New PARCS
Cross Section Model
School of Nuclear Engineering
Purdue University
September 2002
1
Original XS Model in PARCS (1997)




 2
2


( , Tf , Tm, Dm, Sb)     
 Tf 
Tm 
Dm 
Sb 

Dm
Tm
Dm
Sb
Dm 2
 Tf
r
cr
r: XS at unroded reference state
cr: Control rod XS;
Tf: Fuel temperature;
: roded fraction;
Tm: moderator temperature
Sb: Soluble Boron Density; Dm: moderator Density

At most seven cross section data points can be referenced



1 reference state
2 moderator branches
1 branches for each of other variables: Cr,
Tf,Tm,Sb
2
Example of Original Model
comp_num
3
!corner reflector
!-----------------------------------------------------------------------------base_macro 2.956090e-01 1.187820e-03 0.000000e+00 0.000000e+00 2.008080e-02
2.459310e+00 2.526180e-01 0.000000e+00 0.000000e+00
dxs_dppm
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
7.761840e-04 8.446950e-05 0.000000e+00 0.000000e+00
comp_num
4
!fuel 1
!-----------------------------------------------------------------------------base_macro 2.221170e-01 8.717740e-03 4.982770e-03 6.111896e-14 1.824980e-02
8.031400e-01 6.525500e-02 8.390260e-02 1.101520e-12
dxs_dppm
3.478090e-08 1.285050e-07 -1.120990e-09 -1.761878e-20 -1.085900e-07
-9.765100e-06 7.088070e-06 -2.430450e-06 -3.190845e-17
dxs_dtm
-2.033100e-06 2.121910e-07 1.247090e-07 1.430354e-18 8.096760e-07
-1.086740e-04 -3.155970e-05 -4.164390e-05 -5.467221e-16
dxs_ddm
1.356650e-01 1.551850e-03 9.206940e-04 1.023919e-14 2.931950e-02
9.926280e-01 2.526620e-02 2.477460e-02 3.252554e-13
dxs_dtf
-3.091970e-05 3.497090e-05 6.401340e-07 7.154124e-18 -2.755360e-05
-1.372920e-04 -3.718060e-05 -5.630370e-05 -7.391879e-16
cdf
1.0069
0.9307
1.0034
0.9646
1.1040
1.4493
1.0096
1.1580
delcr_comp 1
1 -5 7 -11 !compostions that this set applies
!-----------------------------------------------------------------------------delcr_base 3.732200e-03 2.477700e-03 -1.027860e-04 -1.214480e-15 -3.192530e-03
-2.199260e-02 2.558750e-02 -2.823190e-03 -3.702378e-14
3
Applications of Original Model:
Static and Spatial Kinetics Problems




Eigenvalue Benchmark Problems
IAEA3D, L336, …
OECD NEACRP Rod Eject Benchmarks
Coupled Code Problems
 OECD TMI MSLB
 OECD Peach Bottom Turbine Trip
Problems with Oconnee Control Rod Drive Cracking
(CASMO Tables format)
4
Depletion Capability Added (2000)

Nuclide depletion equation
(Bateman)
Absorb netron
B
β
dN A (t )
 ( Aa   A ) N A (t )   C N c (t )  B N B (t )
dt
A
β
n,γ
C
Neutron Transport Equation (Boltzmann)
1 
1
    (r , E , , t )  t (r , E ) (r , E , , t ) 
S f (r , E , t )
v t
4
    s (r , E '  E , '  ) (r , E ' , ' , t )dE ' d'
' E '
5
Depletion XS Model




 2
2


( , Tf , Tm, Dm, Sb)     
 Tf 
Tm 
Dm 
Sb 

Dm
Tm
Dm
Sb
Dm 2
 Tf
r
cr



( Tf , BU , HIS 1, HIS 2)
 Tf  Tf



( Sb, BU , HIS 1, HIS 2)
Sb Sb



(Tm, BU , HIS 1, HIS 2)
Tm Tm



( Dm, BU , HIS 1, HIS 2)
Dm Dm
 2
 2

( Dm, BU , HIS 1, HIS 2)
Dm 2 Dm 2
cr  cr ( BU , HIS 1, HIS 2)


Burnup and burnup “history” dependence
More than seven data points can be referenced
6
U.S. NRC Coupled Code Analysis
Lattice Code
(HELIOS/NEWT)
Neutron Flux
Solver
(PARCS)
Σ
Cross Section
Library
(PMAX)
T/H code
(RELAP
/TRAC)
Φ
Depletion Code
(DEPLETOR)
7
Application of Depletion Model

DOE NERI Projects:




