9355.0-60
                                                EPA 540-R-96-003
                                                    PB96-963302
                                                    January 1996
DOCUMENTING GROUND-WATER MODELING
          AT SITES CONTAMINATED
      WITH RADIOACTIVE SUBSTANCES
             A Cooperative Effort By

         Office of Radiation and Indoor Air
   Office of Solid Waste and Emergency Response
       U. S. Environmental Protection Agency
            Washington, D.C. 20460

        Office of Environmental Restoration
           U.S. Department of Energy
            Washington, D.C. 20585

   Office of Nuclear Material Safety and Safeguards
          Nuclear Regulatory Commission
            Washington, D.C. 20555

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                                        FOREWORD

This report is the product of the Interagency Environmental Pathway Modeling Working Group.  The
working group includes representatives of the U.S. Environmental Protection Agency' s Office of
Radiation and Indoor Air and Office of Solid Waste and Emergency Response, the U.S. Department of
Energy' s Office of Environmental Restoration, and the U. S. Nuclear Regulatory Commission' s Office
of Nuclear Material Safety and Safeguards.  The purpose of the Working Group is to promote the
appropriate and consistent use of mathematical models in the remediation and restoration process at
sites containing-er contaminated with^adioactive and/or mixed waste materials.  This report
demonstrates a thorough approach to documenting model applications in a consistent manner and is
intended to assist technical staff responsible for identifying and implementing flow and transport models
in support of cleanup decisions at radioactive and hazardous waste sites.  It is hoped that adoption of
the tenets in the report will enhance the understanding between modelers and their managers of what
may be expected in model documentation; facilitate the peer-review process by ensuring that modeling
documentation is complete; ensure the institutional memory is preserved; and institute greater
consistency among modeling reports.

This document is one of several the working group is developing to bring a uniform approach to
solving environmental modeling problems common to all federal agencies.  The interagency working
group has also prepared the following reports:

       •       Computer Models Used to Support Cleanup Decision-Making at Hazardous and
               Radioactive Waste Sites, EPA 402-R-93-005, March 1993.

       •       Environmental Characteristics of EPA, NRC, and DOE Sites Contaminated with
               Radioactive Substances, EPA 402-R-93-011, March 1993.

       •       Environmental Pathway Models-Ground Water Modeling in Support of Remedial
               Decision-Making  at Sites Contaminated with Radioactive Material, EPA 402-R-93-009,
               March 1993.

       •       A Technical Guide to Ground Water Model Selection at Sites Contaminated with
               Radioactive Substances, EPA 402-R-94-012, June 1994.

The Project Officers of the Interagency Working Group (Beverly Ma—EPA, Paul Bean—DOE, Sam
Nalluswami—NRC) acknowledge the cooperation and insight of many staffers in preparing this
document from organizations including EPA Regions 2, 3, 4, 5, 6,  and 8; EPA Office of Emergency
and Remedial Response; EPA Office of Underground Storage Tanks; EPA Robert S. Kerr
Environmental Research Center; EPA Office of Radiation Programs/Las Vegas; EPA National Air and
Radiation Environmental Laboratory; EPA Office of Radiation and Indoor Air Criteria and Standards
Division; DOE Office of Environmental Restoration; and NRC Office of Material Safety and
Safeguards, who graciously agreed to provide review and comment. We also thank their  managers
who permitted them the time to provide us with valuable input.

This report was prepared under EPA Contract 68D20155, Mr. David Back, Project Officer,  Sanford
Cohen & Associates.

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                                     CONTENTS

                                                                                  Page

Foreword	i

Executive Summary	  ES-1

1.      Introduction  	   1-1
       1.1    Purpose of This Manual	   1-1
       1.2    How to Use This Manual	   1-1
       1.3    Key Terms  	   1-2
       1.4    Conceptual Approach  	   1-5
       1.5    Standardization in Ground-Water Modeling  	   1-6

2.      Modeling Objectives and Data Requirements  	   2-1
       2.1    Scoping Phase	   2-1
       2.2    Site Characterization Phase	   2-3
       2.3    Data Requirements  	   2-4
       2.4    Remedial Design and Implementation Phase	2-15

3.      Conceptual Model Development  	   3-1
       3.1    Preliminary Conceptual Model	   3-1
       3.2    Evolution of the Conceptual Model	   3-5
       3.3    Remedial Design and Implementation	3-13

