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Development of a Calculation Methodology to Determine Detector Response in a Spent Fuel Pool

Permanent Link: http://ufdc.ufl.edu/UFE0041319/00001

Material Information

Title: Development of a Calculation Methodology to Determine Detector Response in a Spent Fuel Pool
Physical Description: 1 online resource (93 p.)
Language: english
Creator: Walters, William
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: detector, fuel, importance, monitoring, multiplication, nuclear, proliferation, spent, subcritical
Nuclear and Radiological Engineering -- Dissertations, Academic -- UF
Genre: Nuclear Engineering Sciences thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In this thesis we present a methodology for predicting the response of neutron and gamma detectors in a spent fuel pool (e.g., the Atucha-I reactor) with the aim of detecting gross misinformation (i.e., a missing or stolen fuel assembly). We expand on previous work by Ham et al. To begin, the intrinsic decay sources of the spent fuel is calculated as a function of burnup and time. The burnup distribution in the fuel assembly under reactor conditions was calculated using a combination of ORIGEN-ARP depletion code and the MCNP Monte Carlo code. This calculation shows the non-linearity of the neutron source as a function of burnup and also takes into account the decay time, both of which were ignored previously. The sub-critical multiplication is calculated in the spent fuel pool by using a simplified fission matrix approach. The multiplication factor was found to be as high as ~2 and showed significant spatial variation. The detector response was calculated using the detector importance methodology. The adjoint transport equation was solved using the PENTRAN Sn transport code. This importance calculation showed that ~87% of the neutron response comes from the surrounding 4 assemblies (i.e. one assembly in each direction) and 99% comes from the nearest 16 (i.e. a distance of 2 assemblies in each direction). This contrasts the previous assumption that 100% of the response came from the 4 adjacent assemblies. This detector Field-Of-View (FOV) was relatively insensitive to detector position, showing ~5% difference for a detector at the edge of the pool vs. the middle of the pool. Assembly burnup was also not a large factor, showing less than ~5% difference between a fresh assembly and one at full burnup. These results were combined to look at the predicted detector response for several hypothetical pool configurations. These configurations included the replacement of an assembly with either an inert dummy or a fresh assembly, replacement of several assemblies in a checkerboard pattern and attempted masking of a dummy assembly with a high burnup one. In all of these configurations the changes would be visible for a detector placed adjacent to the assemblies of interest, or on one of the corner assemblies for the checkerboard arrangement. A ratio of neutron response to gamma response was also investigated, but seemed less sensitive to different configurations than that of neutron signal only.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by William Walters.
Thesis: Thesis (M.S.)--University of Florida, 2009.
Local: Adviser: Haghighat, Alireza.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041319:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041319/00001

Material Information

Title: Development of a Calculation Methodology to Determine Detector Response in a Spent Fuel Pool
Physical Description: 1 online resource (93 p.)
Language: english
Creator: Walters, William
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: detector, fuel, importance, monitoring, multiplication, nuclear, proliferation, spent, subcritical
Nuclear and Radiological Engineering -- Dissertations, Academic -- UF
Genre: Nuclear Engineering Sciences thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In this thesis we present a methodology for predicting the response of neutron and gamma detectors in a spent fuel pool (e.g., the Atucha-I reactor) with the aim of detecting gross misinformation (i.e., a missing or stolen fuel assembly). We expand on previous work by Ham et al. To begin, the intrinsic decay sources of the spent fuel is calculated as a function of burnup and time. The burnup distribution in the fuel assembly under reactor conditions was calculated using a combination of ORIGEN-ARP depletion code and the MCNP Monte Carlo code. This calculation shows the non-linearity of the neutron source as a function of burnup and also takes into account the decay time, both of which were ignored previously. The sub-critical multiplication is calculated in the spent fuel pool by using a simplified fission matrix approach. The multiplication factor was found to be as high as ~2 and showed significant spatial variation. The detector response was calculated using the detector importance methodology. The adjoint transport equation was solved using the PENTRAN Sn transport code. This importance calculation showed that ~87% of the neutron response comes from the surrounding 4 assemblies (i.e. one assembly in each direction) and 99% comes from the nearest 16 (i.e. a distance of 2 assemblies in each direction). This contrasts the previous assumption that 100% of the response came from the 4 adjacent assemblies. This detector Field-Of-View (FOV) was relatively insensitive to detector position, showing ~5% difference for a detector at the edge of the pool vs. the middle of the pool. Assembly burnup was also not a large factor, showing less than ~5% difference between a fresh assembly and one at full burnup. These results were combined to look at the predicted detector response for several hypothetical pool configurations. These configurations included the replacement of an assembly with either an inert dummy or a fresh assembly, replacement of several assemblies in a checkerboard pattern and attempted masking of a dummy assembly with a high burnup one. In all of these configurations the changes would be visible for a detector placed adjacent to the assemblies of interest, or on one of the corner assemblies for the checkerboard arrangement. A ratio of neutron response to gamma response was also investigated, but seemed less sensitive to different configurations than that of neutron signal only.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by William Walters.
Thesis: Thesis (M.S.)--University of Florida, 2009.
Local: Adviser: Haghighat, Alireza.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041319:00001