SBWR design
HCBWR Design
Iteration required between PARCS and
Depletor … computationally inefficient
Not able to handle generalized cross
section tables
8
Standard “Two Step” Procedure for
Generating LWR Cross Sections
Lattice
Calculations
Neutronics
Calculation
Output files
XS of
each region
XS library
generator
XS
interpreter
Cross section
library
9
First Step of in
NRC Neutronic Code System
Lattice Codes:
SCALE
HELIOS
….
Input files
for depletion at various base states
and branches at some burnup points
Output files
GenpXS
PMAXS
10
Base State and Branches Performed
with Lattice Physics Code
Branches
Base state
0GWD/T
Fuel temp.
mod temp.
Mod. den.
Soluble B.
Control
Tf1, Tf2…
Tm1, Tm2…
Dm1, Dm2…
ppm1, …
rod …
Fuel temp.
mod temp.
Mod. den.
Soluble B.
Control
Tf1, Tf2…
Tm1, Tm2…
Dm1, Dm2…
ppm1, …
rod …
1GWD/T
2GWD/T
3GWD/T
4GWD/T
5GWD/T
11
Cross Section Library
in NRC Neutronic Code System
Dependent Variables:
Principle Cross Sections :  a , f ,  f ,  tr ,  g   g ' , ADF , CDF ...
Delay Neuton parameters :  , 
Decay Heat parameters :  H ,  H
Xenon & Samarium Cross Sections : aXe ,  aSm , YI , YXe , YPm , YSm ,  I ,  IXe ,  Pm
Local Peaking Factors : f Power , J1 ( for MCPR calculatio n)
Detector information : form functions, multiplier s
2 D Form Functions : flux, power
.......
PMAXS
Independent Variables:
Instantaneous variables : Cr , Md , Sb, Tf , Tm
History variables :
Other variables :
HCr , HMd , HSb , HTf , HTm
Lattice ID , Neutron enegy group ,
Delay Neutron Group, Decay Heat Group,
Location for Local factor, Form function, etc
12
Second Step of in
NRC Neutronic Code System
T/H Code:
PARCS
XS Model:
Interpret XS base on
instantaneous variables
XS of each region
at given history value
PMAXS
Neutronic
Calculation
RELAP
TRAC
….
Power
distribution
Depletor
13
Format of PMAXS in Depletion
Cross Section Model
Appendix B. PMAXS format
----------------------------------------------------------------------
PMAXS (version 1.0, revision-01)
----------------------------------------------------------------------
Last revised 4/2/01
The Format of Purdue Macroscopic Cross Section (XS) Set
----------------------------------------------------------------------
File Data
File identification
Fuel Assembly wise data (repeat for all kinds of assemblies)
Assembly identification
Assembly control data
Assembly Group independent data
Assembly Energy bound information data
Reference state data
Identification of the base state
Control data of the base state
State data of the base state
Principal cross sections of the base state
Scattering cross sections of the base state
Xe/Sm cross sections of the base state
Soluble boron cross section of the base state
Delayed neutron data of the base state
Decay heat data of the base state
Power form function of the base state
Group-wise form function of the base state
Detector information of the base state
Soluble Boron branch case
Identification
Control data
State data
(repeat for all soluble boron branch case)
Derivation of the principal cross sections
Existence
always
always
always
LORD > 0
ISXE=1
ISSB = 1
NDFAM > 0
NDCAY > 0
IPFF = 1
IGFF=1
ISDE=1
IBSB > 0
14
Motivation for New PARCS
Cross Section Model



Old Model has limited accuracy and
applicability for practical cross section data
sets which are multi-dimensional tables (e.g.
Ringhalls)
New Model performs multi-dimensional
interpolation to construct partial derivates
This increases the range of applicability and
yet preserves applicability of old PARCS XSEC
files
15
Advantages of New Model


If there are more than 2 points in
a line, then New Model is actually
quadratic interpolation.
Can obtain good accuracy even
with smaller number of branches
16
Ringhalls Stability Benchmark

Ringhals XS in TABLES format
( EXP, HVO, HCR, VOI , TFU , CRD )   base ( EXP, HVO )
 VOI ( EXP, HVO, VOI )  TFU ( EXP, VOI , TFU )
 CRD ( EXP, VOI , CRD )   HCR ( EXP, CRD , HCR )


Multiple 3-Dimensional tables
Multiple Control rod compositions
17
Application of New Model to Ringhalls

( , Dm, Sb, Tf , Tm)   r ( Dm r , Sb r , Tf r , Tm r )    i i ( Dm r , Sb r , Tf r , Tm r )
i
 Dm
 Tf




Sb


Dm ( , Dm m , Sb r , Tf r , Tm r )
Sb ( , Dm , Sb m , Tf r , Tm r )


