SEFOR MC-3 Model for Core I-E

The multigroup cross-section generation using MC-3 and ENDF/B-VII.1 library followed a two-step procedure and produced output in ISOTXS format. In the first step, a series of transport calculations were carried out using simple 0-D Listing 1 or 1-D cylindrical models Listing 2 to obtain energy self-shielded cross sections over a fine energy grid (> 1,000 energy groups). The 1-D cylindrical model is also shown in Figure 1.

Listing 1: MC-3 input for 0-D model of SEFOR Core I-E bottom grid plate

!                        Na_GP_b (A)
! ============================================================
!
     t_composition(:,  1)=  NA23_7  NA23_A  1.68850E-02  450.00
                            CR50_7  CR50_A  1.99835E-04  450.00
                            CR52_7  CR52_A  3.85357E-03  450.00
                            CR53_7  CR53_A  4.36962E-04  450.00
                            CR54_7  CR54_A  1.08771E-04  450.00
                            FE54_7  FE54_A  8.50997E-04  450.00
                            FE56_7  FE56_A  1.33588E-02  450.00
                            FE57_7  FE57_A  3.08517E-04  450.00
                            FE58_7  FE58_A  4.10573E-05  450.00
                            NI58_7  NI58_A  1.66423E-03  450.00
                            NI60_7  NI60_A  6.41055E-04  450.00
                            NI61_7  NI61_A  2.78666E-05  450.00
                            NI62_7  NI62_A  8.88497E-05  450.00
                            NI64_7  NI64_A  2.26275E-05  450.00
                            B10__7  B10__A  6.60243E-04  450.00
                            B11__7  B11__A  2.65754E-03  450.00
                            C____7  C12__A  8.29451E-04  450.00
/
\$output
     l_isotxs_macroxs    = T
/
EOF
$exe_mcc3
(sfr/sefor/Cross_Section/Core-I-E_450K_ENDF71_step1.inp)

Listing 2: MC-3 input for 1-D model of SEFOR Core I-E standard fuel assembly

!                        FA_6_Fuel_St (K)
! ============================================================
!
     t_composition(:,  1)=  BE9__7  BE9__K  5.39439E-02  450.00
                            O16__7  O16__K  5.39439E-02  450.00
                            CR50_7  CR50_K  1.20548E-04  450.00
                            CR52_7  CR52_K  2.32460E-03  450.00
                            CR53_7  CR53_K  2.63605E-04  450.00
                            CR54_7  CR54_K  6.56154E-05  450.00
                            FE54_7  FE54_K  5.95077E-04  450.00
                            FE56_7  FE56_K  9.34136E-03  450.00
                            FE57_7  FE57_K  2.15727E-04  450.00
                            FE58_7  FE58_K  2.87093E-05  450.00
                            MO1007  MO100K  2.12956E-05  450.00
                            MO92_7  MO92_K  3.28181E-05  450.00
                            MO94_7  MO94_K  2.04554E-05  450.00
                            MO95_7  MO95_K  3.52068E-05  450.00
                            MO96_7  MO96_K  3.68870E-05  450.00
                            MO97_7  MO97_K  2.11189E-05  450.00
                            MO98_7  MO98_K  5.33619E-05  450.00
                            NI58_7  NI58_K  1.32873E-03  450.00
                            NI60_7  NI60_K  5.11828E-04  450.00
                            NI61_7  NI61_K  2.22483E-05  450.00
                            NI62_7  NI62_K  7.09384E-05  450.00
                            NI64_7  NI64_K  1.80668E-05  450.00

     t_composition(:,  2)=  NA23_7  NA23_K  2.39160E-02  450.00

     t_composition(:,  3)=  CR50_7  CR50_K  8.17351E-04  450.00
                            CR52_7  CR52_K  1.57623E-02  450.00
                            CR53_7  CR53_K  1.78728E-03  450.00
                            CR54_7  CR54_K  4.44885E-04  450.00
                            FE54_7  FE54_K  3.48075E-03  450.00
                            FE56_7  FE56_K  5.46400E-02  450.00
                            FE57_7  FE57_K  1.26184E-03  450.00
                            FE58_7  FE58_K  1.67927E-04  450.00
                            NI58_7  NI58_K  6.80694E-03  450.00
                            NI60_7  NI60_K  2.62205E-03  450.00
                            NI61_7  NI61_K  1.13973E-04  450.00
                            NI62_7  NI62_K  3.63413E-04  450.00
                            NI64_7  NI64_K  9.25497E-05  450.00