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c Created on: Wednesday, May 21, 2008 at 14:43 c CELLS c 0.838 mod density c 0.979 mod (outside) c 10.6 uo2 dens c 6.5 zr dens c 5.985 homogenized clad/gap zr dens c OUTSIDE OF TUBE 1 3 0.979 104 21 22 31 32 11 12 imp:n=1 $mod outside tube c COOLANT TUBE 2 2 6.5 101 102 11 31 42 imp:n=1 $inside tube 3 0 10 2 103 11 31 42 imp:n=1 $annulus gas 4 2 6.5 103 104 11 31 42 imp:n=1 $outside tube c OUTSIDE WORLD 10 0 11:42:21:22:31:32 imp:n=0 $outside world c UPPER MODERATOR 5 3 0.979 12 42 104 21 22 31 32 imp:n=1 $upper mod 6 3 0.838 12 42 101 21 31 imp:n=1 c INNER MODERATOR 7 3 0.838 101 11 12 31 112 212 222 232 242 312 322 332 342 352 362 412 422 432 442 452 462 472 482 492 402 imp:n=1 $mod inside tube c R0 11 1 10.6 111 11 12 31 imp:n=1 $pin 1 12 2 5.985 111 112 11 12 31 imp:n=1 c R1 111 1 10.6 211 11 12 31 imp:n=1 112 2 5.985 212 211 11 12 31 imp:n=1 121 1 10.6 221 11 12 imp:n=1 122 2 5.985 222 221 11 12 imp:n=1 131 1 10.6 231 11 12 imp:n=1 132 2 5.985 232 231 11 12 imp:n=1 141 1 10.6 241 11 12 31 imp:n=1 142 2 5.985 242 241 11 12 31 imp:n=1 c R2 211 1 10.6 311 11 12 imp:n=1 212 2 5.985 312 311 11 12 imp:n=1 221 1 10.6 321 11 12 imp:n=1 222 2 5.985 322 321 11 12 imp:n=1 231 1 10.6 331 11 12 imp:n=1 232 2 5.985 332 331 11 12 imp:n=1 241 1 10.6 341 11 12 imp:n=1 242 2 5.985 342 341 11 12 imp:n=1 251 1 10.6 351 11 12 imp:n=1 252 2 5.985 352 351 11 12 imp:n=1 261 1 10.6 3 61 11 12 imp:n=1 262 2 5.985 362 361 11 12 imp:n=1 c R3 3 11 1 10.6 411 11 12 imp:n=1 312 2 5.985 412 411 11 12 imp:n=1 321 1 10.6 421 11 12 imp:n=1 322 2 5.985 422 421 11 12 imp:n=1 331 1 10.6 431 11 12 imp:n=1

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332 2 5.985 432 431 11 12 imp:n=1 341 1 10.6 441 11 12 imp:n=1 342 2 5.985 442 441 11 12 imp:n=1 351 1 10.6 451 11 12 imp:n=1 352 2 5.985 452 451 11 12 imp:n=1 361 1 10.6 461 11 12 imp:n=1 362 2 5.985 462 461 11 12 imp:n=1 371 1 10.6 471 11 12 imp:n=1 372 2 5.985 472 471 11 12 imp:n=1 381 1 10.6 481 11 12 imp:n=1 382 2 5.985 482 481 11 12 imp:n=1 391 1 10.6 491 11 12 31 imp:n=1 392 2 5.985 492 491 11 12 31 imp:n=1 c STRUCT PIN c 3101 1 10.6 401 11 12 31 imp:n=1 3102 2 6.5 402 11 12 31 imp:n=1 c SURFACES *11 pz 0 12 pz 265 *21 p 1.0 0.57735027 0 15.703927 $ pitch/2 / cos30 *22 p 1.0 0.57735027 0 15.703927 *31 py 0 *32 py 13.6 c 61 p 1.0 0.57735027 0 0 c 62 p 1.0 0.57735027 0 0 c 41 pz 100 42 pz 315 51 pz 26.5 5 2 pz 53 53 pz 79.5 54 pz 106 55 pz 132.5 56 pz 159 57 pz 185.5 58 pz 212 59 pz 238.5 101 c/z 0 0 5.410 102 c/z 0 0 5.582 103 c/z 0 0 5.750 104 c/z 0 0 5.790 c r0 111 c/z 0 0 0.535 112 c/z 0 0 0.595 c r1 221 c/z 0.811 1.4047 0.535 222 c/z 0.811 1.4047 0.595 211 c/z 1.622 0 0.535 212 c/z 1.622 0 0.595 231 c/z 0.811 1.4047 0.535 232 c/z 0.811 1.4047 0.595 241 c/z 1.622 0 0.535 242 c/z 1.622 0 0.595 c r2 311 c/z 2.9654 0.7946 0.535 312 c/z 2.9654 0.7946 0.595 331 c/z 0.7946 2.9654 0.535

