1

New PARCSCross Section Model

School of Nuclear Engineering Purdue University

September 2002

2

Original XS Model in PARCS (1997)

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

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

2

2

2

),,,,( DmDm

SbSb

DmDm

TmTm

TfTf

SbDmTmTf crr

3

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

4

Applications of Original Model:Static and Spatial Kinetics Problems

Eigenvalue Benchmark ProblemsIAEA3D, 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)

)()()()()(

tNtNtNdt

tdNBBcCAA

aA

A

B

C

A

n,γ

β β

Absorb netron

''),',',()',',(

),,(4

1),,,(),(),,,(

1

' '

ddEtErEEr

tErStErErtErtv

E

s

ft

Neutron Transport Equation (Boltzmann)

6

Depletion XS Model

2

2

2

),,,,( DmDm

SbSb

DmDm

TmTm

TfTf

SbDmTmTf crr

Burnup and burnup “history” dependence More than seven data points can be referenced

)2,1,,()2,1,,(

)2,1,,()2,1,,(

)2,1,,()2,1,(

2

2

2

2

HISHISBUDmDmDm

HISHISBUDmDmDm

HISHISBUTmTmTm

HISHISBUTfTfTf

HISHISBUSbSbSb

HISHISBUcrcr

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)

ΦΣ

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 Calculation

s

XS library generator

Output files

Cross section library

XS interpreter

Neutronics Calculation

XS of each

region

10

First Step of in NRC Neutronic Code System

GenpXS

Output files

PMAXS

Lattice Codes:SCALEHELIOS

….

Input files

for depletion at various base states

and branches at some burnup points

11

Base State and Branches Performed with Lattice Physics

Code

Base state Branches

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

Fuel temp.

Tf1, Tf2…

mod temp.

Tm1, Tm2…

Mod. den.

Dm1, Dm2…

Soluble B.

ppm1, …

Control

rod …

12

Cross Section Library in NRC Neutronic Code System

PMAXS

Dependent Variables:

.......

,:2

,:

)(,:

,,,,,,,,:&

,:,:

...,,,,,,:

1

'

powerfluxFunctionsFormD

smultiplierfunctionsformninformatioDetector

ncalculatioMCPRforJfFactorsPeakingLocal

YYYYSectionsCrossSamariumXenon

parametersHeatDecayparametersNeutonDelay

CDFADFSectionsCrossPrinciple

Power

PmIXeISmPmXeISma

Xea

HH

ggtrffa

Independent Variables:

etcfunctionFormfactorLocalforLocation

GroupHeatDecayGroupNeutronDelay

groupenegyNeutronIDLatticevariablesOther

HTmHTfHSbHMdHCrvariablesHistory

TmTfSbMdCrvariablesousInstantane

,,

,,

,,:

,,,,:

,,,,:

13

PMAXS Depletor

Neutronic Calculation

XS of each region at given history

value

XS Model: Interpret XS base on

instantaneous variables

Power distributio

n

PARCS T/H Code:

RELAP

TRAC ….

Second Step of in NRC Neutronic Code

System

14

Format of PMAXS in Depletion

Cross Section ModelAppendix B. PMAXS format

----------------------------------------------------------------------

PMAXS (version 1.0, revision-01) ----------------------------------------------------------------------

Last revised 4/2/01 The Format of Purdue Macroscopic Cross Section (XS) Set ----------------------------------------------------------------------

Existence

File Data always

File identification

Fuel Assembly wise data (repeat for all kinds of assemblies) always

Assembly identification Assembly control data Assembly Group independent data Assembly Energy bound information data Reference state data always

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 LORD > 0 Xe/Sm cross sections of the base state ISXE=1 Soluble boron cross section of the base state ISSB = 1 Delayed neutron data of the base state NDFAM > 0 Decay heat data of the base state NDCAY > 0 Power form function of the base state IPFF = 1 Group-wise form function of the base state IGFF=1 Detector information of the base state ISDE=1 Soluble Boron branch case IBSB > 0 Identification Control data State data (repeat for all soluble boron branch case) Derivation of the principal cross sections

15

Motivation for New PARCSCross 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

),,(),,(

),,(),,(

),(),,,,,(

HCRCRDEXPCRDVOIEXP

TFUVOIEXPVOIHVOEXP

HVOEXPCRDTFUVOIHCRHVOEXP

HCRCRD

TFUVOI

base

18

Application of New Model to Ringhalls

 

),,,,(),,,,(

),,,,(),,,,(

),,,(),,,(),,,,(

mrm

rrmrrrm

i

rrrrii

rrrrr

TmTfSbDmTmTm

TmTfSbDmTfTf

TmTfSbDmSbSb

TmTfSbDmDmDm

TmTfSbDmTmTfSbDmTmTfSbDm

rTfTfTf 2/)( rm TfTfTf

If the XS at blue point are also available, New Model gives same XS as Model 2 better than Model 1Other wise New Model gives same XS as Model 1 better than Model 2

The partials will be obtained by piece wise linear interpolation

19

Important to Choose Best Sequence to Evaluate

Variables

 

mD

K

BD

K

fT

K

mT

K

mD Very Strong Strong Strong Very Strong

BD Strong Normal Normal Very Strong

fT Weak Weak Weak Normal

mT Almost no Almost no Almost no Strong

Suggested sequence: Dm DB Tf Tm

20

Example: Moderator temperature and density

 

450

500

550

600

0.30.4

0.50.6

0.70.8

0.9

0.86

0.88

0.9

0.92

0.94

0.96

Temperature

Original

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

),(),(),(),( mrmrr

DmTmDmDm

DmTmTmTmDmTmDmTm

21

Effect of Different Sequence: Using Temperature then Density

 

