1. GENIUS v2 An Extensible Platform for Modeling Advanced Global Fuel Cycles Computational Nuclear Engineering Research Group (CNERG) Kyle Oliver, Paul Wilson, Kathryn Huff, Royal Elmore, Tae Wook Ahn, Kerry Dunn wilsonp@engr.wisc.edu 11/04/2009

2. Overview Background Infrastructure Overview Methods Implementation Analysis Capabilities Future work 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 2

3. Advanced fuel cycles Expected to benefit resource extension and waste management. Used fuel separation and recycle allow continued energy extraction and burnup of transuranics. Currently, used fuel is slated for direct disposal. [Lisowski, P. (2007)] 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 3

4. New Opportunities for International Cooperation Driven by engineering, cost, and proliferation concerns Realistic mechanisms for encouraging GNEP-like user-supplier relationships are not well understood. Changing diplomatic situations introduce potential for supply-chain interruptions. 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 4 [Lisowski, P. (2007)]

5. Systems Analysis Aims to Reduce Decision Risks National Research Council review of Department of Energy R&D noted GNEP’s underemphasis on “conservative economics” and an unrealistic technology development timeline [Board on Energy and Environmental Systems(2008)] National Research Council/National Academy of Sciences report on fuel cycle internationalization advocated an increase in systems analysis activities [Nuclear and Radiation Studies Board (2008)] 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 5

6. SINEMA* defined novel feature set for systems analysis: GENIUS** 1.Support modeling of global regions subject to characteristic nuclear energy demand curves 2.Model facilities and materials discretely instead of as lumped fleets and continuous flows 3.Support fuel cycle design activities including parameter optimization and sensitivity analysis 4.Use a modular, flexible, open, and accessible software architecture *SINEMA = Simulation Institute for Nuclear Enterprise Modeling and Analysis **GENIUS = Global Evaluation of Nuclear Infrastructure Utilization Scenarios 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 6

7. Desired features are largely unavailable (2) Discrete-facilities/ discrete-materials (DF/DM) ‏ (3) Optimization and sensitivity analysis (4) Software architecture 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 7 [Juchau (2006)]

8. GENIUS v1 proof-of-concept for DF/DM systems modeling Modeled current and future reactors in all nuclear states Recorded detailed region-by-region material flow data over 100 year simulation 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 8 [Juchau (2008)]

9. GENIUS v1 Infrastructure Limitations 1.Reliant on hard-coded input file 2.Reliant on somewhat slow and memory- intensive built-in Python data structures 3.No isotopic information in mass flow outputs 4.No capability for modeling of radioactive decay 5.Smallest discrete material quantum is a fuel batch 6.Limited to specific fuel cycles due to procedure-based software architecture 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 9

10. GENUS v1 and Feedback-based Decision Heuristics Hard-coded decision strategies Find local extrema, including those that are “local” in time Interfere with optimization techniques that search the decision space for globally optimal parameter sets Commonly used for facility deployment and material routing [Jain (2006)] 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 10

11. GENIUS V2 Design Goals Detail –Redesign system model to decrease material quantum size, track and report full material and facility histories, and include the notion of institutions Robustness –Re-implement as object-orient C++ code and utilize modern scientific computing libraries Flexibility –Generalize and encapsulate facility behavior to support a wider range of possible fuel cycle designs and cooperation schemes Optimization compatibility –Where possible, remove dependence on decision heuristics to support efforts toward global optimization 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 11

12. Notable Features Discrete Facility/Discrete Material (DF/DM) paradigm Region-Institution-Facility (RIF) hierarchy Modular/extensible facility models Network flow model for material routing Linear program optimization for the Recipe Approximation Problem (RAP) Best-available open source computational science tools/libraries 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 12

13. GENIUS v2 Software Infrastructure Overview 11/04/2009

14. Features of Discrete Simulation Each facility modeled as a distinct entity –All performance characteristics can be unique User-defined Stochastically sampled Generated by simulation wrapper (e.g. optimization) Each facility has unique behavior –Interruptions in operation –Interruptions in supply –Financial performance 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 14

15. Features of Discrete Simulation Discrete quanta of material are exchanged between facilities –No theoretical minimum quanta of material Single assemblies (organized in batches) “Barrels” of separated material –Each object can be created with unique characteristics Objects cease to exist when physical form changes –Individual objects decay independently (on demand) 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 15

16. Features of Discrete Simulation Discrete Facilities + Discrete Materials= –Tracking of material transactions –Modeling of specific supply arrangements contracts political agreements supply interruptions 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 16

17. Hierarchical Data Model Variety of distinct facilities –Enrichment –Fuel Fab –Reactor –Separations –Storage –Repository Modular C++ class structures encapsulate data and behavior of each object 11/04/2009P. Wilson: GENIUS v2 Platform Overview17

18. Hierarchical Data Model Each facility is owned/operated by a specific institution An institution can operation many facilities –Facilities inherit shared (financial) parameters –Preferred trading relationships 11/04/2009 Institution P. Wilson: GENIUS v2 Platform Overview18