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332 c/z 0.7946 2.9654 0.595 321 c/z 2.1708 2.1708 0.535 322 c/z 2.1708 2.1708 0.595 361 c/z 2.9654 0.7946 0.535 362 c/z 2.9654 0.7946 0.595 341 c/z 0.7946 2.9654 0.535 342 c/z 0.7946 2.9654 0.595 351 c/z 2.1708 2.1708 0.535 352 c/z 2.1708 2.1708 0.595 c r3 c 401 c/z 4.553 0 0.535 402 c/z 4.553 0 0.595 411 c/z 4.2784 1.5572 0.535 412 c/z 4.2784 1.5572 0.595 431 c/z 2.2765 3.943 0.535 4 32 c/z 2.2765 3.943 0.595 421 c/z 3.4878 2.9266 0.535 422 c/z 3.4878 2.9266 0.595 441 c/z 0.7906 4.4838 0.535 442 c/z 0.7906 4.4838 0.595 491 c/z 4.553 0 0.535 492 c/z 4.553 0 0.595 481 c/z 4.2784 1.5572 0.535 482 c/z 4.2784 1.5572 0.595 461 c/z 2.2765 3.943 0.535 462 c/z 2.2765 3.943 0.595 471 c/z 3.4878 2.9266 0.535 472 c/z 3.4878 2.9266 0.595 451 c/z 0.7906 4.4838 0.535 4 52 c/z 0.7906 4.4838 0.595 c c DATA c f7:n 521 522 523 524 525 526 527 528 529 520 c (521 522 523 524 525 526 527 528 529 520) c 41 51 61 81 91 101 111 E0 1.75e7 1.0e 6 1.0e 4 1.0e2 1.0e 1 1 20 f4:n 11 111 121 131 141 211 221 231 241 251 261 311 321 331 341 351 361 371 381 391 fs4 51 52 53 54 55 56 57 58 59 T SD4 (1.2629e+02 1.2629e+02 1.2629e+02 1.2629e+02 1.2629e+02 1.2629e+02 1.2629e+02 1.2629e+02 1.2629e+02 1.2629e+02 1.2629e+03) f7:n 11 111 121 131 141 211 221 231 241 251 261 311 321 331 341 351 361 371 381 391 fs7 51 52 53 54 55 56 57 58 59 T SD7 (1.2629e+02 1.2629e+02 1.2629e+02 1.2629e+02 1.2629e+02 1.2629e+02 1.2629e+02 1.2629e+02 1.2629e+02 1.2629e+02 1.2629e+03) fmesh14:n GEOM=xyz ORIGIN 16.0 0 0 IMESH=16.0 IINTS=20 JMESH=16.0 JINTS=10 KMESH=265.0 KINTS=5 EMESH=1.75e 7 1.0e6 1.0e 4 1.0e -2 1.0e1 1 20 EINTS= 1 1 1 1 1 1 1 mode n kcode 100 1 10 100

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ksrc 0 .1 25 0 .1 50 0 .1 75 0 .1 100 0 .1 125 0 .1 150 0 .1 175 0 .1 200 0 .1 225 0 .1 250 c fuel m1 92235.60c 0.0085 $.85% enriched U 92 238.60c 0.9915 8016.60c 2 m2 40000.60c 1 $zirc m3 1002.60c 2 $D2O 8016.60c 1 mt3 hwtr.62t $S(A,B) endf6.3 600K

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c Cr eated on: Wednesday, Sept 26, 2008 c CELLS c r1 4.89 c r2 5.07 c r3 4.55 c c ******************** LATTICE ELEMENT 7 *********************** c c Ring one stuff 201 21 4.89 9 10 imp:n=1 u=7 vol=1374.5895 $first axial zone (center) for ring 1 c c Ring two stuff 209 22 5.07 9 10 11 imp:n=1 u=7 vol=2253.7578 $second axial zone (center) for ring 1 c c Ring three stuff 2017 23 4.55 9 11 12 imp:n=1 u=7 vol=3681.5543 $third axial zone (center) for ring 1 c c Water Above 2029 4 1.0 9 12 imp:n=1 u=7 c 2025 4 1.0 12 imp:n=1 u=7 vol=1 $water region outside rings c c water region 26 4 1.0 101 100 103 102 imp:n=1 u=1 lat=1 fill= 6:6 4:5 0:0 $water region in assy 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7 7 7 7 7 7 7 7 7 1 1 1 1 7 7 7 7 7 7 7 7 7 1 1 1 1 7 7 7 7 7 7 7 7 7 1 1 1 1 7 7 7 7 7 7 7 7 7 1 1 1 1 7 7 7 7 7 7 7 7 7 1 1 1 1 7 7 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 c lattice 27 0 204 205 206 207 1 13 imp:n=1 fill=1 c outside world 28 0 204:205:206:207:1:13 imp:n=0 $outside world c c Surfaces c z surfaces *1 pz 0 $midplane of assy, only model to half 2 pz 79.5 $top of zone 1 source 3 pz 106 $top of zone 2 source 4 pz 132.5 $top of zone 3 source 5 pz 159 $top of zone 4 source 6 pz 185.5 $top of zone 5 source 7 pz 212 $top of zone 6 source

