Depletion Code System 1 Depletion Code System Yunlin

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Depletion Code System 1

Depletion Code System 1

Depletion Code System Yunlin Xu T. K. Kim T. J. Downar School of Nuclear

Depletion Code System Yunlin Xu T. K. Kim T. J. Downar School of Nuclear Engineering Purdue University March 28, 2001 2

Content Motivation What is Depletion? Depletion code system Verification Further improvements 3

Content Motivation What is Depletion? Depletion code system Verification Further improvements 3

Motivation Why do we need depletion code system? Basic tool for Nuclear Reactor fuel

Motivation Why do we need depletion code system? Basic tool for Nuclear Reactor fuel cycle analysis NERI/DOE projects at Purdue SBWR HCBWR Nuclear Power Reactor Analysis – Economics – Safety (throughout core life) 4

What is Depletion? Nuclide density change in nuclear reactor core when operated at power

What is Depletion? Nuclide density change in nuclear reactor core when operated at power Related changes Cross Section Nuclide density (Heavy metal, Cross Section feedback Fission products) Decay Heat Reactivity economic safety Depletion code system must solve coupled nuclide/neutron and temperature/fluid field equations 5

Cm 246 Heavy Metal Chains Pu 243 Cm 245 Am 244 Cm 244 Am

Cm 246 Heavy Metal Chains Pu 243 Cm 245 Am 244 Cm 244 Am 243 Cm 243 m Pu 242 Am 242 Cm 242 Pu 241 Np 240 Pu 240 U 239 Np 239 Pu 239 U 238 Np 238 Pu 238 U 237 U 236 α Am 241 α Np 237 Np 236 Pu 236 U 235 α Th 233 Pa 234 U 234 Pa 233 U 233 Th 232 Pa 232 U 232 Th 231 Pa 231 U 231 (n, 3 n) Th 230 (n, 3 n) α (n, 3 n) Arrow up Arrow down Arrow left Arrow right : neutron capture : (n, 2 n) reaction : electron capture : decay or decay for Am 242 m 6

Equations for Depletion Nuclide depletion equation (Bateman) Absorb netron B β β A n,

Equations for Depletion Nuclide depletion equation (Bateman) Absorb netron B β β A n, γ C Neutron Transport Equation (Boltzmann) 7

Micro vs Macroscopic Depletion Microscopic Macroscopic • Lattice code provide σ • Lattice code

Micro vs Macroscopic Depletion Microscopic Macroscopic • Lattice code provide σ • Lattice code provide Σ • Solve for Nuclide Field from the Bateman equation • N/A (Nuclide density and micro changes are combined) • Σ change depend on Ni and σ • Σ change depend on Burnup • Complicated • Easy to implement • Smaller history effect • Larger history effect 8

Basic Depletion code system Lattice Code (HELIOS) Neutron Flux Solver (PARCS) Σ Cross Section

Basic Depletion code system Lattice Code (HELIOS) Neutron Flux Solver (PARCS) Σ Cross Section Library (PMAX) T/H code (RELAP /TRAC) Φ Depletion Code (DEPLETOR) 9

HELIOS and PMAX HELIOS is a comercial (Studsvik Scandpower) lattice physics code for solving

HELIOS and PMAX HELIOS is a comercial (Studsvik Scandpower) lattice physics code for solving Boltzmann equation with fine energy group, heterogeneous, two-Dimensional models of the fuel lattice Gadolinium pin BP 1 BP 2 HELIOS uses consistent fuel assembly homogenization and energy group collapsing methods to produce few group cross sections at all fuel assembly conditions throughout the burnup cycle. PMAX tabulates the XS’s of the base state and the derivatives or difference of XS of the branches The octant of fuel assembly 10

Base state and Branches Base state 0 GWD/T Branches Fuel temp. mod temp. Mod.

Base state and Branches Base state 0 GWD/T Branches Fuel temp. mod temp. Mod. den. Soluble B. Control Tf 1, Tf 2… Tm 1, Tm 2… Dm 1, Dm 2… ppm 1, … rod … 1 GWD/T 2 GWD/T 3 GWD/T 4 GWD/T 5 GWD/T 11

Reactor Core Configuration Characteristics of Configuration Heterogeneous in Radial Direction - Fuel Assemblies -

Reactor Core Configuration Characteristics of Configuration Heterogeneous in Radial Direction - Fuel Assemblies - Fissionable Absorbers - Control Banks - Reflectors • Homogeneous / Heterogeneous in Axial Direction 12

PARCS Purdue Advanced Reactor Core Simulator A Multidimensional Multigroup Reactor Kinetics Code Based on

PARCS Purdue Advanced Reactor Core Simulator A Multidimensional Multigroup Reactor Kinetics Code Based on the Nonlinear Nodal Method Under NRC Contract Thomas J. Downar Han Gyu Joo Douglas A. Barber Matt Miller 13

PARCS Validation Pressurized Water Reactor: – Reactivity Initiated Transients (CEA, etc. ) – OECD

PARCS Validation Pressurized Water Reactor: – Reactivity Initiated Transients (CEA, etc. ) – OECD TMI Main Steam Line Break (PARCS coupled to RELAP 5 and TRAC-M) Boiling Water Reactor – OECD Peach Bottom Turbine Trip Benchmark – OECD Ringhalls Stability Benchmark (Ongoing) 14

PARCS The Cross Section representation used in PARCS Where Σr: XS at reference state

PARCS The Cross Section representation used in PARCS Where Σr: XS at reference state ppm: soluble boron concentration (ppm) Tf: fuel temperature (k) Tm: moderator temperature (k) D: moderator density (g/cc) 15

