Workshop on RAPID Code System

Transcription

1 Workshop on RAPID Code System Alireza Haghighat Professor & Director Virginia Tech Transport Theory Group (VT 3 G) Nuclear Science & Engineering Lab (NSEL) at Arlington Nuclear Engineering Program, Mechanical Engineering Department Virginia Tech Arlington, VA For One-day Workshop at the NRC, Nov 9, 2017

2 Nuclear Engineering R&D at National Capital Region (NCR) NSEL (Nuclear Science and Enginering Lab), Arlington, VA Operates under auspices of ICTAS* and Mechanical Engineering Department. Virginia Tech Research Center Arlington, VA It engages with various entities/organizations at Virginia Tech and beyond, addressing different applications including: power, security, medicine, and policy *Institute of Critical Technology and Applied Science 2

3 NSEL Collaborations (nsel.ncr.vt.edu) Key R&D Antineutrino detector CHANDLER project for nuclear nonproliferation applications (funded by NSF & VT) Multiphysics for Advanced nuclear Reactor Simulation (MARS) Center (funded by the ICTAS Global Energy and Materials Initiative - GEMI); Creation of a Collaborative Virtual Reality System & Development of VRS-RAPID (funded by office of VP of NCR) Neutron Physics Center, Physics Department (VT) Profs. Huber, Link & Mariani, Phys. Dept. VT: NE, Physics, ME & MSE US: Georgia Tech, NCSU, ORNL, Southern Nuclear EU: Paul Scherrer Institute & Ecole Polytechnique Fédérale de Lausanne, Switzerland; Politecnico di Torino, Italy VT Advanced Computing Research - Visionarium Center Prof. Polys and Dr. Rajamohan, VT-ARC 9

4 US Naval Academy (USNA) Vice Admiral Leidig & Prof. Millett School of Public and International Affairs (SPIA) & Department of Science and Technology in Society Profs. Roberts (SPIA) and Schmid (STS) Mechanical Engineering NCR Profs. Mahajan, Pitchumani & Rahman In collaboration with local universities, government agencies & VT departments, centers and groups NSEL Collaborations (nsel.ncr.vt.edu) Educational Programs Accelerated Master of Engineering in Nuclear Engineering (Jan 2017) Prepared an application for a graduate Certificate in Nuclear Science, Technology, and Policy (NSTP) (Fall 2018) Establishing a CPE activity: Energy Engineering & Innovation (Spring 2018) Has organized various forums, workshops and training courses (technical & policy matters) 4

5 VNEC nonprofit organization Organization Activities Location Virginia Nuclear Energy Consortium (VNEC) nonprofit organization* Promotion of nuclear industry, education and research Membership include: AREVA, B&W, Dominion, GE, Newport News Shipbuilding, UVA, VCU, and VT Prof. Haghighat served as Chairman of the Board, Jan 2015 to July 2016; currently, he serves as the Vice Chairman of the Board Virginia *On June 6, 2016,with help from NEI, VNEC organized the first Virginia Nuclear Energy Summit, and Prof. Haghighat gave an opening talk and participated in two panel discussions. 5

6 NSEL Organization of Workshops/Forums* Year (date) 2011 (Nov 7-11) 2012 (March 11-12) 2012 (Nov 5) 2013 (Aug 7) 2014 (July 20) 2014 (Sept 28) 2014 (Dec 15-18) Title 13 th International Workshop on Particle Transport Simulation of Nuclear Systems ( Symposium on Low Power Critical Facilities (LPCF) in collaboration with SUNRISE (Southeast Universities Nuclear Reactors Institute for Science and Education) ( Forum on Nuclear Regimes: Future Outlooks; sponsors included AREVA, ICTAS, VT-NCR, and partners included Naval Postgraduate school, Federation of American Scientists, and George Washington s Elliot College of International Affairs ( Seminar on nuclear power & education for a group of international reporters (at the request of Department of State) ( a half-day workshop on Advanced particle transport methodologies/tools for nuclear safeguards and non-proliferation, INMM 55 th Annual Meeting, Atlanta, Georgia. (In collaboration with Georgia Tech) A half-day workshop on "Hybrid particle transport methods for solving complex problems in realtime, PHYSOR 2014 International Conference, Kyoto, Japan. (In collaboration with Georgia Tech) MRT Methodologies for Real-Time Simulation of Nuclear Safeguards & Nonproliferation Problems, Modeling and Simulation for Safeguards and Nonproliferation Workshop ORNL. *visit for further details on workshops and related presentations. 6