19. Hierarchical Data Model Each institution operates in a geographic region –Sub-national –National –Super-national A region can have many institutions –Preferred trading relationships –Institutions inherit shared parameters 11/04/2009 REGION Institution P. Wilson: GENIUS v2 Platform Overview19

20. Hierarchical Data Model User specified rules define interactions –Preferred/disallowed trade relationships –Can be specified for interactions between regions, institutions or individual facilities Region, institution and facility rules combined 11/04/2009 REGION Institution REGION Institution REGION Institution P. Wilson: GENIUS v2 Platform Overview20

21. Material Flow Optimization Facilities interact by issuing offers/ requests to manager Interaction rules define the affinity for trade between pairs of facilities Network flow model reconciles offers/ requests Manager issues instructions to simulation objects 11/04/2009 REGION Institution REGION Institution REGION Institution Manager Timer P. Wilson: GENIUS v2 Platform Overview21

22. Full Log of All Material Transactions Data for each transaction includes –Time, shipping facility, receiving facility, material composition Large rich data set for post-processing into variety of visualizations Modern data handling techniques –E.g. SQL databases 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 22

23. Data Visualization Scenario results in large multi- dimensional data sets –Time, shipping facility, receiving facility, material composition Standard tools/methods to reduce data –Filtering –Aggregation –Time-series formation Standard plotting tools with reduced data sets 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 23

24. GENIUS v2 Specific Method Implementation 11/04/2009

25. Facilities as Black Boxes with Clear Interfaces Facility Process lines Upstream buffer (stocks) ‏ Downstream buffer (inventory) ‏ Buffers store materials waiting to be processed or sent to another facility. Process lines store the material being operated upon (converted, enriched, etc.) ‏ Messages are sent to offer or request materials or services. 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 25

26. Facilities Implement Specialized Methods to Process Material Define transformation, T, to convert M feed materials with distinct compositions C in to N product/waste materials with distinct compositions C out, via some calculable amount of work Z : Enrichment example 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 26

27. Reactor Example: Recipe-Based Approach Each fresh fuel recipe is matched with corresponding spent fuel recipe. Simulating non-standard burnups requires specifying multiple fresh/spent pairs. 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 27

28. Separations Example: Matrix-Based ‘Separations Efficiency’ Approach Used fuel from reactors Product and waste streams (representative data) Each row sums to one 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 28

29. Facility models can be improved/replaced Different process models can be implemented with arbitrary (?) complexity –Different physical approximations –Improved resolutions Reactor example –Simple burnup module to calculate output recipe corresponding to achieved input recipe Separations example –Simple process model that relates throughput, input composition and output composition Shared open source development plan 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 29

30. DF/DM Paradigm Introduces Material Routing Problem (MRP) GENIUSv1 uses combination of static, user-specified matching or a simple heuristic. –New orders matched to supplier with the most outstanding capacity if no relationship is specified. –Heuristic contains no consideration of global supply/demand situation. GENIUSv2 should use optimization strategy that somehow minimizes global costs. –Idea: use network flow programming and model suppliers as sources, customers as sinks. 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 30

31. Simple network flow formulation special case of linear programming and easily solvable x ij – flow on arc (i,j) ‏ a ij – unit cost of flow on arc (i,j) ‏ [b ij, c ij ] – flow bounds on arc (i,j) ‏ Minimize flow cost Enforce flow bounds Conserve total flow s i – divergence for node i (signed supply or demand) ‏ [Bertsekas (1998)] 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 31

32. The Nuclear Fuel Cycle is Inherently Multi-Commodity More general objective function and arc constraints Flow conservation for each commodity Can’t measure supply/demand of distinct fuel cycle materials in same units Can’t describe flow of distinct fuel cycle materials according to uniform arc costs, flow bounds 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 32 [Bertsekas (1998)]

33. Split M-commodity Problem Into Sub-problems* -+ +-+ +- - + + - - + + - - + + - - + + - - + + - - + + - - + + + + + + + + + + + + *Can show that the problem is separable if we treat all waste as a single commodity 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 33

34. Construct and solve up to M problems each month Offer queue Request queue Manager Reactor Fuel Fab Reactor + - + --- + + - + - 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 34

35. Artificial Arcs Ensure Feasibility, Trade Affinity Defines Arc Cost + + - - Artificial sink absorbs excess capacity; higher arc costs reflect storage cost, profit loss. $$$ - $ $$ $ Artificial source absorbs excess demand; higher arc costs approximate profit loss. + $$$ Facilities with high mutual affinity for trade (specified by default or user- defined rules) connected by cheaper arcs. 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 35

36. Limitations of Current Formulation Formulation is still naive/greedy (local in time). –One-month time horizon doesn’t consider possibility of waiting for improved match. –Need to develop method for constructing problems that describe longer-time behavior. Formulation minimizes flow costs only... –...not global cost of electricity produced. Must enforce “no-splitting” constraints manually. –Don’t allow orders for certain commodities (i.e., fuel batches) to be split between two suppliers. –Refiling split orders for future re-matching gives sub-optimal behavior. 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 36