4.      Model Application	   4-1
       4.1    Scoping Calculations	   4-2
             4.1.1  Release Analysis - Ground Water	   4-2
             4.1.2  Fate Analysis - Ground Water	   4-3
             4.1.3  Analytical Methods  for Aquifer Flow and Transport	   4-3
             4.1.4  Uncertainty Analysis  	   4-3
       4.2   Site Characterization Modeling 	   4-6
             4.2.1  Code Selection	   4-7
             4.2.2  Model Construction	4-11
                    4.2.2.1  Layering and Gridding 	4-12
                    4.2.2.2 Definition of Boundary and Initial Conditions   	4-13
                    4.2.2.3  Specification of Time  Steps  	4-16
                    4.2.2.4 Specifying  Parameter Values in the Model	4-16
             4.2.3  Calibration of the Model	4-17
             4.2.4  Uncertainty and Sensitivity Analyses	4-19
       4.3    Predictive Simulations	4-21
       4.4   Baseline Risk Assessment	4-21
       4.5    Exposure Estimation-Ground Water	4-22

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                              CONTENTS (Continued)

                                                                               Page

5.     Report Presentation Guidelines  	  5-1
      Modeling Objectives and Data Requirements 	  5-1
      Conceptual Model Development  	  5-2
      Model Application	  5-3

6.     References  	  6-1


Appendix A  Fate and Transport of Radionuclides	A-l

Appendix B  Scoping Analysis Procedures	 B-l

Appendix C  Default Parameter Values	 C-l

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                                      TABLES

No.                                                                             Page

ES-1   Major Steps in Modeling Evaluation Procedures	  ES-5

1-1    General Modeling Approach as a Function of Project Phase	   1-7

2-1    Data Requirements	   2-5

4-1    Bounding Analyses:  Maximum Extent of Contamination  	   4-5
4-2    Bounding Analyses:  Maximum Concentration of Contamination  	   4-6
4-3    Boundary Conditions of Ground-Water Flow Equations  	4-14
4-4    Boundary Conditions of Solute Transport Equations	4-16

5-1    Major Steps in Modeling Evaluation Procedures	   5-9
                                      FIGURES

No.                                                                             Page

ES-1   Exposure Pathways	  ES-1

3-1    Typical Conceptual Model(s) in the Scoping Phase  	   3-2
3-2    Representative Conceptual Model of the Unsaturated Zone  	   3-5
3-3    Representative Conceptual Model of the Saturated Zone	   3-5

4-1    Modes in Which Ground Water May Become Contaminated  	   4-1
4-2    Three-Dimensional View of Model Grid	4-12
4-3    Cross-sectional View of Model Grid	4-13

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                                 EXECUTIVE SUMMARY
This joint EPA/DOE/NRC program is concerned
with the selection and use of mathematical models
that  simulate environmental behavior  and the
impacts  of  radionuclides  via  all  potential
pathways of exposure, including the air, surface
water, ground water,  and terrestrial pathways.
Figure ES-1 gives an overview of these various
exposure pathways.

Though the joint program is concerned with all
pathways, this report  focuses on ground-water
pathways. Ground-water pathways were selected
for first consideration for several reasons.  At
many sites currently regulated by EPA and NRC
or managed by DOE, the principal concern is the
existence of, or potential for, contamination of the
underlying  aquifers.     Compared   to   the
contamination of air, surface water, and terrestrial
pathways, ground-water contamination is more
difficult  to  sample and monitor,  resulting in
greater dependence on  models  to  predict the
locations  and  levels   of   environmental
contamination.
The types of models used to simulate the behavior
of radionuclides in ground water are generally
more complex than models for surface water and
atmospheric pathway transport.   The additional
complexity is necessary to address the complexity
and diversity of settings associated with different
sites.  The methods used to model ground water
are not as standardized as the methods for surface
water and air dispersion modeling, and there is
considerably less  guidance  on  appropriate
methods  for such modeling. The information
presented in this report is consistent with recent
standards on ground-water modelingpublished by
the American Society for Testing and Materials
(ASTM).  ASTM is  a private organization that
publishes consensus  standards for a variety of
fields,  including ground-water modeling.  The
ASTM Subcommittee D 18.21 on Ground-Water
and Vadose Zone Investigations  has approved
seven new  standards related to  ground-water
modeling. These standards have been written in
the form of guides  (not  rigid standards) and
include the following publications:
Pl,l«
Uptake
fa&fftw
«*
V,,Mf
S*l«.G«i«i
!K3f
3XT^
                  Figure ES-1.  Exposure pathways
                                             ES-1