7 NSEL Organization of Workshops/Forums (continued)* Year (date) 2015 (June 23-25) 2016 (May 6) 2016 (June 6) 2016 (Oct 5) 2018 (April 22) Planning for 2018 (Spring or Summer) Title 1 st Workshop on Methodologies for Spent Nuclear Fuel Pool Simulations (Safety and Safeguards) ( Prof. Haghighat was an invited panelist at the 2016 Energy Sustainability and Resiliency, organized by VA Chamber of Commerce; VNEC set an information booth. Virginia Nuclear Energy Summit, organized by VNEC and NEI; Prof. Haghighat opened the Summit & served on two panels A half-day workshop on MRT Methodologies for Real-Time Particle Transport Simulation of Nuclear Systems at the 3th International Conference on Radiation Shielding (ICRS-13) & 19th Topical Meeting of the Radiation Protection & Shielding Division of the American Nuclear Society (RPSD-2016) in Paris, France, Oct 3-6. A 2.5-hour workshop on MRT Methodology and RAPID Code System, PHYSOR 2018, Cancun, Mexico, April A 3-day workshop on RAPID & VRS-RAPID *visit for further details on workshops and related presentations. 7

8 Particle Transport Theory & the MRT Methodology 8

9 Objective Particle Transport Theory Determine the expected number of particles in a phase space (d 3 rded) at time t: n( r, 3 E, ˆ, t) d rded z d 3 r dω Ω de r y x Number density is used to determine angular flux/current, scalar flux and current density, partial currents, and reaction rates. 9

10 Neutronics Simulation Approaches Deterministic Methods Solve the linear Boltzmann equation to obtain the expected flux in a phase space Statistical Monte Carlo Methods Perform particle transport experiments using random numbers (RN s) on a computer to estimate average properties of a particle in phase space 10

11 Deterministic Linear Boltzmann Equation Integro-differential form ) ˆ,, ( ) ˆ ',, ( ), ( ' ' 4 ) ( ) ˆ ',, ( ) ˆ ' ˆ, ', ( ' ' ) ˆ,, ( ), ( ) ˆ,, (. ˆ E r S E r E r d de E E r E E r d de E r E r E r f s Integral form ), ( 0 ) ', ( ' ) ˆ,, ( ') ( ' ) ˆ,, ( s E E r r s R r r e E r e r Q r r d E r streaming collision scattering fission Independent source 11 11

12 Integro-differential - Solution Method Angular variable: Discrete Ordinates (Sn) method: A discrete set of directions { } and associated weights {w m } are selected ˆ m. ( r, E, ˆ m ˆ ) ( r, E) ( r, E, ˆ m m ) q( r, E, ˆ m ) (3D) 23 Jan V V X V3 Z Spatial variable Integrated over fine meshes using FD or FE methods Energy variable m, g, A V ijk d 3 r V m, g ijk ( r ) Integrate over energy intervals to prepare multigroup cross sections, σ g

13 Integral - Solution method Method of Characteristic (MOC): Model is partitioned into coarse meshes and transport equation is solved along the characteristic paths (k) (parallel to each discrete ordinate (n)), filling the mesh, and averaged Q ( ) (0)exp( ) (1 exp( )) g, m, i g, m, i, k tm, i, k g, m, i, k g, itm, i, k g, itm, i, k gi, 13

14 Deterministic - Issues/Challenges/Needs Robust numerical formulations (e.g., adaptive differencing strategy) Algorithms for improving efficiency (i.e., acceleration techniques synthetic formulations and pre-conditioners) Use of advanced computing hardware & software environments Pre- and post-processing tools Multigroup cross section preparation Benchmarking Over the past 30 years, VT 3 G addressed all the above issues 14

15 Monte Carlo Methods Perform an experiment on a computer; exact simulation of a physical process Path-length r ln t Type of collision s Scattering angle 1 t (isotropic scattering) 2 0 Sample S (r, E, Ω) Tally (count) absorbed Precise expected values; i.e., small relative uncertainty, computation time Variance reduction techniques are needed R x x x, requiring large 15

