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  • Welcome to our talk on innovative modeling of radioactive waste disposal at the Mochovce National Radioactive Waste Repository in the Slovak Republic.
    I’d like to acknowledge my co-authors Paul Black, also of Neptune and Company, and Václav Hanušík, of VÚJE Trnava.
  • This outline will help you to follow the logic of the presentation.
  • We share a problem:
    Radioactive wastes from many sources must be handled with care and for a long time – millennia. This is true of other hazardous wastes as well, but radioactive wastes have the special property of changing through time due to decay and ingrowth.
    We wish to assess the potential future effects on the environment and the human population from the disposal of these wastes.
    Furthermore, at the time of construction of the facility, we have the opportunity to make design decisions and waste acceptance decisions that will help to meet long-term harm reduction goals.
  • This slide is self-explanatory.
  • This slide is self-explanatory.
  • The physical system is broken down into discrete parts that can each be approximated by modeling concepts. This system has been divided into the following:
    The near field “source term”, which includes the radionuclide inventory (mass of radionuclide species and the materials in which they reside), and the materials and processes present in the engineered facility.
    The far field natural environment, which here includes groundwater flow and a lake.
    The exposure assessment includes the presence and behavior of receptors, and their physiological responses to exposure to contaminants.
  • Within each of these regions, the processes contributing to contaminant transport are identified. This is part of a larger exercise in identifying all features, events, and processes (FEPs) that could influence the system.
    A typical collection of physical processes is identified here.
    These are readily modeled mathematically, given a number of simplifying assumptions. The modeler must balance the degree of simplification with a level of complexity suitable to make sufficiently reasonable estimates.
    These are vague terms, but they can be quantified through uncertainty and sensitivity analysis.
  • Once the FEPs have been enumerated, the challenge is to reduce them to mathematical relationships. These usually take the form of differential equations, relating fluxes or concentrations to each other.
    This requires an understanding of basic physics, chemistry, geology, and biology, all in the context of environmental science.
    Once the collection of equations is developed, we rely on the computer to solve the system of simultaneous equations. GoldSim is good at this.
  • The equations representing physical (and chemical, hydrogeological, and biological) processes require boundary conditions in order to arrive at a solution. These boundary conditions shape the equations themselves, and are also manifested as input parameters.
    The computer generates results as a function of time for some endpoint of interest. This could be the concentration of a radionuclide at some point in space (such as the possible location of a drinking water well, or a site boundary).
    Generally, the potential health effects to a hypothetical human or ecological receptor is also of great interest. So doses are also commonly used as model endpoints.
  • Now, on to our specific case…
    The National Radioactive Waste Repository is located near Mochovce, about 150 km east of Vienna.
  • The Repository is located in the basin of a small forested watershed. The movement of water is therefore highly likely to be a major contributor to contaminant transport.
    You can see the first vault has been constructed, and is covered by a green roof to protect operations from the weather. Several of these vaults will be built to fill the space inside the rectangle.
  • Here is a view inside a vault that is undergoing filling with concrete boxes, containing various types of radioactive wastes. Once full, the roof will be removed, and a permanent engineered cover will be put in its place.
  • The GoldSim systems modeling software was selected as a modeling platform, since
    it is oriented to modeling systems in a wide range of detail,
    it is inherently probabilistic, allowing for uncertainty and sensitivity analysis,
    it handles complex decay and ingrowth equations effortlessly, even during the transport of radionuclides, and
    GoldSim has been demonstrated to be capable of state-of-the-art modeling of radiological performance assessment at many sites around the world.
    This is a screen shot of the Mochovce GoldSim model.
  • GoldSim has a graphical object-oriented programming environment.
    It provides a number of specialized elements used for modeling of physical systems.
    For this type of modeling, it is best to subdivide the model domain into several physical (and conceptual and mathematical) compartments, and set up the processes that govern the interrelationships between these compartments.
  • Here is an illustration of the engineering design of a single vault. The current plan is to build several of these vaults side by side, until the facility footprint is filled. One double vault may be devoted to unconsolidated soil wastes.
  • Here is the GoldSim implementation of the near field of the Mochovce Repository, including the concrete boxes (in pink) and the neighboring compartments where water will flow (concrete, gravel, and soils).
    Each compartment is populated with certain materials, and is connected to neighboring compartments through physical processes. Connections are made for advection of water, and diffusion in water and air phases.
    In addition to these connections, radioactive decay, chemical solubility, and physical partitioning of radiochemical species are occurring simultaneously.
    We could also add uptake and translocation by plants, animals, and human intruders.
  • Outside of the engineered facility, the natural environment consists of hydrogeological materials (soils, rocks, and groundwater) as well as surface water features: streams and a lake.
    In order to model this effectively in GoldSim, detailed hydrogeological modeling must be abstracted to simpler equations, taking the form of transfer functions. For example, if a concentration C(t) enters the groundwater, a flux of f(C(t)) will appear in the stream. There is, of course, a great deal of uncertainty in that estimate, and that uncertainty must also be accounted for in the model.
