1 Depletion Code System

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

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

4 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)

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

6 Heavy Metal Chains Arrow up :neutron capture Arrow down:(n,2n) reaction Arrow left :electron capture Arrow right:  decay or  decay for Am242 m

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

8 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 N i and σ Σ change depend on Burnup ComplicatedEasy to implement Smaller history effectLarger history effect

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

10 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 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 Gadolinium pin BP1 BP2 The octant of fuel assembly

11 Base state and Branches Base stateBranches 0GWD/T Fuel temp. T f1, T f2 … mod temp. T m1, T m2 … Mod. den. D m1, D m2 … Soluble B. ppm 1, … Control rod … 5GWD/T 4GWD/T 3GWD/T 1GWD/T 2GWD/T Fuel temp. T f1, T f2 … mod temp. T m1, T m2 … Mod. den. D m1, D m2 … Soluble B. ppm 1, … Control rod …

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

13 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

14 PARCS Validation Pressurized Water Reactor: –Reactivity Initiated Transients (CEA, etc.) –OECD TMI Main Steam Line Break (PARCS coupled to RELAP5 and TRAC-M) Boiling Water Reactor –OECD Peach Bottom Turbine Trip Benchmark –OECD Ringhalls Stability Benchmark (Ongoing)

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

16 Coupling of PARCS to TRAC-M/RELAP5 Coupling of PARCS to DEPLETOR T/H Data Map Thermal Hydraulics Memory Structure (A) (A)  (AB) Thermal Hydraulics Input T/H Side Interface Input General Interface Neut. Data Map Neutronics Memory Structure (AB) Memory Structure (B) (AB)  (B) Neut. Side Interface Input Neutronics Input P2DIR DEPLETOR Memory Structure (A) (A)  (AB) Depletor Input Depl. Side Interface Input Neut. Data Map Neutronics Memory Structure (B) (AB)  (B) Neut. Side Interface Input Neutronics Input

17 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 (RELAP5) 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. P2DIR, a module to communicate with DEPLETOR, was created in PARCS (only 5 entry points in PARCS)

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

19 Coupling PARCS/DEPLETOR to TH EOC D2NIR(1) D2NIR(2) D2NIR(4) D2NIR(3) DEPLETION READINP DEPLETOR INITIAL XSB y n D2NIR(2)XSB End RELAP/TRAC R(T)DMR(1) R(T)DMR(2) R(T)DMR(3) End done y n PARCS CHANGECOMI EOC P2DIR(3) P2DIR(4) P2DIR(2) P2DIR(1) depl PREPROC INPUTD depl SSEIG depl extth INIT PDMR(2) PDMR(3) PDMR(1) Thconv SCANINPUT CHANGEDIM depl y y y y y y n n n n n n P2DIR(2) End

20 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.

21 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

22 Gadolinium pin BP1 BP2 The octant of fuel assembly Verification Problem 1: Single Assembly with reflective B.C. Maximum Difference 2×10 -5 Comparison with HELIOS

23 Verification Problem 2 Checkerboard small core with vaccum B.C. Maximum Difference 0.3% Compared with MASTER (KEARI)

24 BWR model Mapping between Neutronic and T/H model Upper Plenum: 400 Lower Plenum: TANK SINK Plenum to Plenum T/H model A B B A Neutronic model

25 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 RELAPVIPREDIFFERENCE TH steps per depletion step % keff pcm fxy % fz % Exit void Fraction Chan % Chan % Maximum fuel Temperature (K) Chan Chan

26 Comparison between RELAP and VIPRE

27 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)

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

29 Thank You !