16 Deterministic vs. Monte Carlo Item Deterministic MC Geometry Discrete/ Exact Exact Energy treatment cross section Discrete Exact Direction Discrete/ Truncated series Exact Input preparation Difficult simple Computer memory Large Small Computer time Small Large Numerical issues Convergence Statistical uncertainty Amount of information Large Limited Parallel computing Complex Trivial 16

17 Why not MC only? Because of the difficulty in obtaining solutions* with reliable statistical uncertainty in a reasonable time: Detailed energy-dependent flux distributions, Time-dependent simulations, Sensitivity analysis, Determination of uncertainties Real-time simulations Eigenvalue problems* face a major difficulty, i.e., lack of source convergence & biased solutions caused by undersampling, High dominance ratio, and/or inter-cycle correlation *Recent Book by Alireza Haghighat on Monte Carlo Methods for Particle Transport, published by CRC Press, Taylor & Francis Group,

18 Why not use advanced hardware? VT 3 G has developed vector and parallel algorithms: Developed two large codes: PENTRAN 1,2,3 (1996) and TITAN 4,5 (2004) Why not use hybrid methods? Deterministic-deterministic (differencing schemes, different numerical formulations, generation of multigroup cross sections, generation of angular quadratures, acceleration techniques) VT 3 G has developed various algorithms; a few have been implemented in PENTRAN and TITAN Monte Carlo-deterministic (variance reduction with the of use deterministic adjoint) VT 3 G has developed CADIS & A 3 MCNP in (1997) 6,7,8 ; CADIS has become popular recently! 18

19 References (related to previous slide) 1) Sjoden G. E. and A. Haghighat, PENTRAN - A 3-D Cartesian Parallel Sn Code with Angular, Energy, and Spatial Decomposition, Proceedings of the Joint International Conference on Mathematical Methods and Supercomputing in Nuclear Applications, Vol. II, , Saratoga Springs, NY, Oct. 6-10, ) Haghighat, A., G.E. Sjoden, and V.N. Kucukboyaci, Effectiveness of PENTRAN s Unique Numerics for Simulation of the Kobayashi Benchmarks, a special issue of the Progress in Nuclear Energy, Vol. 39, No. 2, pp , ) Haghighat, A., H. Aït Abderrahim, and G. E. Sjoden Accuracy and Performance of PENTRAN TM Using the VENUS-3 Benchmark Experiment, Reactor Dosimetry Radiation Metrology and Assessment, ASTM STP 1398, pp , ASTM, Feb ) C. Yi and A. Haghighat, "A three-dimensional block-oriented hybrid discrete ordinates and characteristics method," Nuclear Science and Engineering, Vol. 164(3), pp , ). Haghighat, A., K. Royston, G. Sjoden, C. Yi, and M. Huang, Unique Formulations in TITAN and PENTRAN for Medical Physics Applications, Progress in Nuclear Science and Technology, Volume 4, pp , ) Wagner, J.C. and A. Haghighat, Automated Variance Reduction of Monte Carlo Shielding Calculations Using the Discrete Ordinates Adjoint Function, Nuclear Science and Engineering, 128, , ) Haghighat, A. and J. C. Wagner, Application of A 3 MCNP to Radiation Shielding Problems, Advanced Monte Carlo for Radiation Physics, Particle Transport Simulation and Applications, pp , Springer- Verlag, ) A. Haghighat and J. C. Wagner, "Monte Carlo variance reduction with deterministic importance functions," Progress in Nuclear Energy, Vol. 42(1), pp ,

20 My Journey Particle Transport Algorithms Development Year Methodology Computer code system Wall clock time Former & Current Students VRS-MRT MRT VRS-RAPID RAPID 1 core V. Mascolino Dr. Walters & N. Roskoff 2015 MRT TITAN-IR Dr. Royston 2013 MRT AIMS Drs. Royston & W. Walters MRT Hybrid MC-det. (AVR) Hybrid det. det. Hybrid MC-det. (automated VR - AVR) INSPCT-s ADIES (e ) TITAN (n, ϒ) A 3 MCNP (n, ϒ) 100 s 1000 s cores Dr. W. Walters Dr. B. Dionne Dr. C. Yi Dr. J. Wagner 1996 Parallel (3-D) PENTRAN (n, ϒ) Dr. G. Sjoden 1992 Vector & parallel (2-D) Drs. M. Hunter, R. Mattis & B. Petrovic 1989 Parallel processing (1-D) 1986 Vector processing (1-D) A few processors 20