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8 pz 238.5 $top of zone 7 source 9 pz 265 $top of fuel (zone 8 source) 13 pz 315 $top of shield water c c cylinders for source regions radially 1 0 cz 2.346 $Inner ring radius 11 cz 3.8115 $Middle ring radius 12 cz 5.41 $Outer ring radius c c outer x/y boundary 100 px 7.25 $left boundary of single assy lattice element 101 px 7.25 $right boundary of single assy lattice element 102 py 7.5 $front boundary of single assy lattice element 103 py 7.5 $back boundary of single assy lattice element c c 4X4 assy lattice boundary 204 px 94.25 205 px 94.25 206 py 67.5 207 py 82.5 c c Detector 300 c/z 7.25 7.5 1.27 301 c/z 7.25 7.5 3.0 c DATA CARDS c mode n c c Source sdef erg d1 pos 0 0 0 rad d3 ext d4 axs 0 0 1 si1 H 1.00E 11 1.00E 07 4.14E 07 8.76E 07 1.86E 06 5.04E 06 1.07E05 3.73E 05 1.01E 04 2.14E 04 4.54E 04 1.58E 03 3.35E 03 7.10E03 1.50E 02 2.19E 02 2.42E02 2.61E 02 3.18E 02 4.09E 02 6.74E02 1.11E 01 1.83E 01 2.97E 01 3.69E 01 4.98E 01 6.08E 01 7.43E01 8.21E 01 1.00E+00 1.35E+00 1.65E+00 1.92E+00 2.23E+00 2.35E+00 2.37E+00 2.47E+00 2.73E+00 3.01E+00 3.68E+00 4.97E+00 6.07E+00 7.41E+00 8.61E+00 1.00E+01 1.22E+01 1.42E+01 1.98E+01 sp1 0 1.05148E11 9.19638E11 2.06605E10 6.06981E10 3.00603E09 7.86288E 09 6.3109E08 2.81517E07 7.41587E07 2.26519E06 1.84003E 05 4.5103E05 0.000139905 0.000431693 0.000484179 0.000181718 0.000155726 0.000509543 0.000891512 0.003136615 0.006506781 0.013400301 0.02553993 0.017880462 0.034781517 0.031265696 0.03915118 0.023016072 0.053641386 0.102209945 0.084957308 0.074058262 0.084329483 0.030361627 0.005123054 0.025966851 0.062757408 0.060497238 0.098543446 0.076770467 0.024726268 0.012127072 0.003965344 0.001635359 0.000629332 9.14616E 05 1.96359E05 si3 S 5 6 7 sp3 1.404 2.779 6.442 si4 0 265 si5 0 2.346 sp5 21 1 si6 2.346 3.8115 sp6 21 1 si7 3.8115 5.41 sp7 21 1

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nonu nps 500000 c c Tally Cards f4:n (201
PAGE 80

94240.66c 8.05E04 94241.66c 3.77E05 45103.66c 3.71E04 62149.66c 2.16E06 62151.50c 4.02E06 43099.66c 5.43E04 92235.66c 2.75E03 92236.66c 9.74E04 92238.66c 9.91E01 54131.66c 2.61E04 8016.60c 3.99 1001.60c 3.97 40000.60c 1.20 mt22 lwtr.60t $S(A,B) 294k c fuel ring 3 m23 95241.66c 1.48E04 64155.66c 2.31E06 60143.50c 4.19E04 60145.50c 3.45E04 94239.66c 2.55E03 94240.66c 9.43E04 94241.66c 4.59E05 45103.66c 4.27E04 62149.66c 2.39E06 62151.50c 4.23E06 43099.66c 6.17E04 92235.66c 2.41E03 92236.66c 1.05E03 92238.66c 9.91E01 54131.66c 2.96E04 8016.60c 4.54 1001.60c 5.08 40000.60c 1.27 mt23 lwtr.60t $S(A,B) 294k