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D-5447  Standard Guide  for Application of a
         Ground-Water Flow Model to a Site-
         Specific Problem

D-5490  Standard Guide for Comparing Ground-
         Water Flow Model Simulations to Site-
         Specific Information

D-5609  Standard Guide for Defining Boundary
         Conditions in Ground-Water Modeling

D-5610  Standard  Guide  for Defining  Initial
         Conditions in Ground-Water Modeling

D-5611  Standard  Guide  for  Conducting  a
         Sensitivity Analysis for a Ground-Water
         Flow Model Application

D-5718  Standard  Guide  for Documenting  a
         Ground-Water Flow Model Application

D-5719  Standard   Guide   for   Simulating
         Subsurface Air  Flow using Ground-
         Water Flow Modeling Techniques

This report describes a process by which ground-
water  flow  and transport  modeling  can  be
systematically reviewed during each phase of the
remedial process. The  phases include the initial
scoping phase, the detailed characterization of the
site, and the selection and implementation of
remedial alternatives.

The proper application of the selected model(s) is
as important, if not more important,  than its
selection. No matter how well a model is suited
to a particular application, it could give erroneous
and highly misleading results if used improperly
or  with  incomplete or incorrect input data.
Conversely,  even  a model with very limited
capabilities, or a model used at a site which has
not been well characterized, can give very useful
results if applied properly with a full appreciation
of the limitations of both the model and the input
data.   This  report  describes  the  methods for
applying ground-water flow and transport models
to sites contaminated with  radioactive materials.
The model application process is described in
terms  of the objectives, data availability,  and
various site characteristics and processes requiring
modeling.

A review by EPA of 20 site-specific modeling
studies (LEE95) cited modeling mistakes in all
aspects of the modeling process including:  (1)
misunderstanding  of the  selected  model,  (2)
improper application of boundary conditions and
or initial conditions, (3) misconceptualization, (4)
improper or unjustifiable estimation of input data,
(5) lackof orimproper calibration/verification, (6)
omission of or insufficient sensitivity/uncertainty
analysis,  and (7) misinterpretation of simulation
results. Any of these errors can lead to the use of
faulty assumptions as the basis for remedial and
risk decisions.

This model review guide is designed to provide, at
a minimum,  a means to determine whether proper
modeling protocol has been followed.  In some
cases, the guide provides sufficient information to
ensure that common modeling pitfalls are avoided.
For example, one  of the  errors indicated by
LEE95 was  that,  in  at least one   of  the
investigations, ground-water  extraction well(s)
had been placed too close to the model boundary,
which resulted  in  an underestimation of the
ground-water capture zones predicted for these
wells.  The  section of this guide  dedicated to
model  construction  discusses the   correct
placement of wells relative to model boundaries
and provides a simple means  for determining if
the well  has been placed  too close to  the
boundary.

However, the goal of this review guide is not to
detail  exactly how  ground-water  modeling is
performed.  Instead, the intention is to provide a
means to ensure that all modeling reports are
properly documented and provide sufficient detail
to allow a comprehensive peer review.

A checklist  containing the major review steps is
presented. With this checklist, the analyst for a
specific project  can identify  potential  problem
areas  in  applying  and documenting the model
activities.   The  major steps  in evaluating the
model are listed in Table ES-1. The first step  is to
identify the objectives of the modeling study. Do
                                              ES-2

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the  objectives  correspond  to  the   project's
objectives?

The second step is to examine in detail the site
characterization data provided by the modeler.
Are there sufficient data to characterize the site?
Are there sufficient  data to match its history?
Were aquifer tests and tracer tests performed?  If
so,  how  were they   analyzed?    Does  the
distribution of wells give a sufficient vertical  as
well as horizontal picture?  Are the wells deep
enough to delineate the greatest depths to which
contaminants are expected to migrate?  Do the
data provide information on the soil  profile  as
well as the water levels?