Coupling of PARCS to TRACCoupling of PARCS to M/RELAP 5 DEPLETOR Thermal Depletor Hydraulics

Coupling of PARCS to TRACCoupling of PARCS to M/RELAP 5 DEPLETOR Thermal Depletor Hydraulics Input Neutronics Input Depl. Side T/H Side Interface Input Thermal DEPLETOR Hydraulics T/H P 2 DIR Data Map Neut. Side Interface Input General Interface (A) (AB) Memory Structure (A) Neut. Data Map Neutronics (AB) (B) Memory Structure (AB) Memory Structure (B) 16

Depletion code system based on PARCS In order to minimize the changes to PARCS,

Depletion code system based on PARCS In order to minimize the changes to PARCS, A separate code DEPLETOR was developed The general interface used to couple TH (RELAP 5) and PARCS was used to coupled DEPLETOR to PARCS The message transfer between PARCS and DEPLETOR is performed using the standard message passing interface software PVM. P 2 DIR, a module to communicate with DEPLETOR, 17 was created in PARCS (only 5 entry points in

Algorithm for Depletion code system PARCS DEPLETOR Read inputs Exchange ID Initialize PVM Nodalization

Algorithm for Depletion code system PARCS DEPLETOR Read inputs Exchange ID Initialize PVM Nodalization Calculate XS Receive XS XS & Derivatives Send XS Neutron Flux Calc Send Fluxes Burnup Clac Flux & XS Receive Fluxes EOC END 18

Coupling PARCS/DEPLETOR to TH PARCS RELAP/TRAC PREPROC DEPLETOR SCANINPUT depl INPUTD READINP CHANGEDIM y

Coupling PARCS/DEPLETOR to TH PARCS RELAP/TRAC PREPROC DEPLETOR SCANINPUT depl INPUTD READINP CHANGEDIM y depl n CHANGECOMI P 2 DIR(1) D 2 NIR(1) INITIAL P 2 DIR(2) D 2 NIR(2) XS B INIT R(T)DMR(1) PDMR(2) y extth n y depl n P 2 DIR(4) P 2 DIR(2) R(T)DMR(2) PDMR(2) R(T)DMR(3) PDMR(3) n done y End Thconv y D 2 NIR(4) D 2 NIR(2) XSB SSEIG n y End n EOC DEPLETION n n depl y P 2 DIR(3) D 2 NIR(3) EOC y End 19

Cross Section Model used in Depletor Interpolating XS for a Specified burnup Using a

Cross Section Model used in Depletor Interpolating XS for a Specified burnup Using a Tabular XS Set Calculating the Burnup Distribution. ΔB(i): burnup increment of ith region ΔBc: Core average burnup increment G(i): the heavy metal loading in ith region Gc: total heavy metal loading in the core P(i): Power in ith region Pc: Total power in core. 20

Cross Section Model used in Depletor Calculating XS and Derivatives at Reference States No

Cross Section Model used in Depletor Calculating XS and Derivatives at Reference States No Branch State Case One Branch State Case Two Branch States Case 21

Verification Problem 1: Single Assembly with reflective B. C. Comparison with HELIOS Gadolinium pin

Verification Problem 1: Single Assembly with reflective B. C. Comparison with HELIOS Gadolinium pin BP 1 BP 2 The octant of fuel assembly Maximum Difference 2× 10 -5 22

Verification Problem 2 Checkerboard small core with vaccum B. C. Compared with MASTER (KEARI)

Verification Problem 2 Checkerboard small core with vaccum B. C. Compared with MASTER (KEARI) Maximum Difference 0. 3% 23

BWR model Mapping between Neutronic and T/H model SINK 401 Upper Plenum: 400 301

BWR model Mapping between Neutronic and T/H model SINK 401 Upper Plenum: 400 301 B A A 302 303 B 201 101 Neutronic model TANK 099 202 102 203 103 Lower Plenum: 100 Plenum to Plenum T/H model 24

Comparison between RELAP and VIPRE RELAP and TRAC are transient codes and do not

Comparison between RELAP and VIPRE RELAP and TRAC are transient codes and do not solve the steady-state thermal-hydraulics equations We therefore examined another T/H code, VIPRE (EPRI), which has a steady state option There are three models in VIPRE: HEM, Drift Flux Model, and Two Fluid Model Drift Flux Model was used for preliminary comparison RELAP VIPRE DIFFERENCE TH steps per depletion step 1123 75 -93. 3% keff 1. 0816502 1. 0816311 -1. 9 pcm fxy 1. 0897 1. 0878 -0. 17% fz 1. 8066 1. 8200 0. 74% Exit void Fraction Chan-1 0. 6572 0. 6578 0. 06% Chan-2 0. 7150 0. 7172 0. 22% Maximum fuel Temperature (K) Chan-1 2144. 4 2153. 9 9. 5 Chan-2 1847. 3 1844. 8 -2. 5 25

Comparison between RELAP and VIPRE 26

Comparison between RELAP and VIPRE 26

Comparison between RELAP and VIPRE There is generally good agreement between RELAP and VIPRE

Comparison between RELAP and VIPRE There is generally good agreement between RELAP and VIPRE The only visible difference is the fluid temperature which may be due to the sub-cooled void model. VIPRE provides LEVY and EPRI models (The EPRI model is used in this comparison) 27

Further improvements VIPRE Two Fluid Model History effects in Macroscopic X-sections Predictor-corrector Time integration

Further improvements VIPRE Two Fluid Model History effects in Macroscopic X-sections Predictor-corrector Time integration method Microscopic depletion? 28

Thank You ! 29

Thank You ! 29