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					General Training On Methodologies For
 Geological Disposal in North America
                IAEA Network of Centers of Excellence




     Development of
 groundwater flow and
  transport models for
repository performance
      assessments
          Bruce A. Robinson
    Los Alamos National Laboratory
                              Topics of Discussion

 • Flow and transport modeling methods (Yucca Mountain
   example)
     • Single and multiphase fluid flow
     • Radionuclide transport
     • Computational issues for transport
 • Uncertainty quantification (Nevada Test Site Underground
   Test Area example – courtesy of Andrew Wolfsberg)
     • Model development and structural uncertainty
     • Geochemistry as a constraint on model development
     • Parameter and conceptual uncertainty


General Training On Methodologies For Geological Disposal in North America
                                    IAEA Network of Centers of Excellence    1
      FEHM – Finite Element Heat and Mass
 Uses on Yucca Mountain Project

 • Unsaturated Zone: simulation of radionuclide migration
   from the repository to the water table
 • Saturated Zone
     • Flow model calibrated with head data and flux
       information
     • Transport model to simulate radionuclide migration
       from the water table beneath the repository to the
       compliance boundary



General Training On Methodologies For Geological Disposal in North America
                                    IAEA Network of Centers of Excellence    2
      FEHM – Finite Element Heat and Mass
 Uses on other Similar Projects

 • Nevada Test Site Underground Test Area Project
    • Unsaturated and saturated zone flow models
    • Radionuclide transport prediction and uncertainty
      quantification
 • Los Alamos National Laboratory groundwater program
 • Proposed Romanian LIL Waste Site
    • Flow model development and calibration
    • Radionuclide transport


General Training On Methodologies For Geological Disposal in North America
                                    IAEA Network of Centers of Excellence    3
      Yucca Mountain Saturated Zone Model
• Flow model construction
• Hydrogeologic framework
  model (HFM)
• Grid generation
• Parameter ranges (prior
  values, updated using
  calibration)
• Calibration (FEHM plus
  PEST software)
• Confidence building using
  other data sets
• Transport model
  simulations


General Training On Methodologies For Geological Disposal in North America
                                    IAEA Network of Centers of Excellence    4
                 Head contours and model fit




General Training On Methodologies For Geological Disposal in North America
                                    IAEA Network of Centers of Excellence    5
                            Particle pathways
 • Computed using
   particle tracking
   algorithm
 • Pathways are a
   function of uncertain
   hydrologic
   parameters




General Training On Methodologies For Geological Disposal in North America
                                    IAEA Network of Centers of Excellence    6
   Confidence building: Comparison of model paths
      and paths inferred by geochemistry data




General Training On Methodologies For Geological Disposal in North America
                                    IAEA Network of Centers of Excellence    7
        Saturated zone radionuclide transport




General Training On Methodologies For Geological Disposal in North America
                                    IAEA Network of Centers of Excellence    8
     Neptunium Monte Carlo transport results
 • Calculations shown are for
   illustrative purposes only – see
   Yucca Mountain License
   Application for final results
 • Flow and transport parameters
   sampled randomly from
   uncertainty distributions
 • Breakthrough curves generated
   using FEHM particle tracking
   model – represent mass flux
   crossing compliance boundary
 • These breakthrough curves are
   input to the Yucca Mountain
   Total System Performance
   Assessment model

General Training On Methodologies For Geological Disposal in North America
                                    IAEA Network of Centers of Excellence    9
         Nevada Test Site Underground Test Area

 • Environmental management program to investigate the
   transport of radionuclides in groundwater as a result of
   underground nuclear testing at the NTS
 • In situ radionuclide concentration contours must be
   predicted, not simply mass flux crossing a compliance
   boundary
 • Example is used here to illustrate uncertainty
   quantification issues
     • Model development
     • Geochemistry as a constraint on model development
     • Parameter and conceptual uncertainty

General Training On Methodologies For Geological Disposal in North America
                                    IAEA Network of Centers of Excellence    10
                    The Nevada Test Site (NTS)
                                                                   Rainier Mesa
Pahute
Mesa

                                                                  Yucca
                                                                  Flat
Pahute Mesa
Corrective                                                         Frenchman
Action Unit
(CAU)                                                              Flat
 Model
Domain