     t_composition(:,  4)=  PU2397  PU239K  3.32051E-03  450.00
                            PU2407  PU240K  2.98177E-04  450.00
                            U235_7  U235_K  3.12105E-05  450.00
                            U238_7  U238_K  1.41554E-02  450.00
                            O16__7  O16__K  3.55742E-02  450.00
                            CR50_7  CR50_K  1.09257E-04  450.00
                            CR52_7  CR52_K  2.10686E-03  450.00
                            CR53_7  CR53_K  2.38914E-04  450.00
                            CR54_7  CR54_K  5.94694E-05  450.00
                            FE54_7  FE54_K  5.39338E-04  450.00
                            FE56_7  FE56_K  8.46638E-03  450.00
                            FE57_7  FE57_K  1.95521E-04  450.00
                            FE58_7  FE58_K  2.60202E-05  450.00
                            MO1007  MO100K  1.93009E-05  450.00
                            MO92_7  MO92_K  2.97441E-05  450.00
                            MO94_7  MO94_K  1.85394E-05  450.00
                            MO95_7  MO95_K  3.19091E-05  450.00
                            MO96_7  MO96_K  3.34319E-05  450.00
                            MO97_7  MO97_K  1.91407E-05  450.00
                            MO98_7  MO98_K  4.83636E-05  450.00
                            NI58_7  NI58_K  1.20427E-03  450.00
                            NI60_7  NI60_K  4.63886E-04  450.00
                            NI61_7  NI61_K  2.01643E-05  450.00
                            NI62_7  NI62_K  6.42938E-05  450.00
                            NI64_7  NI64_K  1.63745E-05  450.00

     t_composition(:,  5)=  CR50_7  CR50_K  8.17351E-04  450.00
                            CR52_7  CR52_K  1.57623E-02  450.00
                            CR53_7  CR53_K  1.78728E-03  450.00
                            CR54_7  CR54_K  4.44885E-04  450.00
                            FE54_7  FE54_K  3.48075E-03  450.00
                            FE56_7  FE56_K  5.46400E-02  450.00
                            FE57_7  FE57_K  1.26184E-03  450.00
                            FE58_7  FE58_K  1.67927E-04  450.00
                            NI58_7  NI58_K  6.80694E-03  450.00
                            NI60_7  NI60_K  2.62205E-03  450.00
                            NI61_7  NI61_K  1.13973E-04  450.00
                            NI62_7  NI62_K  3.63413E-04  450.00
                            NI64_7  NI64_K  9.25497E-05  450.00

     t_composition(:,  6)=  NA23_7  NA23_K  2.39160E-02  450.00

     t_composition(:,  7)=  CR50_7  CR50_K  8.17351E-04  450.00
                            CR52_7  CR52_K  1.57623E-02  450.00
                            CR53_7  CR53_K  1.78728E-03  450.00
                            CR54_7  CR54_K  4.44885E-04  450.00
                            FE54_7  FE54_K  3.48075E-03  450.00
                            FE56_7  FE56_K  5.46400E-02  450.00
                            FE57_7  FE57_K  1.26184E-03  450.00
                            FE58_7  FE58_K  1.67927E-04  450.00
                            NI58_7  NI58_K  6.80694E-03  450.00
                            NI60_7  NI60_K  2.62205E-03  450.00
                            NI61_7  NI61_K  1.13973E-04  450.00
                            NI62_7  NI62_K  3.63413E-04  450.00
                            NI64_7  NI64_K  9.25497E-05  450.00