The next  step is  to  review  the conceptual
approach used  by the modeler  to represent the
ground-water  flow  and contaminant transport
processes occurring at the site. Here, the modeler
should attempt to  identify and  list the  key
assumptions used in developing the conceptual
ground-water flow and transport models.  The
justifications  for  the  individual  assumptions
should be carefully examined, in conjunction with
a general review of field information or data on
site characterization provided by  the modeler.
The key objective of the examination shouldbe to
determine if the modeler's conceptual approach is
consistent with the field data and the objectives.
Specific questions  that should  be  addressed
include:

  •  Can a steady flow system be assumed,  or
     must transient flow conditions be considered?

  •  What transport processes are important?

  •  Which of these processes are not considered
     in the conceptual model?

  •  What are the features of site characterization
     that support or  repudiate  the conceptual
     modeling assumptions?

  •  Can two-dimensional  horizontal  flow be
     assumed or must  three-dimensional flow
     conditions be considered?
Assuming the conceptual approach is appropriate,
the  reviewer  should   then  examine  the
methodology selected by the modeler to solve the
flow and transport problems. The objective at this
stage is to identify the particular  analytical or
numerical  model  used  by  the  modeler  and
determine if it can reliably predict solutions to the
ground-water  flow  and transport   problems
identified during the conceptual stage.  Specific
questions that should be addressed include:

  •  Can the  model  treat all  of the  important
    components  or  features  identified  in the
    conceptual model?

  •  Does the model provide the type of results
    that are necessary to satisfy the objectives set
    forth at the beginning of the study?

  •  If a series of flow  and transport models are
    selected, how do they fit together?

  •  Is the computer code well-documented and
    has it received thorough testing?

If a numerical model  is used in obtaining the
solution, the following question pertaining to
spatial and temporal approximations also should
be asked:

  •  Are the grids and  time increments selected
    for  the  flow  and  transport  simulations
    sufficiently  refined  to   give results  of
    acceptable accuracy?

  •  Are the  grids   free  of  numerical
    instability caused  by rapid changes in
    grid spacing or time step size?

Next, the critical input parameters and boundaries
of the model shouldbe identified and the rationale
for selecting the parameter values and boundary
conditions  assessed.  Are the parameter values
based on site-specific data or on previous studies?
What  data  support  the  selected   boundary
conditions? It is  the modeler's responsibility to
insure that this  result  is consistent with field
evidence. Specific questions may include:
                                              ES-3

-------
•   Are the boundary conditions consistent with
    the  conceptual  model  and with  natural
    hydrologic boundaries? (Watch for arbitrary
    boundaries, such as geographic boundaries)

•   Will the selected boundaries influence model
    predictive simulations because they are too
    close to the area of interest?

•   Are the parameter values consistent with the
    conceptual model and within the range of
    reported or measured values?

•   Are  the parameter values  assigned in  a
    patchwork pattern? (A common problem is
    that parameters are adjusted on a block-by-
    block basis  to achieve  a good calibration
    without regard for geologic evidence)

If the model is calibrated to the  field data, the
comparison of the observed and simulated results
should be examined. History matching or model
calibration  refines  estimates  of  hydrologic
parameters and boundary conditions by comparing
the model results with observed data.  Estimates
of parameters  are  changed to improve  the
comparison.   It is important to constrain  the
changes so that physically realistic parameters are
specified; this generally requires an experienced
ground-water hydrologist.  The history matching
procedure can be done either by a trial and error
or by  automatic regression.   No matter which
approach is selected, sensitivity analysis will be
part of the matching phase.  If the model is not
calibrated, clear justification should be provided.
Specific  areas to evaluate in model calibration
include:
    reasonable range in order to achieve  the
    calibration goals?

•   Does the model report discuss the rationale
    for selection of the final calibrated model
    parameters?

In the final phase of the study, the future behavior
of the system is predicted.  Generally, this is the
shortest part of a study. Predictions are based on
the results using the best estimate of the system's
parameters   obtained  by   history   matching.
Because the set of parameters is not unique, it is
important  to  assess the  uncertainty  in  the
predicted results, which is usually accomplished
by using a sensitivity analysis.  The model's
predictive  results  and the sensitivity analysis
should be  examined to determine if sufficient
conservatism has been made in the simulation.
Any  numerical  error  that   may  have  been
introduced  as  a result of inappropriate solution
techniques or poor choice of grid spacing and time
increment should be assessed carefully.