21 Remarks Particle transport-based methodologies are needed for real-time simulation Even Fast particle transport codes, with parallel and hybrid algorithms, are slow because of large number of unknowns 21

22 Development of Particle Transport Formulations and Methodologies for Real-Time Calculations Physics-Based transport methodologies are needed: Based on problem physics partition a problem into stages (subproblems), For each stage employ response method and/or adjoint function methodology Pre-calculate response-function or adjoint-function using an accurate and fast transport code Solve a linear system of equations to couple all the stages *Haghighat, A., K. Royston, and W. Walters, MRT Methodologies for Real-Time Simulation of Nonproliferation and Safeguards Problems, Annals of Nuclear Energy, pp ,

23 Application of the Nondestructive testing: Optimization of the Westinghouse s PGNNA active interrogation system for detection of RCRA (Resource Conversation and Recovery Act) (e.g., lead, mercury, cadmium) in waste drums (partial implementation of MRT; 1999) 1 Nuclear Safeguards: Monitoring of spent fuel pools for detection of fuel diversion (funded by LLNL); Developed INSPCT-s code system (2007) 2 Nuclear nonproliferation: Active interrogation of cargo containers for simulation of special nuclear materials (SNMs) (2013) (in collaboration with GaTech); developed the AIMS (Active Interrogation for Monitoring Special-nuclear-materials) code system (2013) 3,4 Image reconstruction for SPECT (Single Photon Emission Computed Tomography): Realtime simulation of an SPECT device for generation of project images using an MRT methodology and Maximum Likelihood Estimation Maximization (MLEM); Developed the TITAN-IR code system (filed for a patent, June 2015) 5,6 23

24 References for previous slide 1) B. Petrovic, A. Haghighat, A. Dulloo, and T. G. Congedo, Hybrid Forward Monte-Carlo - Adjoint Sn Methodology for Simulation of PGNAA Systems, Proceedings of the Mathematics and Computation, Reactor Physics and Environmental Analysis in Nuclear Applications, Vol. 2, , Madrid, Spain, Sept , ) Walters, W., A. Haghighat, S. Sitaraman, and Y. Ham, Development of INSPCT-S for Inspection of Spent Fuel Pool, Journal of ASTM International, American Institute of Physics, NY, Volume 9, Issue 4, ) Royston, K., A. Haghighat, W. Walters, C. Yi and G. Sjoden, Determination of Angular Current at a Detector Window Using a Hybrid Adjoint Function Methodology, Progress in Nuclear Science and Technology, Volume 4, pp , April ) 48. Walters, W., A. Haghighat, K. Royston, C. Yi, and G. Sjoden, A Response Function Methodology to Calculate Induced Fission Neutron Flux Distribution in an Active Interrogation System, Progress in Nuclear Science and Technology, Volume 4, pp , April ) Royston, K. and A. Haghighat, Preliminary Results of a New Deterministic Iterative Image Reconstruction Algorithm, Proc. ANS RPSD 2014, Knoxville, TN, September 14-18, ) 49. Haghighat, A., K. Royston, G. Sjoden, C. Yi, and M. Huang, Unique Formulations in TITAN and PENTRAN for Medical Physics Applications, Progress in Nuclear Science and Technology, Volume 4, pp ,

25 RAPID code system & VRS-RAPID 25

26 Modeling of Nuclear Systems (cores, pools & casks) Commonly used approach - Monte Carlo Simulation Source Convergence in eigenvalue MC is difficult due to undersampling (due to absorbers), HDR, intergeneration correlation These effects are difficult to detect Computation times are very long, especially to get detailed information Changing system configuration (for design and analysis) requires complete recalculation

