1. 1 Fuel Cycle Analysis Methods for Advanced Reactor Concepts Yunlin Xu T.K. Kim D. Tinkler T.J. Downar Purdue University Sept. 12, 2001 The 2001 ANS International Topic Meeting on Mathematics and Computation

2. 2 Content Motivation Depletion Code system Verification Application on SBWR Further Improvements

3. 3 Motivation NERI/DOE projects at Purdue SBWR: evolutionary “Generation III+” HCBWR: revolutionary “Generation IV” We need a ‘depletion code system’ for Neutonic designing: Fuel cycle analysis Safety analysis (throughout core life)

4. 4 Total Height 24.6 m Internal Diameter 6.0 m Fuel Length 2.74 m Chimney Height 9 m SBWR Reactor Vessel

5. 5 SBWR Containment (GE) Gravity Driven Coolant System (GDCS) Automatic Depressurizatio n System (ADS) Passive Containment Cooling System (PCCS) Suppression Pool

6. 6 HCBWR--principle HCBWR FBR LWR

7. 7 HCBWR- strategy

8. 8 HCBWR- Purdue/BNL design Tight lattice hard spectrum long cycle length Thorium as fertile negative void coefficient all through the cycle

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

10. 10 HELIOS Gadolinium pin BP1 BP2 The octant of fuel assembly 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.

11. 11 GENPXS and PMAXS The PMAXS file structures GENPX read the outputs of HELIOS and generate PMAXS files PMAXS tabulates the XS’s of the base state and the derivatives or difference of XS of the branches and related information

12. 12 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 …

13. 13 PARCS Purdue Advanced Reactor Core Simulator A Multidimensional Multigroup Reactor Kinetics Code Based on the Nonlinear Nodal Method Under NRC Contract T. J. Downar etc

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

15. 15 Coupling of Code System D2NIR P2DIR DEPLETOR Depletor Input Nuclide Field/ Burunup PARCS Neutronics Input Thermal Hydraulics Field Thermal Hydraulics Input PDMRRDMR RELAP /TRAC Neutron Field Q Q T,ρ

16. 16 Coupling of Code System 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

17. 17 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

18. 18 PARCS Cross Section 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)

19. 19 Burnup and History Calculation in Depletor 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. History( moderator density)

20. 20 Multidimension linear interpolation History 1 History 2 Burnup

21. 21 Reference XS and Derivatives x0x0 xrxr No branch x1x1 x0x0 xrxr One branch x i+1 x0x0 xrxr xixi x xixi x0x0 xrxr x More than One branch for(ppm,Tf,Tm)

22. 22 Reference XS and Derivatives x2x2 x0x0 xrxr x1x1 Two branches for D More than Two branches for D x i x i+1 x i+2 x 0 x r x x i x i+1 x 0 x r x i+2 x

23. 23 Gadolinium pin BP1 BP2 The octant of fuel assembly Verification Maximum Difference 2×10 -5 Comparison with HELIOS Problem 1: Single Assembly with reflective B.C.

24. 24 Verification Maximum Difference 0.3% Compared with MASTER (KEARI) Problem 2 Checkerboard small core with vaccum B.C.

25. 25 600 MWe SBWR Design Fresh fuel, 69 Once burned Fuel, 69 Twice burned Fuel, 45 Total 732 Fuel Assemblies

26. 26 Fuel Assembly Design (GE 8x8) (8 Gd Rods) Percent Enrichments (3.95 wt% average) –2.4 –3.3 –3.7 –4.2 –5.3 –5.6 –Gd (1.8)

27. 27 RELAP5 Model Currently uses 63 Core channels Models Vessel Only –From Cold to Hot Leg –Inlet: Feedwater Tank –Outlet: Turbine Side Similar Models built for 200 and 1200 MWe

28. 28 Neutronics to TH Mapping 1 1 1 1 1 1 1 1 1 2 2 3 3 3 1 1 1 5 7 8 8 9 10 9 1 1 5 7 12 14 14 15 13 16 13 1 1 6 12 12 19 20 19 18 17 18 17 1 1 6 11 26 25 23 24 23 22 21 22 21 1 1 6 11 33 27 28 27 28 29 30 29 30 32 1 5 12 26 27 36 37 36 38 34 34 39 40 35 1 1 7 12 25 28 37 44 43 41 34 34 41 42 35 1 5 12 19 23 27 36 43 49 48 45 47 45 46 45 1 1 7 14 20 24 28 38 41 48 54 50 51 50 51 52 1 2 8 14 19 23 29 34 34 45 50 56 56 57 58 55 1 2 8 15 18 22 30 34 34 47 51 56 56 58 57 55 1 4 9 13 17 21 29 39 41 45 50 57 58 64 63 62 1 4 10 16 18 22 30 40 42 46 51 58 57 63 61 60 1 4 9 13 17 21 31 35 35 45 53 55 55 62 59 59 856 Neutronics Channels 732 (Fuel), 124(Reflector) 63 TH Fuel Channels, 2 Bypass

29. 29 Preliminary Comparison of 600 MWe Core TH Properties ABWRGE SBWRPurdue SBWR (BOC) Power3926 MWt2000 MWt Core Flow Rate52.2X10 6 kg/hr27.2X10 6 kg/hr27.0X10 6 kg/hr Power Density50.6 kW/liter41.5 kW/liter MCPR1.171.32-- Average Core Void Fraction 0.4080.4340.448 Core Pressure7.274 MPa7.239 MPa7.22 MPa Core Pressure Drop0.168 MPa0.048 MPa0.038 MPa Average Exit Quality0.140.1430.157

30. 30 Axial/Radial Power Profiles (BOC)

31. 31 Depletion Results B (GWd/MT) C.R. Notches (798) Max PeakRadial PeakAxial PeakB Average (GWd/MT) 0.0004861.7961.3071.30213.9 1.14561.7431.2801.25415.0 2.24561.7971.2711.25816.1 3.34561.8761.2631.27217.2 4.44561.9841.2621.29918.3 5.54632.1421.2961.35519.4 6.64982.3421.3321.44020.5 7.74982.3271.3501.44421.6 8.84912.1601.3531.38622.7 9.94221.8841.3441.25223.8 11.02171.8361.3251.38224.9 12.102.0691.3041.36826.0

32. 32 Other Related Works VIPRE as a T/H solver for Depletion system An EPRI code, with steady state option Used for 200MW and 1200 MW SBWR design Used for HCBWR analysis Used for Ringhalls Benchmark problem Successfully treat the history effect

33. 33 Further improvements Predictor-corrector Time integration method Microscopic depletion?

34. 34 Thank You !