 Tm


m
r
Tf ( , Dm , Sb , Tf , Tm )
Tm ( , Dm , Sb , Tf , Tm m )
Tf  Tf  Tf r
Tf m  (Tf  Tf r ) / 2
The partials will be obtained by piece wise linear interpolation
If the XS at blue point are also available,
New Model gives same XS as Model 2
better than Model 1
Other wise
New Model gives same XS as Model 1
better than Model 2
18
Important to Choose Best
Sequence to Evaluate Variables
K
Dm
K
DB
K
 Tf
Dm
Very Strong
Strong
Strong
Very Strong
DB
Strong
Weak
Normal
Weak
Normal
Weak
Very Strong
Normal
Almost no
Almost no
Almost no
Strong
Tf
Tm

K
Tm
Suggested sequence:

Dm DB Tf Tm
19
Example:
Moderator temperature and density
Original
Dm
1.0
0.96
0.9
Original Data
point
0.94
0.8
0.92
0.7
0.9
0.6
0.88
Selected
point
0.5
0.86
0.9
0.8
600
0.7
550
0.6
0.4
Density
0.4
500
0.5
0.3
450
0.3
Temperature
(Tm, Dm)  (Tm r , Dm r )  Tm
415
515
615
Tm




Dm
Tm (Tm m , Dm r )
Dm (Tm, Dm m )
20
Effect of Different Sequence:
Using Temperature then Density
(Tm, Dm)  (Tm r , Dm r )  Tm




Dm
Tm (Tm m , Dm r )
Dm (Tm, Dm m )
error of linear interpolation, rms=0.01202
linear interpolation
0.04
0.96
0.02
0.94
0.92
0
0.9
-0.02
0.88
-0.04
1
0.86
1
0.8
0.8
600
500
0.4
450
500
0.4
550
0.6
Density
600
550
0.6
Density
450
Temperature
Temperature
21
Effect of Different Sequence:
Using Density then Temperature
( Dm, Tm)  ( Dm r , Tm r )  Dm




Tm
Dm ( Dm m , Tm r )
Tm ( Dm, Tm m )
linear interpolation
error of linear interpolation, rms=0.00098
-3
x 10
0.96
2.5
2
0.94
1.5
0.92
1
0.5
0.9
0
-0.5
0.88
-1
0.86
-1.5
600
600
1
550
0.9
0.8
500
0.7
0.9
0.8
500
0.6
0.7
0.6
0.5
450
Temperature
1
550
0.5
450
0.4
0.3
Density
Temperature
90% error reduced
0.4
0.3
Density
22
Tree structure of states at which
XS/partials are calculated or stored
Ref.
CR
calcul
XS
Dm1
Dm
partials
calcul
XS
SB
partials
Tf1
Tfr
Tf1m
calcul
XS
Tf2
Tf2m
Tmr
Tm1
Sbr
1: no
Dmr
Sbr
Tfr
Tmr
Tf
partials
Tm
partials
Dm1m
Dmr
Dm2
Dm3
calcul
XS
Dm2m
Dm3m
Sb1
Sb1m
Sb2
Sb2m
Tm1m
Sbr
Tm2
Tmr
Tm3
2:SS
Tm2m
Tm3m
Sbr
3:B4C
XS at reference states
Calculate & Store
Sb3
Sb3m
XS
calculate
Tfr
Tf3
Tf3m
XS already
calculated
Partials
store
23
New PMAXS/XSEC Format
1
Branches information
XS Set wise data
2
XS Set identification
3
Dimension data
4
Burnup and Restart information
History case wise data (repeat for each history case)
5
History case identification
Reference state data
6
State identification
XS Data Block (repeat for each burnup point)
7
Burnup point identification
8
Principal cross sections
9
Scattering cross sections
10
ADF
11
CDF
12
Local Power Peaking Factors
13
Power form function
14
Group-wise form function
15
Detector information
16
Xe/Sm cross sections
17
Delayed neutron data
18
Decay heat data
19
End Label of XS Block
Existence
NBRA>1
Always
Always
Always
NEXP>1
Always
Always
Always
Always
Always
NBURN>1
Always
Always
Optional
Optional
Optional
Optional
Optional
Optional
Optional
Optional
Optional
Always
Control rod branch cases (same structure with Ref. state case)
Moderator density branch cases (same structure)
Soluble Boron branch cases (same structure)
Fuel temperature branch cases (same structure)
IBCR>0
IBMD>0
IBSB > 0
IBTF>0
Moderator temperature branch cases (same structure)
IBTM >0
*The data in XS Block are original data for reference state, data difference for CR branch case, and partials
for other branches
1
Branches information (repeat for all type of branches structures)
XS Set wise data
2
XS Set identification
3
Dimension data
Reference state data
6
State identification
XS Block
8
Principal cross sections
9
Scattering cross sections
10
ADF
11
CDF
12
Local Power Peaking Factors
13
Power form function
14
Group-wise form function
15
Detector information
16
Xe/Sm cross sections
17
Delayed neutron data
18
Decay heat data
19
End Label of XS Block
Existence
NBRA>1
Always
Always
Always
Always
Always
Always
Always
Always
Optional
Optional
Optional
Optional
Optional
Optional
Optional
Optional
Optional
Always
Control rod branch cases (same structure with Ref. state case)
Moderator density branch cases (same structure)
Soluble Boron branch cases (same structure)
Fuel temperature branch cases (same structure)
IBCR>0
IBMD>0
IBSB > 0
IBTF>0
Moderator temperature branch cases (same structure)
IBTM >0
*The data in XS Block are original data for reference state, data difference for CR branch case, and partials
for other branches
24
New Model Successfully Applied to
Previous TRACM/PARCS Benchmarks

