GENIUS v2 An Extensible Platform for Modeling Advanced Global Fuel Cycles Computational Nuclear Engineering Research Group (CNERG) Kyle Oliver, Paul Wilson,

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

[email protected]

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)]


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.


[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)]


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


Desired features are largely unavailable

(2) Discrete-facilities/ discrete-materials

(DF/DM)

(3) Optimizationand sensitivity analysis

(4) Software architecture


[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


[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


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)]


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


GENIUS v2

Software Infrastructure Overview

11/04/2009

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



• 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)



• Discrete Facilities + Discrete Materials=– Tracking of material transactions– Modeling of specific supply arrangements

• contracts • political agreements• supply interruptions


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



• 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


• 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



• 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


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


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


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


GENIUS v2

Specific Method Implementation

11/04/2009

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


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


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

...

...

...

...

...


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.


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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+

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-

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*Can show that the problem is separable if we treat all waste as a single commodity


Construct and solve up to M problems each month

Offer queue

Request queue

Manager

Reactor

Fuel Fab

Reactor

+

-+

- - -

+

+

-+

-


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.


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.


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


GENIUS v2

Analysis Capabilities

11/04/2009

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


Supplier-of-last-resort Becomes Preferred Supplier

Case 1

Case 2


Time-dependent Affinity Changes in 4 Region Problem

Scenario summary

Scenario rules

Default affinities

“User states” dependenton Region 1 for fuel


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.


Closed Fuel Cycle Scenario to Test Recipe Approximation

Parameters for thermal MOX recycle scenario

Facility deployment for thermalMOX recycle scenario


“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.


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.


GENIUS v2

Coming Developments

11/04/2009

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


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


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?


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


Development Concepts

• Agent-based modeling of individual facilities, institutions and regions

• Advanced algorithms for material matching of separated materials

• Integration of external optimization toolkits


Questions?

[email protected]

http://cnerg.engr.wisc.edu

11/04/2009

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.


Documents

GENIUS v2 An Extensible Platform for Modeling Advanced Global Fuel Cycles Computational Nuclear Engineering Research Group (CNERG) Kyle Oliver, Paul Wilson,