27 RAPID s MRT Methodology* RAPID formulation is based on: Fission Matrix (FM) method (for fission source distribution) Adjoint function methodology (for detector response or dose) The above techniques are incorporated into a linear system of equations with pre-calculated FM coefficients and adjoint functions. Pre-calculations: FM coefficients and adjoint-function distributions (or detector response coefficients) are pre-calculated via a proprietary* MRT strategy for different assembly types, burnups, cooling times, and detector types and positions. *Patent application no. US 62/582,709: RAPID Particle Transport Methodology for Real-time Simulation of Nuclear Systems 27

28 Derivation of Fission Matrix (FM) Formulation Eigenvalue formulation in operator form is expressed by Where, Hψ( p) = 1 k Fψ( p) p = ( r, E, Ω) H = Ω + σ t r, E 0 de 4π dω σ s( r, E E, μ 0 ) F = χ(e) de 4π 0 4π dω νσ f ( r, E ) 28

29 , Derivation of FM Formulation (cont) We may rewrite above equation as S p = 1 k AS p Where, S = Fψ, F = 1 4π 0 de A = FH 1 χ, & 4π dω νσ f( r, E ) 29

30 Fission Matrix Method Eigenvalue formulation F i = 1 k j=1 N a i,j F j k is eigenvalue F j is fission source, S j is fixed source in cell j a i,j is the number of fission neutrons produced in cell i due to a fission neutron born in cell j. Subcritical multiplication formulation F i = N (a i,j F j + b i,j S j ), j=1 b i,j is the number of fission neutrons produced in cell i due to an independent source neutron born in cell j. 30

31 Determination of FM Coefficients (Pool - 81 Assemblies) Brute force approach: For a typical spent nuclear fuel pool with a sub-region of 9x9 assemblies: N = = 21, 384 total fuel pins Considering 24 axial segments per rod, then N = 513,216 Standard FM would require N = 513,216 separate fixedsource calculations to determine the coefficient matrix A matrix of size N x N = E+11 total coefficients (> 1 TB of memory is needed) Pool - 9x9 array of assemblies The straightforward approach is clearly NOT feasible Multi-layer, regional approach ( Filed for patent, application no. US 62/582,709 ) Determine coefficients as a function of different parameters Process coefficients for problem of interest Assembly- 19x19 array 31

32 ,Calculation of Detector Response or Dose - Adjoint Function Methodology Forward Transport Equation where H H q ˆ ( r, E) t 0 de' in V on for n ˆ ˆ d' ( r, E' s E, ˆ ' ˆ ) Adjoint Transport Equation where H H ˆ ( r, E) t q on for n 0 0 de' 0 4 in V ˆ d' ( r, E E', ˆ ˆ ') s ˆ

33 ,Calculation of Detector Response or Dose - Adjoint Function Methodology (cont) Forward approach R d dv de V d 0 4 d ( r, E) ( r, E, ˆ ) d The commutation relation between the forward and adjoint transport equations H H q q 0 Then, q q If we consider q d R q

34 , Demonstration- Adjoint Function Methodology (cont) Standard Where, R d H S Adjoint Methodology Where, R S H d 34

35 Determination of Detector Response (R) or Surface Dose (D) Forward transport Where, o R, [d n = Σ d 1 o D, [d n = f n ( R or D =< ψd n > cm mrem hr # cm 2 s )] ], or Adjoint-function methodology by Where, R or D =< ψ S > H ψ = d n

36 Status of RAPID Thus far, has been used for Simulation of spent fuel pools and storage casks, and reactor cores. Current capability Calculates system eigenvalue, subcritical multiplication, axially-dependent pin-wise fission neutron, gamma, and/or antineutrino distributions, and detector responses or surface radiation dose. When used in conjunction with measurements, e.g., for safeguards application, it can identity potential fuel diversion or misplacement. Ongoing work trapid: time-dependent algorithms for RAPID for reactor kinetics (solid and liquid fuel); brapid: a 3-D, FM-based burnup calculation algorithm for RAPID; and, A response-function formulation (with the use of CADIS methodology) has been developed for determination of detector response (this replaces the existing capability of using the pre-calculated detailed deterministic adjoint function distributions) 36