Finally, the validity of the modeler's conclusions
should be reviewed. Do these conclusions satisfy
the original objectives? The modeler should trace
back each conclusion to ensure that the conclusion
is  valid   and  follows   from   supporting
documentation. Is there sufficient information to
allow the modeling study to be reproduced?

It is the reviewer's responsibility to review data
and modeling results.   It is critical that  the
reviewer has  sufficient experience to interpret
data and assess the conceptualization as well as to
evaluate the results.
    Have calibration criteria been established and
    have  these  criteria  been  met  by  the
    calibration?

    Are calibration errors (differences between
    measured    and   computed
    heads/concentrations) spatially biased? (e.g.,
    too high in one area of the model and too low
    in another)

    Were model parameters  varied beyond  a
                                              ES-4

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           Table ES-1.  Major Steps in Modeling Evaluation Procedures
MODELING AND EVALUATION CRITERIA
APPRAISAL
Yes
No
Comments
CHAPTER 2
OBJECTIVES AND DATA REQUIREMENTS
Are the purpose and scope outlined?
Are the objectives consistent with decision-making needs?
Are the objectives satisfactory?
Are a site description and waste disposal history provided?
Are the data requirements for the proposed modeling outlined?
Are the sources of data adequately presented?
Are data uncertainties discussed?
Is the probable sensitivity of the future modeling results presented for the
data?
Are the potential data limitations and weaknesses provided?
Are the plans to resolve data limitations discussed?






























CHAPTER 3
CONCEPTUAL MODEL DEVELOPMENT
Is the physical framework discussed in detail?
Both regional and local?
Is the hydro geologic framework described in detail?
Both regional and local?
Is the nature of the contaminant source term described?
Are the hydraulic boundaries described in detail?
Are data base deficiencies clearly identified and modeling implications
discussed?
Is the conceptual model consistent with the field data?
Are the uncertainties inherent in the conceptual model discussed?
Are the simplifying assumptions outlined?
Are the assumptions justified?
Are the natural boundaries or the aquifer system described?
Are the following figures and/or tables included:
• Map showing location of study area.
• Geologic map and cross sections indicating the areal and vertical extent of
the system.




































In some instances tabular representation of the data may be appropriate.





                                         ES-5

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Table ES-1 (Continued)
MODELING AND EVALUATION CRITERIA
• Topographic map with the surface water bodies.
• Contour maps showing the tops and/or bottoms of the aquifers and
confining units.
• Isopach maps of hydro stratigraphic units.
• Maps showing extent and thicknesses of stream and lake sediments.
• Maps indicating discrete features (e.g., faults), if present.
• Maps and cross sections showing the unsaturated zone properties (e.g.,
thickness, Ksat).
• Potentiometric surface maps of aquifer(s) and hydraulic boundaries.
• Maps and cross sections showing storage properties of the aquifers and
confining units.1
• Maps and cross sections showing hydraulic conductivity of the aquifers,
confining units and stream and lake sediments.
• Maps and hydrographs of water-budget information.
• Maps and cross sections indicating transport parameters (e.g., Kj).1
• Areal and cross sectional isoconcentration maps of primary contaminants
in soil and ground water.
• Time-series graphs of contaminant concentrations.
• Relevant source-term inventory information.
APPRAISAL
Yes














No














Comments














CHAPTER 4
MODEL APPLICATION
Section
(4.1) SCOPING ANALYSIS
Are scoping analyses performed?
Do scoping results lead to proposed modeling approach?
(4.2) SITE CHARACTERIZATION MODELING
(4.2.1) Code Selection
Is the rationale for the selection clearly presented for proposed code(s)?
Are the general features of the code(s) presented?
Are the assumptions and limitations of the code(s) presented and compared
to the conceptual model?
Is the basis for regulatory acceptance presented?
Is the source documentation for the code included?
Is an executable version of the code included?

































