Press,
New York, New York, 1976.

4. Duderstadt, James and Louis Hamilton, Nuclear Reactor Analysis, John Wiley &
Sons, Inc., New York, New York, 1976

5. General Electric Company, "TGBLA06A; General Electric Lattice Physics
Method," DRF A00-05526, October, 1994. (Proprietary Information)

6. General Physics Corporation, "BWR Generic Fundamentals: Chapter 9 Core
Thermal Limits," Columbia, Maryland 1993. (Proprietary Information)

7. Glasstone, Samuel and Walter H. Jordan, Nuclear Power and its Environmental
Effects, American Nuclear Society, La Grange Park, Illinois, 1980.

8. Global Nuclear Fuels, "PANAC11 User's Manual," UM-0021 Rev. 1, February
2001. (Proprietary Information)

9. Hida, Kazuki and Ritsuo Yoshioka, "Optimal Axial Enrichment Distribution of the
Boiling Water Reactor Fuel Under the Haling Strategy," Nuclear Technology, 80,
pp. 423-430, March 1988.

10. Hirano, Yasushi, Kazuki Hida, Koichi Sakurada, and Munenari Yamamoto,
"Optimization of Fuel Rod Enrichment Distribution to Minimize Rod Power
Peaking throughout Life with BWR Fuel Assembly," Journal of Nuclear Science
and Technology, 34, pp. 5-12, January 1997.

11. Kazimi, Mujid and Neil Todreas, Nuclear Systems 1: Thermal Hydraulic
Fundamentals, Taylor and Francis, Bristol, PA, 1993

12. Lahey, R.T. and F.J. Moody, The Thermal Hydraulics of a Boiling Water Nuclear
Reactor, American Nuclear Society, La Grange Park, Illinois, 1979.