37 RAPID Code System Flowchart Stage 1 Stage 3 Pre-calculation using P 3 RAPID* Stage 2 Stage 4 Stage 5 Stage 6 * P 3 RAPID: Pre- and Post-Processing module for RAPID 37

38 I 2 S-LWR (Spent Fuel Pool) I 2 S-LWR FUEL ASSEMBLY 19x19 fuel lattice 335 fuel rods, 24 control/guide tubes, 1 instrumentation tube U 3 Si 2 fuel enriched to 4.95 wt-% 235 U SPENT FUEL POOL Based on AP1000 SFP Consider a 9x9 segment of SFP (81 assemblies) Storage cell walls made of Metamic (B4C- Al) between SS plates Assembly in a Storage Cell 9x9 Segment of SFP 38

39 p 3 RAPID Burnup Calculation (SCALE-TRITON) Stage 1 Need : Material composition & Intrinsic source Use: SCALE TRITON The TDEPL option used to invoke NEWT 2D & ORIGEN For: Enrichment of 4.95 wt-%; Burnups: 37, 59 GWd/MTHM; and, Cooling Times: 14 days, 1 & 9 years Quarter assembly model used. 49 different fuel materials (considering octal symmetry) 39

40 p 3 RAPID FM Coefficient Stage 2 Using information from Stage 1, Ncase =Ncase+1 (for different burnups, cooling times, enrichments, lattice, etc) Automatically, generate 49 MCNP input files for performing fixed-source calculations Process fission tallies to determine FM Coefficients (pin-wise, axially dependent per inch) Ncase < Max-case RAPID FM Coefficient Database 40

41 Determination of Detector Response in a Spent Fuel Pool Stage 3 Center side Detector is placed on top of a fuel assembly; determine FOV Corner Model contains surrounding assemblies: three types of assemblies (shown in figure) are identified: o Center o Side o Corner A 3-D PENTRAN Adjoint model is developed for each assembly type Axially, models include 15 cm of fuel plus a detector of height 5 cm and 10 cm of water on top of the detector

42 PENTRAN Adjoint Calculation For a Center Assembly Dose c alculation Information on PENTRAN Calculation Model size 83.57x83.57x29 cm 3 Z-level, 6 5 x-y mesh Group 1 Group 2 Stage 4 Adjoint-function, radial distribution at different z-levels 2 groups S10 Quadrature set 94,578 meshes Wall-clock time = 279 sec, on one core

43 BREAK (10:00 10:15 am) 43

44 Benchmarking of RAPID 44

45 RAPID vs. MCNP Spent fuel pool 45

46 Test Cases Performed eigenvalue calculations for a 2x2 segment of the reference SFP. 4 test cases are defined, each containing different combinations of burnups/cooling times Fuel region of the model partitioned into 32,256 fission regions (tallies) (for 1344 pins with 24 axial levels) Reference MCNP eigenvalue parameters are: 10 6 particles per cycle, 400 skipped cycles 400 active cycles Burnup [GWd/MTHM] Cooling Time [years*] 0 GWd/MTHM 0 yr 37 GWd/MTHM 0 yr CASE 1 37 GWd/MTHM 0 yr 0 GWd/MTHM 0 yr * 0 year cooling time refers to ~14 days 0 GWd/MTHM 0 yr 59 GWd/MTHM 0 yr CASE 2 CASE 3 CASE GWd/MTHM GWd/MTHM GWd/MTHM GWd/MTHM yr yr yr yr 0 GWd/MTHM 0 yr 37 GWd/MTHM 0 yr 59 GWd/MTHM 9 yr 37 GWd/MTHM 9 yr 37 GWd/MTHM 9 yr 59 GWd/MTHM 9 yr 46 46

47 Comparison of Eigenvalues Case MCNP Keff RAPID Rel. Diff. (RAPID vs. MCNP) (pcm) (± 4 pcm) (± 4 pcm) (± 3 pcm) (± 3 pcm)

48 Comparison of pin-wise fission density (axially integrated) CASE 1 CASE 2 CASE 3 CASE 4 RAPID Calculated Fission Densities Normalized Fission Density 1e 03 1e 04 Normalized Fission Density 1e 03 1e 04 Normalized Fission Density 1e 03 1e 04 Normalized Fission Density 1e 03 1e 04 Relative Difference w/ MCNP Reference % Relative Difference % Relative Difference % Relative Difference % Relative Difference Relative Difference for assembly FD totals 48