         ES-6

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Table ES-1 (Continued)
MODELING AND EVALUATION CRITERIA
Is the source code readily available for inspection?
Does the code have a history of use?
Is the code well documented?
Is the code adequately tested?
Are the hardware requirements compatible with those available?
(4.2.2) Model Construction
(4.2.2.1) Layering and Gridding:
Is the domain of the grid large enough so that the boundaries will not
interfere with the results?
Do the nodes fall near pumping centers on existing and potential future wells
and along the boundaries?
Is the grid oriented along the principal axes of hydraulic conductivity?
Is the grid discretized at the scale appropriate for the problem?
Are areas of sharp contrasts (e.g., hydraulic conductivity, concentration,
gradient) more finely discretized?
Is the Peclet number less than 2?
Do adjacent elements vary in size by a distance less than a factor of 1.5?
Are strong vertical gradients within a single aquifer accommodated by
multiple planes or layers of nodes?
If matrix diffusion is important, are the confining units adequately
discretized in the relevant regions of the model?
Is the grid more finely spaced along the longitudinal direction of simulated
contaminant plumes?
Is the aspect ratio less than 100:1?
Are the following figures included:
• Grid presented as an overlay of a map of the area to be modeled.
• A vertical cross section(s) which displays the vertical layering of the
model grid.
(4.2.2.2) Boundary and Initial Conditions
Is justification provided for the selection of all boundary and initial
conditions?
Are model boundaries consistent with natural hydro logic features?
Are the boundary and initial conditions consistent with the conceptual
model?
APPRAISAL
Yes

























No

























Comments

























         ES-7

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Table ES-1 (Continued)
MODELING AND EVALUATION CRITERIA
Are the uncertainties associated with the boundaries and initial conditions
addressed?
Are the boundaries far enough away from any pumping/injection centered to
prevent "boundary effects"?
Are transient boundaries discussed?
Is the rationale given for simplifying the boundaries from the conceptual
model discussed?
Are the values for the assigned boundaries presented?
(4.2.2.3) Specification of Time Steps
Is the Courant criterion satisfied?
(4.2.2.4) Model Parameterization
Are data input requirements fully described?
Is the discussion of the data well founded with respect to Objectives and
Data Review Section?
Are the interpretation and extrapolation methods (e.g., Kriging) adequately
presented?
Do the figures and tables completely describe the data input with respect to
discrete components of the model?
Are the model parameters within the range of reported or measured values?
(4.2.3) MODEL CALIBRATION
Has calibration been attempted?
Is the rationale for model calibration approach presented?
Are the calibration procedures described in detail?
Are the calibration criteria presented?
Does the calibration satisfactorily meet specified criteria?
Is the rationale presented for selecting convergence criteria?
Are code convergences and numerical instabilities discussed?
Do the calibrated parameters fall within their expected ranges?
Are discrepancies explained?
Has the calibration been tested against actual field data?
Are the differences between steady-state and transient calibrations
presented?
Could other sets or parameters have calibrated the code just as well? Is this
discussed?
APPRAISAL
Yes


























No


























Comments


























         ES-5

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Table ES-1 (Continued)
MODELING AND EVALUATION CRITERIA
Are areal and cross-sectional representations of the final calibrated results
included for both hydraulic heads and radionuclide plume(s)?
Does calibration of the model take into account the inconsistency between
point measurements at wells and areal averages of model output?
Is the match between the calibration targets and final parameters shown
diagrammatically?
Were calibrating errors presented quantitatively through the use of
descriptive statistics?
If particle-tracking was performed, are these results shown?
Is the calibrated model consistent with the conceptual model?
Are any changes to the conceptual model discussed and justified?
Is non-uniform areal recharge applied? Is this approach justified?
Does the calibration prop erly account for vertical gradients?
Is the calibrated hydraulic conductivity field consistent with the geologic
logs and aquifer stress tests?
Are the convergence criteria appropriate?
Was a mass balance performed?
Is the water-balance error less than 1%?
Are the mass balance results for the calibrated model discussed?
Is the model's water balance consistent with known flows of rivers and levels
of lakes?
APPRAISAL
Yes















No















Comments















         ES-9

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Table ES-1 (Continued)
MODELING AND EVALUATION CRITERIA
(4.2.4) SENSITIVITY ANALYSES
Was a sensitivity analysis performed?
Is the approach to the sensitivity analysis detailed?
Were all input parameters selected for investigation?
If not, was rationale presented for excluding parameters?
Was a sensitivity analysis performed on the boundary conditions?
Are the ranges of parameters appropriate?
Were sufficient simulations performed? Was justification provided?
Was the relevance of the sensitivity analysis results to the overall project
objectives discussed?
Are the results presented so that they are easy to interpret?
Were sensitivity analyses performed for both the calibration and the
predictive simulations?
APPRAISAL
Yes