  • The far field calculations are abstracted into GoldSim with a few simple elements. If it is found that this part of the model is significant to determining exposures to receptors, then it can be refined as needed, if suitable information exists.
  • Here is a typical set of results. Different radionuclides behave differently, of course, due to variations in half-life, partitioning chemistry, and dose conversion factors. This graph is simply a qualitative example, and would look similar for concentrations or for doses as a function of time.
  • Uncertainty exists in all aspects of modeling, from conceptualization to parameter development to the abstraction of processes. By accounting for these many sources of uncertainty, we can at least generate results that, if not accurate representations of reality, are consistent with our state of knowledge of the problem.
    As we better understand our depiction of reality and how it differs from real phenomena, we can improve our conceptualization through refining the most significant parts of the model.
  • Self explanatory.
  • Self explanatory.
  • The Mochovce model is in a rudimentary form, but has the possibility of being extended to perform a wide range of useful analyses. This has been done at other radioactive waste sites, and other types of physical systems.
    An advanced model can provide guidance to many kinds of decisions related to the site. Bad decisions can be expensive and even dangerous.
    It is our experience that money spent on effective modeling will be saved many times over in making efficient, robust, and defensible decisions.
  • Self explanatory.
  • Closing image.
    Note the repository in the forested watershed, with the creek flowing through the fields.
    To the east is the former townsite of Mochovce, which was demolished to make a site for the Mochovce Nuclear Power Plant. Only the church and graveyard remain from the original town.
    The industrial site to the east in this view consists of two nuclear power plants, each with four cooling towers. Four cooling towers can be seen in a row in the northeast part of the complex, and four in a square arrangement in the southeast corner.
  • the presentation

    1. 1. EGU General Assembly 2007 Neptune and Company, Inc. Los Alamos, NM, USA A Systems Modeling Approach forA Systems Modeling Approach for Performance Assessment of the MochovcePerformance Assessment of the Mochovce National RadioactiveNational Radioactive Waste Repository, Slovak RepublicWaste Repository, Slovak Republic John Tauxe, PhD, PE Paul Black, PhD Václav Hanušík VÚJE, Inc. Trnava, Slovakia
    2. 2. EGU General Assembly 2007 Presentation OutlinePresentation Outline • physical system modeling • introduction to the facility • conceptual system model • mathematical model • computer model • future work
    3. 3. 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
    4. 4. 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.
    5. 5. EGU General Assembly 2007 Are models too abstractAre models too abstract to 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.” ¹ We 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
    6. 6. 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.
    7. 7. 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?
    8. 8. EGU General Assembly 2007 Mathematical Coupling ofMathematical 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 solubilityatmospheric resuspension ∑ ∏= ≠ − − − = i j jk jk t ii j e NN 1 )0(1121 )( λλ λλλ λ  CDJ sw ∇−= θ ~ h n K vx ∇= CDJ sa ∇−= θ ~ soilRatm CfQ ×= solaq CC ≤ aqHair CKC ×= soil w b dwater CKC ×        += θ ρ 1
    9. 9. EGU General Assembly 2007 System ModelingSystem Modeling model input parameters modeled processes modeling results average annual precipitation = N( µ=55 cm, σ=35 cm ) examples: time dose h n K vx ∇= water movement follows Darcy’s Law:
    10. 10. EGU General Assembly 2007 Location Map forLocation Map for Mochovce, SlovakiaMochovce, Slovakia Wein (Vienna) Bratislava Mochovce
    11. 11. EGU General Assembly 2007 Repository in a Small WatershedRepository in a Small Watershed Wein (Vienna) Trnava Bratislava Mochovce
    12. 12. EGU General Assembly 2007 Inside a Vault StructureInside a Vault Structure
    13. 13. EGU General Assembly 2007 The Mochovce GoldSim ModelThe Mochovce GoldSim Model
    14. 14. 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
    15. 15. EGU General Assembly 2007 Engineering Design • Near FieldEngineering Design • Near Field
    16. 16. EGU General Assembly 2007 Near Field CalculationsNear Field Calculations
    17. 17. EGU General Assembly 2007 Repository Far Field EnvironmentRepository Far Field Environment repository stream to lake Mochovce NPP
    18. 18. EGU General Assembly 2007 Far Field CalculationsFar Field Calculations
    19. 19. EGU General Assembly 2007 Typical ResultsTypical Results Any state or condition of the model can be tracked and graphed through time (e.g. concentrations, flow rates, doses). Thiscouldbe concentrationordose.
    20. 20. 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
    21. 21. 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.
    22. 22. 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
    23. 23. 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
    24. 24. 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).
    25. 25. EGU General Assembly 2007 Mochovce, SlovakiaMochovce, Slovakia repository This presentation can be found here: 7