37. Recipe Approximation Problem C1C1 C req x1x1 x2x2 x3x3 C2C2 C3C3 Available “barrels” of recycle material Requested fuel recipe Must preserve stoichiometry of components after they are separated! Choose fractions to attempt matching of target recipe w/r/t stoichiometry, total mass, and total neutronics. 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 37

38. Linear Programming Approximation Technique to Minimize Vector Residuals Minimize sum of isotope-wise relative deviation from recipe, r. Choose a fraction of each barrel, x b M bi is the mass of isotope i in barrel b Normalized objective function coefficients encourage matching of more than just the most abundant isotope Constrain the neutronics performance, w, to match the recipe within  w Constrain the total mass, m, to match the recipe within  m 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 38 [Ferris (2008)]

39. k ∞ as a Candidate Neutronics Metric 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 39

40. GENIUS v2 Analysis Capabilities 11/04/2009

41. Affinities Affect Fuel Routing in 3 Region Problem Scenario summary Case 1: Insts 1 & 4’s affinities w/foreign fabricator = default values Case 2: Insts 1 & 4’s affinities w/foreign fabricator manually increased 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 41

42. Supplier-of-last-resort Becomes Preferred Supplier Case 1 Case 2 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 42

43. Time-dependent Affinity Changes in 4 Region Problem Scenario summary Scenario rules Default affinities “User states” dependent on Region 1 for fuel 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 43

44. Supply cut-off vs. Supply competition Case 1Case 2 Different uranium source distribution could affect cost of generation in fuel provider region and/or its dependent user regions. 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 44

45. Closed Fuel Cycle Scenario to Test Recipe Approximation Parameters for thermal MOX recycle scenario Facility deployment for thermal MOX recycle scenario 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 45

46. “Best Fit” Barrels Get Preference Barrels from Np-Pu stream in months with no spent MOX “pollutants” have nearly correct ratio of isotopes. Higher fraction of available Np-Pu than available U used in approximations. 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 46

47. Study on Impact of Neutronics Constraint No neutronics constraint used in scenario plotted in previous slide. Variability caused by number, size, and composition of available barrels. 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 47

48. GENIUS v2 Coming Developments 11/04/2009

49. Economics by Post-Processing Detailed cash-flow models –Facility specific financial parameters influenced by institutional ownership and region of operation –Summation over all facilities in institution for institutional cash-flows Can examine statistical variations in financial parameters 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 49

50. Posited scenarios Disruption of specific supply relationships between geographic regions –How robust/resilient is the global system to accommodating disruptions in single relationships? –Corollary: How much risk does a country expose itself to by relying on a supplier country? –Technical vs. political vs. upstream supply disruptions 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 50

51. Posited Scenarios Impact of national decisions on fuel cycle technology on global fuel cycle development –Do certain technology choices enable creative supply relationships? Assessment of trans-national material flows –What are the batch sizes of those flows? –What is the opportunity for diversion? 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 51

52. Multi-level Optimization Framework Material flow problem –Posed as a global optimization problem at each time step –Responds to user-defined deployment scenario Large input data set to define deployment Pre-processing tools assist in stand-alone use System optimization to be accomplished by invoking optimization toolkits to search input decision space 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 52

53. Development Concepts Agent-based modeling of individual facilities, institutions and regions Advanced algorithms for material matching of separated materials Integration of external optimization toolkits 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 53

54. Questions? wilsonp@engr.wisc.edu http://cnerg.engr.wisc.edu 11/04/2009

55. References Bertsekas, D. P. (1998). Network Optimization: Continuous and Discrete Models. Athena Scientific, Nashua, NH. Board on Energy and Environmental Systems (2008). Review of DOE’s nuclear energy research and development program. Technical report, National Research Council,Washington, DC. Accessed 5 January 2009 from http://www.nap.edu/catalog/11998.html. Ferris, M. C., Mangasarian, O. L., and Wright, S. J. (2008). Linear Programming with Matlab. MPS-SIAM Series on Optimization. Society for Industrial and Applied Mathematics, Philadelphia, PA, first edition. Jain, R. and Wilson, P. P. H. (2006). “Transitioning to global optimization in fuel cycle system study tools.” Transactions of the American Nuclear Society, 95, pages 162–3. Juchau, C. (2008). “Development of the global evaluation of nuclear infrastructure and utilization scenarios (GENIUS) nuclear fuel cycle systems analysis code.” Master’s thesis, Idaho State University. Juchau, C. A. and Dunzik-Gougar, M. L. (2006). A review of nuclear fuel cycle systems codes. Technical report, SINEMA LDRD Project. Accessed 13 February 2007 from http://thesinema.org/. Lisowski, P. (2007). Global Nuclear Energy Partnership. In Global Nuclear Energy Partnership Annual Meeting, Litchfield Park, AZ. Global Nuclear Energy Partnership. Nuclear and Radiation Studies Board (2008). Internationalization of the nuclear fuel cycle: Goals, strategies, and challenges [prepublication copy]. Technical report, National Academy of Sciences, National Research Council, and Russian Acadmy of Sciences,Washington, DC. Accessed 6 January 2009 from http://www.nap.edu/catalog/12477.html. 11/04/2009 P. Wilson: GENIUS v2 Platform Overview 55