No










Comments










        ES-10

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                                 CHAPTER 1 INTRODUCTION
1.1   Purpose of This Manual

A review by EPA of 20 site-specific modeling studies
(LEE 95) cited modeling mistakes in all aspects of the
modeling process including: (1) misunderstanding of
the   selected  model, (2)  improper  application  of
boundary  conditions and  or  initial conditions,  (3)
misconceptualization, (4) improper  or unjustifiable
estimation  of input data,  (5)  lack  of or improper
calibration/verification, (6) omission of or insufficient
sensitivity/uncertainty  analysis,   and    (7)
misinterpretation of simulation results.  All of these
errors could lead to the use of faulty assumptions as the
basis for remedial and risk decisions.
Chapter 2 — Modeling Objectives and Data Review

The goal of Chapter 2 is to illustrate the connection
between the modeling objectives and data requirements
for each phase in the remedial process. Specifically, it
should allow the reviewer to ensure that the modeling
report identifies:

  • the data needed for modeling.
  • the origins of data.
  • how the data will be used to meet modeling
    objectives.

Chapter 3 — Conceptual Model Development
This manual is designed to provide, at a minimum, a
means to determine whether proper modeling protocol
has been followed.  In some cases, the guide provides
sufficient information to ensure that common modeling
pitfalls  are  avoided.  Specific  goals  of this manual
include:

  •  Enhance  understanding  between managers
     and modelers of what is expected in terms of
     modeling documentation.

  •  Facilitate the peerreview process by ensuring
     that the modeling documentation is complete.

  •  Ensure that institutional memory is created
     and/or utilized.

  •  Institute greaterconsistency among modeling
     reports.

It is not the goal of this manual to detail exactly how
ground-water  modeling is  performed.   Instead, it is
intended to provide a means to ensure that all modeling
reports  can be properly  documented  and  provide
sufficient detail to allow a comprehensive peer review.
Furthermore, this document is not intended to be used
as a sole reference for reviewing modeling application
studies.  Rather it is intended to  be used along with
other published general references (e.g., EPA87, 88a,
88b, 94a, 94b, 94c, 94d, ASTM93, 94, 95).

1.2  How to Use This Manual

This  manual has been  designed  to provide a basic
understanding  of  modeling  terminology,  modeling
approaches,  and  documentation  requirements  to
facilitate the peer review process.  The content's of its
five chapters and three appendices are  outlined below.
This chapter is designed to ensure that the reviewer has
sufficient  information to assess the adequacy of the
conceptual model presented in the modeling report.

Chapter 4 — Model Application

This chapter discusses model application in each phase
of  the   remedial   process  (i.e.,   scoping,  site
characterization, remedial selection and design).

Before designing the field investigation, it is advisable,
that at a minimum, a series of scoping calculations be
made to assess the potential importance of the ground-
water pathway.  The scoping section in Chapter 4 is
closely linked to calculational methods presented in
Appendix B and  is intended to provide a means for
making preliminary estimates of the rate of contaminant
migration and the expected down-gradient contaminant
concentrations using a calculator.  General equations,
data requirements, and example  problems are given.
An integral part of the discussion is a description of the
dominant  physical and chemical  processes that  may
affect the  fate and transport of radionuclides.  A basic
understanding of these processes will give a general
appreciation  of the  complexity  of the controlling
processes, and of the limitations inherent in the scoping
calculations.

Application   of  the   model   during   the  site
characterization and remedial phases generally is fairly
sophisticated and typically will  be  undertaken by
experienced modelers.    Therefore,  these  sections
emphasize the overall modeling approach and methods
that can be used as simple reality  checks on modeling
performed by others. Guidelines are given as to which
information  should be requested  to facilitate  a  peer
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Chapter 5 — Report Presentation Guidelines

This  chapter summarizes  the previously presented
guidelines for the presentation of reports and provides
a step-by-step checklist to facilitate the review of the
modeling activities.

Appendix A - Fate and Transport of Radionuclides

This appendix consists of a discussion of ground-water
flow and physical and chemical transport processes that
affect the mobility of radionuclides in ground water.