     t_composition(:,  8)=  NA23_7  NA23_K  2.39160E-02  450.00
/
\$geometry
     c_boundary_condition = reflective
     i_mesh =           1       1       1       3       1
                        3       1       1
     r_location = 1.11426 1.28366 1.37726 3.32428 3.41451
                  4.05154 4.21200 4.22537
     i_composition =    1       2       3       4       5
                        6       7       8
/
\$output
     l_isotxs_macroxs    = T
/
EOF
$exe_mcc3
(sfr/sefor/Cross_Section/Core-I-E_450K_ENDF71_step1.inp)
Mesh model of SEFOR Core I-E fuel assemblies: (a) Standard Assembly (SA), (b) SA with a B$_4$C rod (AFA)

Figure 1: Mesh model of SEFOR Core I-E fuel assemblies: (a) Standard Assembly (SA), (b) SA with a BC rod (AFA)

These detailed cross sections were then applied to an approximate RZ model of the full SEFOR reactor core Listing 3. The TWODANT code was used to perform the neutron transport calculation within this RZ geometry (Alcouffe et al., 1984).

Listing 3: TWODANT input for modeling SEFOR Core I-E

 ngroup=        1041
 niso=          18
mt= 18, nzone= 18,
im= 15, it= 29,
jm= 11, jt= 43,
igeom=7, isn=10, maxlcm=195000000, maxscm=19200000,
t
xmesh= 0.0000   4.2254  40.7480  40.9665  42.0419  42.8828
      43.0905  43.2972  43.5029  43.7076  43.9113  44.1142
      53.4860  58.2630  73.5530  87.0340 ,
ymesh= 0.0000  30.7450  41.5320  42.4845  94.9136  95.8661
      99.1481 100.1006 133.6233 134.5758 145.3628 165.6018 ,
xints= 1  9  1  1  1  1  1  1  1  1  1  2  1  4  3  ,
yints= 7  3  1  13 1  1  1  7  1  3  5  ,
zones= 1  1  1  1  1  1  1  1  1  1  1  3  4  5  7  ;
       2  9  13 13 13 13 9  9  13 13 13 3  4  6  7  ;
       2  10 14 14 14 14 10 10 14 14 14 3  4  6  7  ;
       2  11 15 15 15 15 17 17 18 18 18 3  4  6  7  ;
       2  10 14 14 14 14 10 10 14 14 14 3  4  6  7  ;
       2  12 16 16 16 16 12 12 16 16 16 3  4  6  7  ;
       2  10 14 14 14 14 10 10 14 14 14 3  4  6  7  ;
       2  11 15 15 15 15 17 17 18 18 18 3  4  6  7  ;
       2  10 14 14 14 14 10 10 14 14 14 3  4  6  7  ;
       2  9  13 13 13 13 9  9  13 13 13 3  4  6  7  ;
       2  8  8  8  8  8  8  8  8  8  8  3  4  5  7  ;
t
lib=isotxs,balxs=0,
t
 matls=
 REG_01  REG_01      0.10000E+01;
 REG_02  REG_02      0.10000E+01;
 REG_03  REG_03      0.10000E+01;
 REG_04  REG_04      0.10000E+01;
 REG_05  REG_05      0.10000E+01;
 REG_06  REG_06      0.10000E+01;
 REG_07  REG_07      0.10000E+01;
 REG_08  REG_08      0.10000E+01;
 REG_09  REG_09      0.10000E+01;
 REG_10  REG_10      0.10000E+01;
 REG_11  REG_11      0.10000E+01;
 REG_12  REG_12      0.10000E+01;
 REG_13  REG_13      0.10000E+01;
 REG_14  REG_14      0.10000E+01;
 REG_15  REG_15      0.10000E+01;
 REG_16  REG_16      0.10000E+01;
 REG_17  REG_17      0.10000E+01;
 REG_18  REG_18      0.10000E+01;
 assign=
 REG_01  REG_01       1.0;
 REG_02  REG_02       1.0;
 REG_03  REG_03       1.0;
 REG_04  REG_04       1.0;
 REG_05  REG_05       1.0;
 REG_06  REG_06       1.0;
 REG_07  REG_07       1.0;
 REG_08  REG_08       1.0;
 REG_09  REG_09       1.0;
 REG_10  REG_10       1.0;
 REG_11  REG_11       1.0;
 REG_12  REG_12       1.0;
 REG_13  REG_13       1.0;
 REG_14  REG_14       1.0;
 REG_15  REG_15       1.0;
 REG_16  REG_16       1.0;
 REG_17  REG_17       1.0;
 REG_18  REG_18       1.0;
t
ievt=1,isct=3,ith=0,ibl=1,ibr=0,ibt=0,ibb=0,
epsi=0.0001,iitl=100,iitm=100,oitm=50,epso=0.000001,
fluxp=0,xsectp=0,fissrp=0,sourcp=0,angp=0,geomp=0,
insors=0,raflux=0,rmflux=1,iquad=-2,influx=0,
(sfr/sefor/Cross_Section/Core-I-E_450K_ENDF71_step1.twodant.inp)