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function out1=fissionMatrix(ftype,nx,ny,S,xbu,xt) %fmatrix(ftype,nx,ny,Sint,xbu,xt) %ftype type of fuel (1 = NU, 2 = SEU *not implemented*) %nx number of assemblies in x direction %ny number of assemblies in y direction %S intrinsic source of each assembly size=(x,y,G) %xbu burnup of each assembly (x,y) % 0=fresh 1=inert %xt cooling time of each assembly (x,y) ix=0; iy=0; fmult=ones(nx,ny); F=ones(nx,ny); Fold=ones(nx,ny); if ftype==2 %SEU fuel M(1,1)=0.21715; M(1,2)=0.05778; M(2,1)=0.05778; M(2,2)=0.01894; M(3,1)=0.00369; M(1,3)=0.00369; M(3,2)=0.00188; M(2,3)=0.00188; M2(1,1)=0.21926; M2(1,2)=0.05800; M2(2,1)=0.05800; M2(2,2)=0.01889; M2(3,1)=0.00370; M2(1,3)=0.00370; M2(3,2)=0.00186; M2(2,3)=0.00186; M3(1,1)=0.22141; M3(1,2)=0.05811; M3(2,1)=0.05811; M3(2,2)=0.01881; M3(3,1)=0.00369; M3(1,3)=0.00369; M3(3,2)=0.00190; M3(2,3)=0.00190; else %NU fuel %FISSION MATRIX COEFFICIENTS Mt(:,:,1,1)=[2.13E 01 4.98E02 2.70E03; 4.56E02 1.38E02 1.22E03; 2.18E03 1.11E03 0]'; Mt(:,:,1,2)=[2.14E 01 4.98E02 2.69E03; 4.57E02 1.37E02 1.22E03; 2.17E03 1.08E03 0]'; Mt(:,:,1,3)=[2.15E 01 5.00E02 2.66E03; 4.58E02 1.38E02 1.22E03; 2.17E03 1.08E03 0]'; Mt(:,:,2,1)=[ 2.18E01 5.14E02 2.78E03; 4.71E02 1.43E02 1.26E03; 2.25E03 1.14E03 0]'; Mt(:,:,3,1)=[ 2.05E01 4.77E02 2.57E03; 4.37E02 1.33E02 1.17E03; 2.09E03 1.05E03 0.00E+00]'; Mt(:,:,4,1)=[ 1.93E01 4.45E02 2.41E03; 4.08E 02 1.24 E 02 1.09E03; 1.95E03 9.83E04 0.00E+00]'; Mt(:,:,2,2)=[ 2.20E01 5.16E02 2.78E03; 4.74E02 1.42E02 1.26E03; 2.25E03 1.13E03 0]'; Mt(:,:,3,2)=[2.06E01 4.79E02 2.57E03; 4.40E 02 1.32E02 1.17E03; 2.07E 03 1.04E03 0]';

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Mt(:,:,4,2)=[1.94E01 4.45E02 2.39E03; 4.09E 02 1.22E02 1.09E03; 1.91E 03 9.69E04 0]'; Mt(:,:,2,3)=[2.21E01 5.18E02 2.75E03; 4.75E 02 1.42E02 1.27E03; 2.26E 03 1.13E03 0]'; Mt(:,:,3,3)=[2.07E01 4.79E02 2.55E03; 4.41E 02 1.32E02 1.17E03; 2.07E 03 1.02E03 0]'; Mt(:,:,4,3)=[1.95E01 4.45E02 2.37E03 4.09E 02 1.22E02 1.10E03 1.93E 03 9.56E04 0]'; %COOLING TIME AND BURNUP FOR THESE COEFFICIENTS t=[30 1 1 30]; bu=[5000 5000 8000 8000]; for ix=1:nx %FOR EACH ASSEMBLY for iy=1:ny if ((ix==1) || (ix==nx) || (iy==1) || (iy==ny)) %EDGE assembly ii=2; if ((ix==1) || (ix==nx)) && ((iy==1) || (iy==ny)) %CORNER assembly ii=3; end else %INTERIOR assembly ii=1; end if xbu(ix,iy)<0 %INERT assembly fmult(ix,iy)=0; end if xbu(ix,iy)<4000 %FRESH assembly xbu(ix,iy)=5000; end %Interpolate FM coefficient in cooling time and burnup bM1=Mt(:,:,2,ii)+(Mt(:,:,3,ii)Mt(:,:,2,ii))/(bu(3)bu(2))*(xbu(ix,iy)bu(2)); bM2=Mt(:,:,1,ii)+(Mt(:,:,4,ii)Mt(:,:,1,ii))/(bu(4)bu(1))*(xbu(ix,iy)bu(1)); tM1=bM1+(bM2bM1)/(t(1)t(2))*(xt(ix,iy) t(2)); M(ix,iy,:,:)=tM1*fmult(ix,iy); end end end %make sure FM coefficient array is big enough M=padarray(M,[0 0 nx ny],0,'post'); maxerr=1; newerr=0;

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iter=0; %GaussSiedel Iteration solve for F while (maxerr>0.000001) iter=iter+1; maxerr=0; for ix=1:nx for iy=1:ny Fold(ix,iy)=F(ix,iy); F(ix,iy)=0; for iix=1:nx for iiy=1:ny F(ix,iy)=F(ix,iy)+M(ix,iy,abs(iixix)+1,abs(iiyiy)+1)*(Fold(iix,iiy)... +S(iix,iiy)); end end newerr=abs((F(ix,iy)Fold(ix,iy))/(Fold(ix,iy)+1e 10)); if newerr>maxerr maxerr=newerr; end end end if iter>2000 maxerr=0; end end Fp=F/sum(sum(S)); mult=sum(sum(Fp)); out1=F; end

