GENIUS v2 An Extensible Platform for Modeling Advanced Global Fuel Cycles Computational Nuclear...
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Transcript of GENIUS v2 An Extensible Platform for Modeling Advanced Global Fuel Cycles Computational Nuclear...
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
11/04/2009
Overview
• Background
• Infrastructure Overview
• Methods Implementation
• Analysis Capabilities
• Future work
11/04/2009 P. Wilson: GENIUS v2 Platform Overview 2
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
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)]
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
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
Desired features are largely unavailable
(2) Discrete-facilities/ discrete-materials
(DF/DM)
(3) Optimizationand sensitivity analysis
(4) Software architecture
11/04/2009 P. Wilson: GENIUS v2 Platform Overview 7
[Juchau (2006)]
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)]
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
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
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 optimization11/04/2009 P. Wilson: GENIUS v2 Platform Overview 11
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
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
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
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
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
11/04/2009 P. Wilson: GENIUS v2 Platform Overview 17
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
InstitutionInstitution
P. Wilson: GENIUS v2 Platform Overview 18
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 parameters11/04/2009
REGION
Institution
InstitutionInstitution
P. Wilson: GENIUS v2 Platform Overview 19
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 Overview 20
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 Overview 21
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
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
Facilities as Black Boxes with Clear Interfaces
Facility
Process linesUpstream 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
Facilities Implement Specialized Methods to Process Material
• Define transformation, T, to convert M feed materials with distinct compositions Cin to N product/waste materials with distinct compositions Cout, via some calculable amount of work Z:
• Enrichment example
11/04/2009 P. Wilson: GENIUS v2 Platform Overview 26
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.
Cin1
Cin2
Cin3
Cout1, Bu=45
Cout2,Bu=45
Cout3,Bu=45
Cout1,Bu=44
Cout3,Bu=44
Cout3,Bu=43
Cout2,Bu=43
Cout1,Bu=43
TZ= 44 GWd
MTH
TZ= 43 GWd
MTH
TZ= 45 GWd
MTH442,
outBu=C
11/04/2009 P. Wilson: GENIUS v2 Platform Overview 27
Separations Example: Matrix-Based ‘Separations Efficiency’ Approach
C in
Cout1
C inU
C inNp
C inPu
...C in
Cs
C inSr
Cout2 Cout
S...
.999.0005.0005
...00
.0010.99950.9995
...00
000...
.999
.999
...
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
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 plan11/04/2009 P. Wilson: GENIUS v2 Platform Overview 29
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
Simple network flow formulation
• special case of linear programming and easily solvable
xij – flow on arc (i,j)
aij – unit cost of flow on arc (i,j)
[bij, cij] – flow bounds on arc (i,j)
Minimize flow cost
Enforce flow bounds
Conserve total flow
si – divergence for node i (signed supply or demand)
[Bertsekas (1998)]11/04/2009 P. Wilson: GENIUS v2 Platform Overview 31
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)]
Split M-commodity Problem Into Sub-problems*
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*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
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
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
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
Recipe Approximation Problem
C1 Creq
x1 x2 x3
C2 C3
Available “barrels” of recycle material Requestedfuel 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
Linear Programming Approximation Technique to Minimize Vector Residuals
Minimize sum of isotope-wise relative deviation from recipe, r.
Choose a fraction of each barrel, xb
Mbi is the mass of isotope i in barrel b
Normalized objective function coefficients encourage matching of more than just the most abundant isotope
mr
wr
b
mxm
wxw
bx
rxMy
,10
subject to
ycyx
,min
01
01
ir
ii
irm
rrc
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)]
k∞ as a Candidate Neutronics Metric
11/04/2009
0
0
,,
,,
,,,
,
,
,
,
bbib
iiawrif
bbib
iiawrif
bbib
iiaw
bbib
iiar
bbib
iif
wr
bbib
iia
bbib
iif
w
wr
bbib
iia
bbib
iif
a
f
xMw
xMw
xMxMwxM
w
xM
xM
wxw
xM
xM
kxw
P. Wilson: GENIUS v2 Platform Overview 39
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
Supplier-of-last-resort Becomes Preferred Supplier
Case 1
Case 2
11/04/2009 P. Wilson: GENIUS v2 Platform Overview 42
Time-dependent Affinity Changes in 4 Region Problem
Scenario summary
Scenario rules
Default affinities
“User states” dependenton Region 1 for fuel
11/04/2009 P. Wilson: GENIUS v2 Platform Overview 43
Supply cut-off vs. Supply competition
Case 1 Case 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
Closed Fuel Cycle Scenario to Test Recipe Approximation
Parameters for thermal MOX recycle scenario
Facility deployment for thermalMOX recycle scenario
11/04/2009 P. Wilson: GENIUS v2 Platform Overview 45
“Best Fit” Barrels Get Preference
Barrels from Np-Pu stream inmonths 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
Study on Impact of Neutronics Constraint
No neutronics constraintused 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
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
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
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
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
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
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