EGU General Assembly 2007
Neptune and Company, Inc.Los Alamos, NM, USA
A Systems Modeling Approach for A Systems Modeling Approach for Performance Assessment of the Mochovce Performance Assessment of the Mochovce
National RadioactiveNational RadioactiveWaste Repository, Slovak RepublicWaste Repository, Slovak Republic
John Tauxe, PhD, PEPaul Black, PhD
http://www.neptuneandco.com/~jtauxe/egu07
Václav Hanušík
VÚJE, Inc.Trnava, Slovakia
EGU General Assembly 2007
Presentation OutlinePresentation Outline
• physical system modeling
• introduction to the facility
• conceptual system model
• mathematical model
• computer model
• future work
EGU General Assembly 2007
What is the problem?What is the problem?
• Radioactive wastes exist. Sources: nuclear power, nuclear medicine, industry, and (in some countries) nuclear weapons
• They pose a long-term health hazard.At risk: workers, the general public, the environment
• How should they be managed?Considerations: worker exposure, containment, release to the environment, future harm reduction
EGU General Assembly 2007
Why use modeling?Why use modeling?
• Models provide insight into the problem.Important processes can be identified.The effects of uncertainty can be quantified.
• Models help to evaluate alternatives.Cost/benefit of alternatives can be performed.
Relative effectiveness can be evaluated.
• Models communicate technical issues.Transparent modeling is accessible to the public.
Visualization of processes increases understanding.
EGU General Assembly 2007
Are models too abstractAre models too abstractto be of use?to be of use?
• “Essentially all models are wrong...We know that none of the results are correct per se, though we have defined an envelope of plausible estimates, conditioned on knowledge.
• ...but some are useful.” ¹We gain insight into what is important, and can demonstrate relative effects of mitigation (of doses, for example).
¹ Box, George E. P.; Norman R. Draper (1987). Empirical Model-Building and Response Surfaces, p. 424
EGU General Assembly 2007
Physical System Modeling OverviewPhysical System Modeling Overview
a radioactive waste disposal facility in Tennessee USA
Near field:Radiological materials leak out of stacked concrete vaults.
example: Human and ecological health effects arise from exposure to contaminants transported through an engineered (near field) and natural (far field) environment to a biological (physiological) environment
Far field:Contaminants migrate through geologic materials.
Physiological exposure:Human or ecological receptors are exposed by several pathways.
EGU General Assembly 2007
Physical System ProcessesPhysical System Processes
Near field:• decay / ingrowth• advection / dispersion• diffusion• dissolution • precipitation • containment degradation
The processes involved in this exposure modeling are radiological, physical, chemical, geological, and biological.
Far field:• decay / ingrowth• advection / dispersion• dilution• colloidal transport• chemical transformation• biological uptake and translocation
Physiological exposure:• habitation• drinking water• eating plant and animal foodstuffs• breathing• pharmacokinetics and dose response
These (and more) can be modeled in any degree of detail.
An important question: What degree of detail is appropriate?
EGU General Assembly 2007
Mathematical Coupling of Mathematical Coupling of Modeled ProcessesModeled Processes
Physical processes are modeled as coupled partial differential equations:
radioactive decay and ingrowth
gaseous diffusion
aqueous diffusion
aqueous advection
soil/water chemical partitioning
air/water partitioning
chemical solubilityatmosphericresuspension
i
jjk
jk
t
ii
jeNN
1)0(1121
)(
CDJ sw ~
hnK
vx
CDJ sa ~
soilRatm CfQ solaq CC
aqHair CKC
soilw
bdwater CKC
1
EGU General Assembly 2007
System ModelingSystem Modeling
model input parameters
modeled processes
modeling results
average annual precipitation = N( =55 cm, =35 cm )
examples:
timedo
se
hnKvx
water movement follows Darcy’s Law:
EGU General Assembly 2007
Location Map for Location Map for Mochovce, SlovakiaMochovce, Slovakia
Wein(Vienna)
Bratislava
Mochovce
EGU General Assembly 2007
Repository in a Small WatershedRepository in a Small Watershed
Wein(Vienna)
Trnava
Bratislava
Mochovce
EGU General Assembly 2007
Computer Modeling in GoldSim*Computer Modeling in GoldSim*
• materials are defined (Water, Soil, etc.)
• compartmentalization of model domain uses Cell and Pipe elements
• connections between compartments define transport pathways
• Source elements contain initial radionuclide inventory (Species)
• contaminants disperse along pathways
• calculations are done through time
• GoldSim is natively probabilistic
*Information about GoldSim™ is available from www.goldsim.com
EGU General Assembly 2007
Repository Far Field EnvironmentRepository Far Field Environment
repository
stream
to lake
Mochovce NPP
EGU General Assembly 2007
Typical ResultsTypical ResultsAny state or condition of the model can be tracked and graphed through time (e.g. concentrations, flow rates, doses).
Thi
s co
uld
be
conc
entr
atio
n or
dos
e.
EGU General Assembly 2007
Managing UncertaintyManaging Uncertainty
• We know that our knowledge is incomplete. Of that we are certain.
• How can we allow and account for imperfect knowledge?
• Each modeling parameter and process has inherent uncertainty and variability, and therefore so must our results.
no single answer is correct
a collection of answers reflects our knowledge
time
dose
time
dose
EGU General Assembly 2007
Why Probabilistic Modeling?Why Probabilistic Modeling?
• Uncertainty Analysis
UA allows a more honest answer, based on our state of knowledge.
• Sensitivity Analysis
SA provides insight into which modeling aspects (parameters and processes) are important.
EGU General Assembly 2007
Probabilistic AnalysisProbabilistic Analysis
• modeling parameters are defined stochastically, capturing uncertainty
• Monte Carlo is handled by GoldSim
• sensitivity analysis performed on results using the open source R software
• sensitive parameters are identified
• value-of-information analysis performed
• revisions through Bayesian updating
EGU General Assembly 2007
Future Work • ExtensionsFuture Work • Extensions
Performance assessment modeling can be extended to help with
• worker safety
• facility design
• optimization of operations
• development of waste acceptance criteria
• efficient use of monetary resources
EGU General Assembly 2007
ConclusionsConclusions
• Thoughtful stochastic physical system modeling can capture our state of knowledge.
• Defensible and transparent decisions can be made using such models.
• A system model can do much more than radiological performance assessment (worker risk, optimization, cost/benefit).
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