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PARAMETERS FOR MEMORY ALLOCATION using F90: maxmem, maxpcs, maxgcm, maxxsg 2000 2 4 47 maxcmc, maxcrs, maxmmc, maxmed, maxfmc, maxfin 4 2 2500 100 2500 100 maxgrp, maxglc, maxswp, maxqdm, maxmat, maxleg 47 47 4 3 14 3 maxsrc, maxslc, maxcmr, maxlin, maxarr, nctlim 1 1 4 228 117500 183 / -----------------Start Problem Deck--------------2dNU55 loglevel 2 generated by PENMSHXP version 1.7 (June 2008) Total Number of Fine Meshes: 10000 Total Numb er of Coarse Meshes: 4 Number of zlevs: 1 Number of coarse mesh per z lev: 4 6 7 8 9 10 / / -------------BLOCK I (GENERAL PROBLEM info.)----------/ ngeom=3d modadj=1 ngroup=47 1 isn=4 nmatl=14 ixcrs=2 jycrs=2 kzcrs=1 lodbal=0 timcut=0. tolmgd= 0.200 decmpv= 4 1 1 T / / -----------------BLOCK II(geometry) -----------------/ / x coarse mesh position / xmesh= 0.0000E+00 1.4500E+01 2.9000E+01 / / x fine mesh distribution for zlev= 1 / ixfine=50 50 50 50 / / x medium mesh distribution for zlev= 1 / ixmed=50 50 50 50

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/ / y coarse mesh position / ymesh= 0.0000E+00 1.5000E+01 3.0000E+01 / / y fine mesh distribution for zlev= 1 / jyfine=50 50 50 50 / / y medium mesh distribution for zlev= 1 / jymed=50 50 50 50 / / z coarse mesh position / zmesh= 0.0000E+00 1.2700E+01 / / z fine mesh distribution for zlev= 1 / kzfine=1 1 1 1 / / z medium mesh distribution for zlev= 1 / kzmed=1 1 1 1 / / material distribution for zlev= 1 / nmattp=1 4R6 6R5 40R4 2Q50 2R6 8R5 40R4 9R5 41R4 1Q50 8R5 42R4 7R5 43R4 5R5 15R4 10R11 20R4 3R5 14R4 16R11 33R4 18R11 30R4 22R11 27R4 24R11 25R4 10R11 6R10 10R11 23R4 8R11 12R10 8R11 21R4 8R11 14R10 8R11 20R4 6R11 18R10 6R11 19R4 7R11 18R10 7R11 18R4 6R11 7R10 6R9 7R10 6R11 17R4 6R11 7R10 8R9 7R10 6R11 16R4 6R11 6R10 10R9 6R10 6R11 16R4 5R11 6R10 12R9 6R10 5R11 15R4 6R11 5R10 14R9 5R10 6R11 5Q50 15R4 5R11 6R10 12R9 6R10 5R11 16R4 6R11 6R10 10R9 6R10 6R11 16R4 6R11 7R10 8R9 7R10 6R11 17R4 6R11 7R10 6R9 7R10 6R11 18R4 7R11 18R10 7R11 19R4 6 R11 18R10 6R11 20R4 8R11 14R10 8R11 21R4 8R11 12R10 8R11 23R4 10R11 6R10 10R11 25R4 24R11 27R4 22R11 30R4 18R11 33R4 16R11 37R4 10R11 420R4 nmattp=2 420R4 10R11 37R4 16R11 33R4 18R11 30R4 22R11 27R4 24R11 25R4 10R11 6R10 10R11 23R4 8R11 12R10 8R11 21R4 8R11 14R10 8R11 20R4 6R11 18R10 6R11 19R4 7R11 18R10 7R11 18R4 6R11 7R10 6R9 7R10 6R11 17R4 6R11 7R10 8R9 7R10 6R11 16R4 6R11 6R10 10R9 6R10 6R11 16R4 5R11 6R10 12R9 6R10 5R11 15R4 6R11 5R10 14R9 5R10 6R11 5Q50 15R4 5R11 6R10 12R9 6R10 5R11 16R4 6R11 6R10 10R9 6R10 6R11 16R4 6R11 7R10 8R9 7R10 6R11 17R4 6R11 7R10 6R9 7R10 6R11 18R4 7R11 18R10 7R11 19R4 6R11 18R10 6R11 20R4 8R11 14R10 8R11 21R4 8R11 12R10 8R11 23R4 10R11 6R10 10R11 25R4 24R11 27R4 22R11 30R4 18R11 33R4 16R11 37R4 10R11 420R4 nmattp=3 322R4 6R11 40R4 14R11 34R4 18R11 30R4 22R11 27R4 24R11 25R4 26R11 23R4 9R11