                                                                                NTS
   General Training On Methodologies For Geological Disposal in North America
                                       IAEA Network of Centers of Excellence          11
             The Pahute Mesa Model Domain
                    Black
                    Mountain                   Pahute Mesa
                    Caldera                                                   • 50 x 50 km
                                                                              • Substantial
                                                                                elevation
                                                                                changes
                                                                              • Rough
                                                Timber                          topography
                                                Mountain

                   Oasis
                   Valley

                                                              Testing Areas 19 and 20




                   Timber Mountain Caldera                       Silent Canyon
General Training On Methodologies For Geological Disposal in North America       Caldera
                                    IAEA Network of Centers of Excellence                  12
             Sparse Data is a Universal Issue
Two models of the
buried Silent
Canyon Caldera
                                Black                    Pahute Mesa
below Pahute
                                Mountain
Mesa.

Different
conceptual
models of the
geometry of the
caldera structure,
faults, and
stratigraphy.
                                                          Timber
                                                          Mountain

We have 7
different HFMs


General Training On Methodologies For Geological Disposal in North America
                                    IAEA Network of Centers of Excellence    13
   Stratigraphic Framework Model Uncertainty

Two Alternative
conceptualizations
of the structural
framework model
below Pahute
Mesa




We have 7
different HFMs




 General Training On Methodologies For Geological Disposal in North America
                                     IAEA Network of Centers of Excellence    14
   Uncertainty Quantification – A Practical Question
                Which is more important to consider?
                  Conceptual model uncertainty
                  Parametric uncertainty

                                                         cumulative


                                                                             alternative
       p
                                                                             conceptual
                                                                             models




General Training On Methodologies For Geological Disposal in North America
                                    IAEA Network of Centers of Excellence          15
       Flow Model Uncertainty Quantification
 • 21 steady-state FEHM flow models calibrated with PEST
    • 7 alternative hydrostratigraphic framework models
      (HFMs)
    • 3 alternative recharge models
 • Flow models were ranked for goodness of fit against
   independent geochemical mixing simulations
   (Wolfsberg et al., 2006)




General Training On Methodologies For Geological Disposal in North America
                                    IAEA Network of Centers of Excellence    16
 Geochemical analysis using reverse particle tracking
                                         NW
Exit locations at
top of model for
particles released
at well ER-OV-3c                                                         NE
                                                             NC
1 Million particles
released at each                                                               East
well

Exit locations
compared with
geochemical
source locations                    Recharge

Geochemical
residuals identified
  General Training On Methodologies For Geological Disposal in North America
                                      IAEA Network of Centers of Excellence     17
     Transport Model Uncertainty Quantification
• Transport model considers
   • 35 transient, spatially distributed sources
   • 12 species: conservative, sorbing, and colloidal
• Uncertain transport parameters in heterogeneous materials
   • Fracture properties: aperture, spacing, fracture porosity
   • Matrix diffusion coefficient
   • Matrix porosity
   • Sorption Kds of reactive species
   • Mobile fraction of aqueous plutonium available for colloid-
      facilitated transport
   • Colloid mobility
• Convolution-integral solution for transport on steady-state flow fields
  (transient source release) (Robinson and Dash, 2007)
• Results presented as locations where concentrations exceed the
  standards within 1000 years for greater than 5% of realizations
  General Training On Methodologies For Geological Disposal in North America
                                      IAEA Network of Centers of Excellence    18
             Calculating in situ concentrations
 • Computer code PLUMECALC provides a means for
   computing resident or flux-averaged concentrations from
   particle tracking information and source term
    • Particle tracking (FEHM) : advection, dispersion
    • Source term: radionuclide mass flux vs. time
    • PLUMECALC: computes in situ concentrations in the
      presence of sorption and matrix diffusion




General Training On Methodologies For Geological Disposal in North America
                                    IAEA Network of Centers of Excellence    19
      Contaminant predictions are affected by flow
            model conceptual uncertainty
                               Type I              Type II
                               model               model




                                    Time at which 5% of
                                    realizations exceed
                                    standard



                 Type III
                 model




General Training On Methodologies For Geological Disposal in North America
                                    IAEA Network of Centers of Excellence    20
               Monte Carlo Null Space Analysis
1. Permits definition of insensitivity range per parameter (permeability)
2. Generation of multiple, equiprobable calibrated models, each re-parameterized

Method:
•    Assume selected calibrated model parameters are expected values
•    Add insensitive component of a random perturbation to each calibrated value, for any
     number of realizations

    For example:




     General Training On Methodologies For Geological Disposal in North America
                                         IAEA Network of Centers of Excellence    21
                Monte Carlo Null Space Results




•   Results above are for identical transport parameters (only flow parameters are
    varied)
•   Conclusion: Significant uncertainty due to flow parameters exists even within a
    given hydrogeologic conceptual model


    General Training On Methodologies For Geological Disposal in North America
                                        IAEA Network of Centers of Excellence         22
                                  Conclusions
 • Confidence in natural system model results are obtained
   through a synthesis of available information and robust
   uncertainty quantification
 • Computational tools exist for:
     • Flow and transport model calibration
     • Radionuclide transport prediction
     • Uncertainty quantification
 • Conceptual model uncertainty is important to consider
 • Predictive uncertainty within the constraints provided by
   the calibrated model must also be quantified


General Training On Methodologies For Geological Disposal in North America
                                    IAEA Network of Centers of Excellence    23
                                Backup Slides




General Training On Methodologies For Geological Disposal in North America
                                    IAEA Network of Centers of Excellence    24
          Particle tracking method - advection

                                                •     Trajectory and travel times of particles are
                                                      computed within a cell by velocity
                                                      interpolation (Pollack, 1988).
                                                •     Dispersion is modeled with a random-
        Computational Cell                            walk algorithm (Tompson and Gelhar,
        and Particle Pathway                          1993).
                                                •     Matrix diffusion and sorption are modeled
                                                      using a transfer function approach.




Q1                                 Q2




General Training On Methodologies For Geological Disposal in North America
                                    IAEA Network of Centers of Excellence                 25
         Particle tracking method – sorption and diffusion
    Transfer Function Approach
                                                     Determination of Particle Travel Time
•      Transfer function corresponds
       to a distribution of residence
       times that reproduces an
       analytical solution
•      Travel time through each cell is
       computed based on the
       transport properties in that cell
•      Similar approach is used in the
       unsaturated zone




      General Training On Methodologies For Geological Disposal in North America
                                          IAEA Network of Centers of Excellence        26
      Particle tracking method –diffusion submodel

  Parallel Fracture Model                             Dimensionless Groups




                                                                  t                        z
                                                         T10         R            0 
                                                                 0                        v
                        2b

                                                               ( R ' D' 0 )1/ 2
                                                       1 
               2B                                                     b

                                                                 R ' 1/ 2
                                                       1  (         ) ( B  b)
                                                                D' 0
          Parameters:
           - q (specific discharge)
           - fm (matrix porosity)                  Solution: Sudicky and Frind (1982)
           - ff (fracture porosity)
           - B (fracture spacing)
           - D (diffusion coefficient)
           - Rf (retardation factor)


General Training On Methodologies For Geological Disposal in North America
                                    IAEA Network of Centers of Excellence                      27
                           PLUMECALC Theory
                       Convolution-Based Particle Tracking (CBPT)


 • Superposition principle is applied:

                               

                    
             ~, )  m( ,  t )e kt c( , ~, )dt
      c( , x
                               0
                                       ˆ x

 Mass density function                       c( , ~, t )
                                             ˆ x

  Concentration information in the integral is obtained from the
    composite behavior of particles passing through a computational
    grid cell


General Training On Methodologies For Geological Disposal in North America
                                    IAEA Network of Centers of Excellence    28
                 PLUMECALC demonstration
                    Inle t                                           Outle t


                 Solute
                 Source
                      y      z


                                         x




General Training On Methodologies For Geological Disposal in North America
                                    IAEA Network of Centers of Excellence      29
             Romanian concept on LIL waste disposal




                                                 Cernavoda




                                                                       disposal area
                                                   lock

Digitized map of the topography                           dam
                                                                              Saligny
 and the main features of the
                                                                              village
          Saligny site

 General Training On Methodologies For Geological Disposal in North America
                                     IAEA Network of Centers of Excellence              30
             Romanian concept on LIL waste disposal

       LIL waste                  near surface repository
       selected site :             Saligny

                           disposal cell
cementitious                                                    Saligny site
 waste-form




 General Training On Methodologies For Geological Disposal in North America
                                     IAEA Network of Centers of Excellence     31
     3-D stratigraphic model of Saligny site




              Unsaturated zone                                  Saturated zone


Flow models developed, followed by radionuclide transport calculations
 General Training On Methodologies For Geological Disposal in North America
                                     IAEA Network of Centers of Excellence       32

				
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