OECD MSLB & PBTT Benchmarks: NEMTAB format
* NEM-Cross Section Table Input
*
* T Fuel
Rho Mod.
Boron ppm. T Mod.
5
6
0
0
*
*******
X-Section set #
1
1
*
*
Group No. 1
*
***************
Diffusion Coefficient Table
*
.5000000E+03 .7602200E+03 .8672700E+03 .9218800E+03
.6413994E+03 .7114275E+03 .7694675E+03 .7724436E+03
.8100986E+03 .1467049E+01 .1469641E+01 .1470751E+01
.1477128E+01 .1401975E+01 .1404351E+01 .1405441E+01
.1411216E+01 .1353822E+01 .1356107E+01 .1357086E+01
.1362596E+01 .1352366E+01 .1354638E+01 .1355630E+01
.1361236E+01 .1345620E+01 .1347891E+01 .1348843E+01
.1354390E+01 .1322122E+01 .1324319E+01 .1325308E+01
.1330615E+01
*
***************
Total Absorption X-Section Table
.1500000E+04
.7813064E+03
.1471347E+01
.1405939E+01
.1357581E+01
.1356125E+01
.1349338E+01
.1325803E+01
25
Application of New XSEC Model to OECD
Ringhalls Instability Benchmark
Axial Power Distribution (HZP)
3.5
PARCS-ENTRÉE XS-NoADF
Keff = 1.11430
3
Relative Power
2.5
PARCS-PMAXS-ADF
Keff = 1.11400
2
ENTRÉE-ADF
keff=1.11508
PARCS-PMAXS-No ADF
Keff = 1.11465
1.5
ENTRÉE -No ADF
keff=1.11473
1
0.5
0
0
5
10
15
20
25
30
Axial level
Entree No ADF
Entree ADF
PARCS-PMAXS-No ADF
PARCS-PMAXS-ADF
PARCS-ENTREE XS-No ADF
26
Continuing Cross Section Work

Future work


New interface between PARCS and Depletor
(12/31/02)
GENPXS to convert other lattice code cross
sections to PMAXS(e.g. CASMO, ORNL
SCALE/NEWT) (FY03)
27
Modifications of Cross Section
Model for ESBWR
Task 3: Modifications in Spatial Kinetics Feedback
Task 3.1: Lattice Physics (Purdue)
 Improve cross section model in PARCS for ATRIUM-10 and
GE-12/14
 The cross section model in PARCS will be improved to
provide feedback based on both bypass liquid
temperature and channel internal fluid field.
 Concerning fuel temperature feedback, the cross section
model will be updated to handle both full length and part
length fuel rods.
 Perform lattice physics calculations
 The work on this subtask will be completed by November
28
30, 2002.
Advanced BWR Fuel Design
GE-12 Fuel Configuration
29
Advanced BWR Fuel Design
ATRIUM-10
Framatome
SVEA-96 (ABB)
Westinghouse 1/3 part length
full length
2/3 part length
30
Modifications for ESBWR (cont.)
Task 3.2: Monte Carlo Studies (Purdue)
 A new energy partitioning algorithm will be
developed for PARCS taking into account bypass
water regions, water rod regions, intra-channel fluid
regions, and fuel rods.
 A Monte Carlo calculation will be performed to
validate this new algorithm. All results will be
documented.
 The Monte Carlo study will be completed by
December 31, 2002.
31
Modifications for ESBWR (cont.)
Task 3.3/3.4: Modify Mapping / Test Spatial Kinetics
Feedback (ISL)



Modify Mapping to Accommodate new assembly cross
section model
To test the spatial kinetics feedback with a Browns Ferry
full core model will be built and a sample steady-state and
control rod move transient calculation will be performed.
The spatial kinetics model feedback testing will be
completed by February 28, 2003.
32
ESBWR Core Configuration
33