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10R10 9R11 21R4 8R11 14R10 8R11 20R4 7R11 16R10 7R11 19R4 7R11 18R10 7R11 18R4 6R11 9R10 2R9 9R10 6R11 17R4 6R11 7R10 8R9 7R10 6R11 16R4 6R11 6R10 10R9 6R10 6R11 16R4 5R11 6R10 12R9 6R10 5R11 15R4 6R11 5R10 14R9 5R10 6R11 5Q50 15R4 5R11 6R10 12R9 6R10 5R11 16R4 6R11 5R10 12R9 5R10 6R11 16R4 6R11 6R10 10R9 6R10 6R11 16R4 7R11 7R10 6R9 7R10 7R11 17R4 6R11 20R10 6R11 18R4 7R11 18R10 7R11 19R4 7R11 16R10 7R11 21R4 8R11 12R10 8R11 23R4 9R11 8R10 9R11 24R4 26R11 26R4 22R11 29R4 20R11 32R4 16R11 36R4 12R11 519R4 nmattp=4 322R4 6R11 40R4 14R11 34R4 18R11 30R4 22R11 27R4 24R11 25R4 26R11 23R4 9R11 10R10 9R11 21R4 8R11 14R10 8R11 20R4 7R11 16R10 7R11 19R4 7R11 18R10 7R11 18R4 6R11 9R10 2R9 9R10 6R11 17R4 6R11 7R10 8R9 7R10 6R11 16R4 6R11 6R10 10R9 6R10 6R11 16R4 5R11 6R10 12R9 6R10 5R11 15R4 6R11 5R10 14R9 5R10 6R11 5Q50 15R4 5R11 6R10 12R9 6R10 5R11 16R4 6R11 5R10 12R9 5R10 6R11 16R4 6R11 6R10 10R9 6R10 6R11 16R4 7R11 7R10 6R9 7R10 7R11 17R4 6R11 20R10 6R11 18R4 7R11 18R10 7R11 19R4 7R11 16R10 7R11 21R4 8R11 12R10 8R11 23R4 9R11 8R10 9R11 24R4 26R11 26R4 22R11 29R4 20R11 32R4 16R11 36R4 12R11 519R4 flxini=4R0.000 mathmg=4R0 T / / ------------BLOCK III (CROSS SECTIONS) ----------/ lib=file:nuall.xs legord=1 legoxs=3 nxtyp=1 ihm=50 iht=3 ihs=4 ihng=0 chig=1.0000E+00 46R0.0000E+00 13Q47 nxcmnt=2 T / / ------------BLOCK IV (CONTROL OPTIONS) -------------/ ncoupl=1 nprtyp=1 nrdblk=0 tolin=2.00E03 tolout=1.00E05 dtwmxw=0.95 maxitr=1000 10 methit=1 / / Starting or selected differencing scheme,for each coarsemesh, for z level= 1 / ndmeth=2 2 2 2 nzonrb=4 0.999 0 methac=1 T / -----------------BLOCK V(source) -----------------/ nsdef=0 nscmsh=1 sref=3R0.000 serg=4.43E 01 1.72E01 5.83E 02 3.97E 02 2.17E 02 5.94E 02 6.42E 02 3.69E 02

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2.43E02 1.71E 02 1.02E 02 5.86E 03 3.96E 03 2.88E 03 2.32E 03 2.20E 03 2.10E03 2.04E 03 1.89E 03 1.72E 03 1.50E 03 1.30E 03 1.13E 03 1.04E 03 9.83E04 9.27E 04 9.05E 04 8.92E 04 9.08E -04 9.39E 04 9.51E 04 9.61E 04 9.59E04 9.49E 04 9.44E 04 9.40E 04 9.27E 04 9.02E 04 8.65E 04 8.11E 04 7.66E04 9.99E 04 1.26E 03 1.28E 03 1.25E 03 1.38E 03 1.50E 03 smag=1 spacpf=1 1 2500 4R7.14286E 02 46R0.00000E+00 2Q50 2R7.14286E02 2348R0.00000E+00 T / / ------------BLOCK VI (BOUNDARY CONDITIONS) --------/ / var type Group albedos ibback=1 47R1 ibfrnt=0 jbeast=1 47R1 jbwest=0 kbsout=1 47R1 kbnort=1 47R1 T / / ------------BLOCK VII (PRINTING CONDITIONS) --------/ / nxspr=0 nmatpr=1 ngeopr=1 nsrcpr=0 nsumpr=1 meshpr=2I1 -4 nfdump=1 nsdump=0 njdump=0 nadump=0 T

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function [r1,r2,r3,r4,r5,r6,r7,r8]= detResponse(bfiss,bimp,bsrc,Imp,Impg,bmult,fBU,fcoolTime,fRexp,fmult) %function [r1,r2,r3,r4,r5]=detResponse(bfiss,bimp,bsrc,Imp,impg,burnmult,fBU,fcoolTime, fRexp); %input: %bfiss account for subcritical multiplication? (testing purposes) %bimp account for detector FOV? (testing purposes) %bsrc account for source non linearity w/ burnup (testing purposes) %imp neutron importance (from readImportance) %impg gamma importance (from readImportance) %bmult burnup multiplier (to account for errors in predicted local burnup) % %output: %r1 predicted neutron response %r2 predicted neutron response uncertainty due to 1% burnup uncertainty %r3 experimental response vs. predicted %r4 experimental response in x,y form %r5 sum of squares error %r6 gamma to neutron ratio %r7 normalized gamma to neutron ratio %r8 predicted gamma uncertainty fuelType=1; %only NU fuel %read in assembly configuration BU=textread(fBU)'; coolTime=textread(fcoolTime)'; Rexp=textread(fRexp); nx=size(BU,1); ny=size(BU,2); %read in source database [sdat,budat,tdat]=srcrd2('nu2.src'); [sdatg,budatg,tdatg]=srcrd2('nu2g.src'); %Interpolate source distributions tBU=reshape(BU,[nx*ny,1])*bmult; tt=reshape(coolTime,[nx*ny,1]); Sint=sourceInterp2(sdat,budat,tdat,tBU,tt); Sint01=sourceInterp2(sdat,budat,tdat,tBU*1.01,tt); Sg=sourceInterp2(sdatg,budatg,tdatg,tBU,tt); Sg01=sourceInterp2(sdatg,budatg,tdatg,tBU*1.01,tt); nG=size(Sint,3); nGg=size(Sg,3); Sint=reshape(Sint,[nx,ny,3,nG]); Sint01=reshape(Sint01,[nx,ny,3,nG]); Sg=reshape(Sg,[nx,ny,3,nGg]); Sg01=reshape(Sg01,[nx,ny,3,nGg]); %calculate subcritical multiplication SintTot=sum(sum(Sint,4),3);

