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

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

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

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)

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

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

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

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

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

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

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

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

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

Format of PMAXS in Depletion Cross Section Model

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

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

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

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

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

Example: Moderator temperature and density Tm 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  

Effect of Different Sequence: Using Temperature then Density  

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

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

New PMAXS/XSEC Format

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

Application of New XSEC Model to OECD Ringhalls Instability Benchmark

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)

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.

Advanced BWR Fuel Design GE-12 Fuel Configuration

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

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.

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.

ESBWR Core Configuration