49 MCNP prediction Fission Density (Case 1) Fission Density 1-σ Relative Uncertainty 0 GWd/MTHM 0 yr 37 GWd/MTHM 0 yr 37 GWd/MTHM 0 yr 0 GWd/MTHM 0 yr 49

50 RAPID vs. MCNP Fission Density (Case 1) 0 GWd/MTHM 0 yr 37 GWd/MTHM 0 yr 37 GWd/MTHM 0 yr 0 GWd/MTHM 0 yr RAPID MCNP % Relative Difference 50

51 MCNP prediction Fission Density (Cases 2-4) Fission Density Case 2 Case 3 Case 4 1-σ Relative Uncertainty 51

52 0 GWd/MTHM 0 yr 59 GWd/MTHM 0 yr 59 GWd/MTHM 0 yr 0 GWd/MTHM 0 yr RAPID vs. MCNP Fission Density (Case 2) RAPID MCNP % Relative Difference 52

53 RAPID vs. MCNP Fission Density (Case 3) 59 GWd/MTHM 9 yr 37 GWd/MTHM 0 yr 37 GWd/MTHM 0 yr 59 GWd/MTHM 9 yr RAPID MCNP % Relative Difference 53

54 RAPID vs. MCNP Fission Density (Case 4) 59 GWd/MTHM 9 yr 37 GWd/MTHM 9 yr 37 GWd/MTHM 9 yr 59 GWd/MTHM 9 yr RAPID MCNP % Relative Difference 54

55 Computation Time Case Cores MCNP Time (min) Cores RAPID Time (min) Speedup (17 hrs) (17 hrs) (18 hrs) (19 hrs)

56 RAPID vs. MCNP Spent Fuel Cask 56

57 GBC-32 Cask Computational Benchmark Geometry 32 Fuel assemblies Stainless steel (SS304) cylindrical canister Inter-assembly Boral absorber panels Height of the canister: cm Fuel assembly 17x17 Optimized Fuel Assembly (OFA) 25 instrumentation guides Fresh UO 2 4% wt. enriched fuel pins Active height: cm 57

58 RAPID vs. MCNP Single assembly model # pins = 264; #axial levels = 24; # tallies = 6336 Case MCNP RAPID k eff (± 2 pcm) k eff relative difference - 53 pcm Fiss. density adjusted rel. uncertainty 0.48% - Fission density relative diff % Computer 16 cores 1 core Time 666 min (11.1 hours) 0.1 min (6 seconds) Speedup - 6,666

59 RAPID vs. MCNP FULL Cask model #assemblies = 32; # pins = 264; #axial levels = 24; # tallies = 202,752 Case MCNP RAPID k eff (± 1 pcm) Relative Difference - 39 pcm Fission density rel. uncertainty 1.15% - Fission density relative diff % Computer 16 cores 1 core Time 13,767 min (9.5 days) min (35 seconds) Speedup - 23,533

60 Calculated Axially-Dependent, Pin-wise Fission Density in the GBC-32 Benchmark Using RAPID With a quarter Blanked Inside view

61 RAPID vs. Serpent FULL Cask, with Spent Fuel #assemblies = 32; # pins = 264; #axial levels = 48; # tallies = 405,504 Comparison of k eff for different CASK models with different burnups Burnup (MWd/MT) Serpent (3σ) RAPID Rel. Diff (pcm) Fresh fuel ± 30 pcm , ± 30 pcm , ± 33 pcm , ± 33 pcm , ± 33 pcm , ± 33 pcm

62 RAPID vs. Serpent FULL Cask, Checkerboard Models #assemblies = 32; # pins = 264; #axial levels = 48; # tallies = 405,504 Comparison of k eff for different checkerboard CASK models Model Serpent (3σ ) RAPID Rel. Diff (PCM) ± 36 pcm ± 33 pcm ± 33 pcm

63 RAPID vs. Serpent FULL Cask, Computation Time RAPID: #assemblies = 32; # pins = 264; #axial levels = 48; # tallies = 405,504 Serpent: only 12 axial levels, and fission source convergence has not been examined

