1. New PARCS Cross Section Model
School of Nuclear Engineering
Purdue University
September 2002

2. Original XS Model in PARCS (1997)
r: XS at unroded reference state
cr: Control rod XS; : roded fraction;
Tf: Fuel temperature; 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

3. Example of Original Model
comp_num !corner reflector !
base_macro e e e e e-02
e e e e+00
dxs_dppm e e e e e+00
e e e e+00
comp_num !fuel 1
base_macro e e e e e-02
e e e e-12
dxs_dppm e e e e e-07
e e e e-17
dxs_dtm e e e e e-07
e e e e-16
dxs_ddm e e e e e-02
e e e e-13
dxs_dtf e e e e e-05
e e e e-16
cdf
delcr_comp !compostions that this set applies
delcr_base e e e e e-03
e e e e-14

4. 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)

5. Depletion Capability Added (2000)
Nuclide depletion equation (Bateman) B C A
n,γ β
Absorb netron
Neutron Transport Equation (Boltzmann)

6. Depletion XS Model Burnup and burnup “history” dependence
More than seven data points can be referenced

7. U.S. NRC Coupled Code Analysis
Lattice Code
(HELIOS/NEWT)
Cross Section Library
(PMAX)
Neutron Flux Solver (PARCS)
Depletion Code
(DEPLETOR)
T/H code
(RELAP /TRAC) Φ Σ

8. 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

9. Standard “Two Step” Procedure for Generating LWR Cross Sections
Lattice Calculations
Neutronics Calculation
XS of each region
Output files
XS library generator
XS interpreter
Cross section library

10. First Step of in NRC Neutronic Code System
Input files
for depletion at various base states
and branches at some burnup points
Lattice Codes:
SCALE
HELIOS ….
Output files
GenpXS
PMAXS

11. Base State and Branches Performed with Lattice Physics Code
0GWD/T
Fuel temp.
Tf1, Tf2…
mod temp.
Tm1, Tm2…
Mod. den.
Dm1, Dm2…
Soluble B.
ppm1, …
Control
rod …
5GWD/T
4GWD/T
3GWD/T
1GWD/T
2GWD/T

12. Cross Section Library in NRC Neutronic Code System
Dependent Variables:
PMAXS
Independent Variables:

13. Second Step of in NRC Neutronic Code System
T/H Code:
RELAP
TRAC ….
PMAXS
Depletor
Neutronic Calculation
XS of each region at given history value
XS Model: Interpret XS base on instantaneous variables
Power distribution
PARCS

14. Format of PMAXS in Depletion Cross Section Model

15. 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

16. 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

17. Ringhalls Stability Benchmark
Ringhals XS in TABLES format
Multiple 3-Dimensional tables
Multiple Control rod compositions

18. Application of New Model to Ringhalls
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

19. Important to Choose Best Sequence to Evaluate Variables
Suggested sequence:
Dm DB Tf Tm

20. Example: Moderator temperature and densityTm Dm
415
515
615
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
Selected point
Original Data point

21. Effect of Different Sequence: Using Temperature then Density

22. Effect of Different Sequence: Using Density then Temperature
90% error reduced

23. Tree structure of states at which XS/partials are calculated or stored

24. New PMAXS/XSEC Format

25. 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.
******* X-Section set # 1
* Group No. 1
*************** Diffusion Coefficient Table
E E E E E+04
E E E E E+03
E E E E E+01
E E E E E+01
E E E E E+01
E E E E E+01
E E E E E+01
E E E E E+01
E+01
*************** Total Absorption X-Section Table

26. Application of New XSEC Model to OECD Ringhalls Instability Benchmark

27. 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)

28. 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 30, 2002.

29. Advanced BWR Fuel Design
GE-12 Fuel Configuration

30. Advanced BWR Fuel Design
ATRIUM-10
Framatome
SVEA-96 (ABB)
Westinghouse
1/3 part length
full length
2/3 part length

31. 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.

32. 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.

33. ESBWR Core Configuration