Fluxes from the transport calculations included both neutron leakage and spatial self-shielding effects. In the second step, the flux distributions from TWODANT were used within MC-3 to condense the fine-energy grid cross sections to the ANL 33-group structure as shown in Listing 4.

Listing 4: MC-3 input for step 2 calculation

\$library
     c_mcclibdir  ="$lib_mcclibdir"
     c_pwlibdir   ="$lib_pwlibdir"
     c_twodantexe ="$exe_twodant"
/
\$control
     c_group_structure       = ANL33
     c_externalspectrum_ufg  = rzmflx
     c_geometry_type         = mixture
     i_number_region         = 1
     i_scattering_order      = 3
     l_twodant               = F
     l_pendf                 = T
/
\$material
!
! ============================================================
!                        Na_GP_b (A)
! ============================================================
!
     i_externalspectrum(1)= 1

     t_composition(:,  1)=  NA23_7  NA23_A  1.68850E-02  450.00
                            CR50_7  CR50_A  1.99835E-04  450.00
                            CR52_7  CR52_A  3.85357E-03  450.00
                            CR53_7  CR53_A  4.36962E-04  450.00
                            CR54_7  CR54_A  1.08771E-04  450.00
                            FE54_7  FE54_A  8.50997E-04  450.00
                            FE56_7  FE56_A  1.33588E-02  450.00
                            FE57_7  FE57_A  3.08517E-04  450.00
                            FE58_7  FE58_A  4.10573E-05  450.00
                            NI58_7  NI58_A  1.66423E-03  450.00
                            NI60_7  NI60_A  6.41055E-04  450.00
                            NI61_7  NI61_A  2.78666E-05  450.00
                            NI62_7  NI62_A  8.88497E-05  450.00
                            NI64_7  NI64_A  2.26275E-05  450.00
                            B10__7  B10__A  6.60243E-04  450.00
                            B11__7  B11__A  2.65754E-03  450.00
                            C____7  C12__A  8.29451E-04  450.00
/
\$output
     l_isotxs_macroxs    = F
     l_isotxs_ascii      = T
/
EOF
(sfr/sefor/Cross_Section/Core-I-E_450K_ENDF71_step2.inp)

The ISOTXS cross section file was converted into the ISOXML format using the ISOXML utility in Griffin. Microscopic cross sections were generated for reactor core temperatures ranging from 350 °F to 750 °F, with increments of 50 °F for Core I-E. The model included 18 homogenized zones including the bottom grid plate, core top (Na_steel), downcomers (inside or outside the vessel DC_IV/DC_OV), radial reflectors and radial shields, as well as various homogenized fuel assembly regions.

References

  1. R E Alcouffe, F W Brinkley, D R Marr, and R D O'Dell. User's guide for twodant: a code package for two-dimensional, diffusion-accelerated, neutral-particle transport. revision 1. Technical Report, Los Alamos National Lab., NM (USA), 10 1984. URL: https://www.osti.gov/biblio/5985401, doi:10.2172/5985401.[BibTeX]