64 RAPID vs. SERPENT Reactor Core 64

65 RAPID vs. SERPENT PWR Core model* RAPID has been applied to several large PWR problems, based on the NEA/OECD Monte Carlo Performance Benchmark Problem. 241 assemblies, 264 pins per assembly 100 axial levels 6.4 million cells FM coefficients are pre-calculated using the SERPENT Monte Carlo code for different core configurations. *A paper has been submitted for publication 65

66 Sample Result RAPID vs. SERPENT K eff & Fission Density X-Y reactor core layout. Pin-wise Fission Source k-eigenvalue SERPENT: ±1.0 pcm RAPID : ±1.4 pcm Diff. : 5.3 pcm Pin-wise fission source RMS error : 0.30% SERPENT 1σ : 0.20% Axial source comparison RAPID-Serpent Difference Computation time SERPENT requires 1000 hrs RAPID requires 0.23 Hrs 66

67 Experimental Benchmarking of RAPID US Naval Academy Subcritical Facility 67

68 ( , , ) ( , , ) origin: ( 0.00, 0.00, ) extent = ( 61.50, 61.50) Model Description - USNA-SC A cylindrical pool with natural uranium (fuel) and light water (moderator) There are a total of 268 fuel rods, arranged in a hexagonal lattice Fuel: hollow aluminum tubes containing 5 annular fuel slugs Neutron source: PuBe 03/10/16 12:03:22 c Original Assembly Burnup file = sdir=xsdi 03/10/16 12:03:23 c Original Assembly Burnup file = sdir=xsdi R = cm probid = 03/10/16 12:03:22 basis: XY ( , , ) ( , , ) origin: ( 0.00, 0.00, ) extent = ( 61.50, 61.50) probid = 03/10/16 12:03:22 basis: XZ ( , , ) ( , , ) origin: ( 0.00, 0.00, ) extent = ( 80.00, 80.00) 9.68 cm cm cm cm 68

69 ( , , ) ( , , ) origin: ( 0.00, 0.00, ) extent = ( 61.50, 61.50) Comparison of Calculation vs. Experiment 3 He detector is used to measure neutron count rates throughout the core To compare the measured and calculated counts, we obtain a detector efficiency factor (Eff) Eff is obtained based on least-squares minimization of calculate (c) and measure (m) counts as follows Eff = i c im i i c i 2 Where, i refers to position within the core 69

70 ( , , ) ( , , ) origin: ( 0.00, 0.00, ) extent = ( 61.50, 61.50) Calculated C/E and Estimated Uncertainty Estimation of uncertainty in f = C m σ f = σ c 2 m 2 + c2 2 σ m m 4 70

71 RAPID Detector Response or Surface Dose Calculation 71

72 Determination of Detector Response (R) or Surface Dose (D) Forward transport Where, o R, [d n = Σ d 1 o D, [d n = f n ( R or D =< ψd n > cm mrem hr # cm 2 s )] ], or Adjoint-function methodology by Where, R or D =< ψ S > H ψ = d n

73 115.0 Example - Pre-calculation of Importance Function for Cask dosimetry Field-Of-View (FOV) Monte Carlo Model PENTRAN Model Moving Backward away from dosimeter 90% cm Air Fuel H 2 0 SS xy view Dosimeter D = g i ψ i,g (χ g S i )

74 Example - Determination of a detector response, as placed on top each fuel assembly in a pool By moving the detector on top of each fuel assembly in the pool of 9x9 assemblies Normalized detector response RAPID calculates detector response by using 2 N R= cell g=1 i=1 ψ i,g (χ g S i ) 74

75 VRS-RAPID* Web Application RAPID is incorporated into a Web application, referred to as the Virtual Reality System (VRS) for RAPID. VRS-RAPID provides a collaborative Virtual Reality environment for a user to build models, perform simulation, and view 3-D diagrams in an interactive mode. 3-D diagrams can be projected onto a virtual system environment (e.g., a pool) for further analysis and training purposes. Additionally, VRS-RAPID outputs can be coupled with an immersive facility such as the VT s HyberCube System, as shown in this figure. *Filed for a patent, Oct

76 A Demo for the VRS-RAPID Web Application 76

77 Thanks! Questions? 77