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Smult=fissionMatrix(fuelType,nx,ny,SintTot,BU,coolTime); Sfiss=calcFiss(Smult,Sint); Sfiss01=calcFiss(Smult,Sint01); Stot=Sint+Sfiss; Stot01=Sint01+Sfiss01; %calibrate the efficiency to the measured data Eff=calibrate(Rexp,Imp,Stot,Stot01); %predict detector responses [Rcalc,rerr]=calculateR(Eff,Imp,Stot,Stot01); [Rcalcg,rgerr]=calculateR(1,Impg,Sg,Sg01); %calculate sum of squares error of predicted vs. measured rnew=zeros(nx+1,ny+1); s umsq=0; for i=1:size(Rexp,1) rnew(Rexp(i,1),Rexp(i,2))=Rexp(i,3); sumsq=sumsq+(Rexp(i,3)Rcalc(Rexp(i,1),Rexp(i,2)))^2; Rexp(i,4)=Rcalc(Rexp(i,1),Rexp(i,2)); end r1=Rcalc; r2=rerr; r3=Rexp; r4=rnew; r5=sumsq; r6=Rcalcg./r1; r7=r6/mean(mean(r6)); r8=rgerr./Rcalcg; end function y=calcFiss(Smult,Sint) s=Sint; for ix=1:size(Smult,1) for iy=1:size(Smult,2) SintTot=sum(sum(Sint(ix,iy,:,:))); s(ix,iy,:,:)=Sint(ix,iy,:,:)*(Smult(ix,iy))/(SintTot+1e10); end end y=s; end function y=calibrate(r,imp,s,s01) x=zeros(size(r,1),1); for iexp=1:size(r,1) [x(iexp),err]=getR(1,r(iexp,1),r(iexp,2),imp,s,s01); end tr=r(:,3); eff=sum(x.*tr)/sum(x.*x); y=eff; end %calculate response for each detector location function [y,yerr]=calculateR (eff,imp,s,s01) nx=size(s,1); ny=size(s,2);

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r=zeros(nx+1,ny+1); err=zeros(nx+1,ny+1); for ix=1:(nx+1) for iy=1:(ny+1) [r(ix,iy),err(ix,iy)]=getR(eff,ix,iy,imp,s,s01); end end y=r; yerr=err; end %calculate response and error for a single detector location function [y,err]=getR(eff,ix,iy,imp,s,s01) nx=size(s,1); ny=size(s,2); %distance from detector to each assembly indx=(ix2:ix+1); indx=indx(indx>0);indx=indx(indx<(nx+1)); indy=(iy2:iy+1); indy=indy(indy>0);indy=indy(indy<(ny+1)); iix=ind xix+1; iix=abs(iix(iix<1)); iiy=indyiy+1; iiy=abs(iiy(iiy<1)); %calculate R=IMP*S rt=imp(iix,iiy,1:3,:).*s(indx,indy,1:3,:); rt01=imp(iix,iiy,1:3,:).*s01(indx,indy,1:3,:); rtt=sum(sum(rt,4),3); rtt01=sum(sum(rt01,4),3); dr=rtt01rtt; err=eff*sqrt(sum(sum(dr.^2))); r=eff*sum(sum(sum(sum(rt)))); y=r; end

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Proc. of the INMM 48th Annual Meeting, Computational Methods of Neutron Transport, Proc. of the INMM 50th Annual Meeting Proc. of the American Nuclear Society Winter Meeting PENTRAN-Parallel Environment Neutral Particle TRANsport Version 9. 4x.5 ORIGEN -ARP: Automatic Rapid Pr ocessing for Spent Fuel Depletion, Decay and Source Term Analysis, SCALE5.1 Manual SCALE: A Modular Code System for Performing Standardized Computer Analyses for Licensing Evaluations Proceedings of IAEA Technical Committee M eeting

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PENMSH Express Manual DEV -XS: A Cross Section Development Primer for PENTRAN/PENBURN Version 2.0