450500

550600

0.4

0.6

0.8

10.86

0.88

0.9

0.92

0.94

0.96

Temperature

linear interpolation

Density

450500

550600

0.4

0.6

0.8

1-0.04

-0.02

0

0.02

0.04

Temperature

error of linear interpolation, rms=0.01202

Density

),(),(),(),( mrmrr

DmTmDmDm

DmTmTmTmDmTmDmTm

22

Effect of Different Sequence: Using Density then Temperature

 

0.30.4

0.50.6

0.70.8

0.91

450

500

550

600

0.86

0.88

0.9

0.92

0.94

0.96

Density

linear interpolation

Temperature

),(),(),(),( mrmrr

TmDmTmTm

TmDmDmDmTmDmTmDm

0.30.4

0.50.6

0.70.8

0.91

450

500

550

600

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

x 10-3

Density

error of linear interpolation, rms=0.00098

Temperature

90% error reduced

23

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

calcul

XS Dm

partials calcul

XS SB

partials calcul

XS Tf

partials calcul

XS Tm

partials

Dm1 Dm1m Tf1 Tf1m

Tmr Tfr Tm1 Tm1m

Sbr

Tf2 Tf2m

Dmr

Sb1 Sb1m Dm2 Dm2m

Sb2 Sb2m

1: no

Dm3 Dm3m

Sbr

Tm2 Tm2m Tmr

2:SS

Tm3 Tm3m

Sbr

Tfr

Dmr Sbr Tfr Tmr

3:B4C

Sb3 Sb3m

Tf3 Tf3m

XS at reference states Calculate & Store

XS calculate

XS already calculated

Partials store

24

New PMAXS/XSEC Format Existence

1 Branches information NBRA>1 XS Set wise data Always

2 XS Set identification Always 3 Dimension data Always 4 Burnup and Restart information NEXP>1 History case wise data (repeat for each history case) Always 5 History case identification Always Reference state data Always 6 State identification Always XS Data Block (repeat for each burnup point) Always 7 Burnup point identification NBURN>1 8 Principal cross sections Always 9 Scattering cross sections Always 10 ADF Optional 11 CDF Optional 12 Local Power Peaking Factors Optional 13 Power form function Optional 14 Group-wise form function Optional 15 Detector information Optional 16 Xe/Sm cross sections Optional 17 Delayed neutron data Optional 18 Decay heat data Optional 19 End Label of XS Block Always Control rod branch cases (same structure with Ref. state case) IBCR>0 Moderator density branch cases (same structure) IBMD>0 Soluble Boron branch cases (same structure) IBSB > 0 Fuel temperature branch cases (same structure) 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

Existence 1 Branches information (repeat for all type of branches structures) NBRA>1 XS Set wise data Always

2 XS Set identification Always 3 Dimension data Always Reference state data Always 6 State identification Always XS Block Always 8 Principal cross sections Always 9 Scattering cross sections Always 10 ADF Optional 11 CDF Optional 12 Local Power Peaking Factors Optional 13 Power form function Optional 14 Group-wise form function Optional 15 Detector information Optional 16 Xe/Sm cross sections Optional 17 Delayed neutron data Optional 18 Decay heat data Optional 19 End Label of XS Block Always Control rod branch cases (same structure with Ref. state case) IBCR>0 Moderator density branch cases (same structure) IBMD>0 Soluble Boron branch cases (same structure) IBSB > 0 Fuel temperature branch cases (same structure) 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

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. 5 6 0 0******** X-Section set # 1 1** Group No. 1**************** Diffusion Coefficient Table * .5000000E+03 .7602200E+03 .8672700E+03 .9218800E+03 .1500000E+04 .6413994E+03 .7114275E+03 .7694675E+03 .7724436E+03 .7813064E+03 .8100986E+03 .1467049E+01 .1469641E+01 .1470751E+01 .1471347E+01 .1477128E+01 .1401975E+01 .1404351E+01 .1405441E+01 .1405939E+01 .1411216E+01 .1353822E+01 .1356107E+01 .1357086E+01 .1357581E+01 .1362596E+01 .1352366E+01 .1354638E+01 .1355630E+01 .1356125E+01 .1361236E+01 .1345620E+01 .1347891E+01 .1348843E+01 .1349338E+01 .1354390E+01 .1322122E+01 .1324319E+01 .1325308E+01 .1325803E+01 .1330615E+01**************** Total Absorption X-Section Table

26

Application of New XSEC Model to OECD Ringhalls Instability

Benchmark

Axial Power Distribution (HZP)

0

0.5

1

1.5

2

2.5

3

3.5

0 5 10 15 20 25 30

Axial level

Re

lati

ve

Po

we

r

Entree No ADF Entree ADF PARCS-PMAXS-No ADF PARCS-PMAXS-ADF PARCS-ENTREE XS-No ADF

PARCS-ENTRÉE XS-NoADFKeff = 1.11430

ENTRÉE-ADFkeff=1.11508

ENTRÉE -No ADFkeff=1.11473

PARCS-PMAXS-ADFKeff = 1.11400

PARCS-PMAXS-No ADFKeff = 1.11465

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 FeedbackTask 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 Advanced BWR Fuel Design

GE-12 Fuel ConfigurationGE-12 Fuel Configuration

30

ATRIUM-10ATRIUM-10FramatomeFramatome

SVEA-96 (ABB)SVEA-96 (ABB)WestinghouseWestinghouse

1/3 part length1/3 part length

full lengthfull length

2/3 part length2/3 part length

Advanced BWR Fuel Design

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 ESBWR Core Configuration