Appendix B - Scoping Analysis Procedures

This appendix discusses in detail a series  of screening
calculations that can be used to estimate  radionuclide
transit times and concentrations.

Appendix C - Default Parameter Values

Typical values of parameters that are frequently used in
modeling studies are presented.

1.3  Key Terms

The  key terms and concepts that are fundamental to
understanding this report are explained  below.

Conceptual Model. The conceptual model of a  site is a
flow diagram, sketch, and/or a description of a site and
its  setting.   The conceptual  model  describes  the
subsurface  physical  system  including  the  nature,
properties, and variability of the aquifer  system (e.g.,
aquifers,  confining  units), and also  the  types  of
contaminants or wastes at a site, where they are located,
and how they are being transported off site by runoff,
percolation  into the ground and transport in  ground
water, or suspension or volatilization into the  air and
transport by the prevailing meteorological conditions.
The  conceptual model also attempts to visualize the
direction and path followed by the contaminants, the
actual or potential locations of the receptors, and the
ways in which receptors maybe exposed, such as direct
contact with the source, ingestion of contaminated food
or water, or inhalation of airborne contaminants.

As information about a site accumulates, the conceptual
model is continually revised and refined, in order to
consolidate   site   and regional hydrogeologic  and
hydro logic data into a set of assumptions and concepts
that can be evaluated quantitatively. More specifically,
the conceptual model identifies and describes important
aspects   of  the physical  hydrogeologic system  or
subsystem for a given purpose.  At a  minimum, the
system conceptualization should include:  the geologic
and hydrologic framework, media type (e.g., fractured
or porous), the nature of relevant physical and chemical
processes,  time dependence,  dimensionality of the
system, initial and  boundary conditions, hydraulic
properties, and sources and sinks (water budget). The
conceptualmodel shouldnot only be consistent with the
physical system but also must be internally consistent.
Each of the components typical of the hydrogeological
conceptual model is briefly discussed below.

Geologic framework. The geologic framework is the
distribution and configuration of the transmissive (e.g.,
sands and  gravels) and  nontransmissive  (e.g., clay)
geologic units. Of primary interest are the thickness,
continuity, lithology,  and geologic structure  of those
units relevant to the study.

Hydrologic framework. The hydrologic framework in
the conceptualmodel includes the physical extent of the
flow system, hydrologic features that affect or control
the ground-water flow system, analysis of ground-water
flow directions, and media type. The conceptual model
must address the degree to which the system behaves as
a porous media. If the system is significantly fractured
or solution  channeled, the conceptual model must
address these issues.

Hydraulic properties. The hydraulic properties include
the  transmissive  and  storage characteristics of the
geologic units (aquifers)  and properties of the fluids.
Specific examples of aquifer and  fluid properties
include   transmissivity,   hydraulic   conductivity,
storativity, fluid viscosity, and densities.

Sources and sinks.   Sources and/or  sinks of water
and/or gas  affect  the pattern and rate of flow  and
therefore will affect the transport of radionuclides from
the source. The most common examples of sources and
sinks include pumping or injection wells,  infiltration,
evapotranspiration, drains, and flow from surface water
bodies.

Boundary and initial conditions.  Boundary conditions
are the conditions  the modeler specifies, typically on
the  perimeter  of  the model  domain,  as known or
estimated flux, head, or concentration values in order to
solve for the unknowns in the problem domain. These
values may be associated with either the ground-water
flow or the  contaminant transport  aspects of the
problem.  Ground-water boundaries may be described
in terms  of where  water and/or radionuclides  are
flowing into or out of the ground-water system. Many
different types of boundaries exist, including surface
water bodies, ground-water divides, rainfall, wells, and
geologic features such as faults and sharp  contrasts in
lithology.   These  real-world  boundaries  must  be
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translated into their mathematical counterparts which
include fixed-head or concentration, constant flux, or
head-dependent flux. The most common contaminant-
source  type  boundaries  either  specify  the  source
concentration  or  prescribe  the  mass  flux  of
contamination entering the system.  Initial conditions
are defined  as  values  of ground-water elevation,
pressure, flow volumes, or contaminant concentrations
which are  initially assigned to interior areas of the
modeled regions at the start of the simulation.

Transport  processes.     Various  mechanical  and
geochemical   processes  affect   the   transport  of
radionuclides by flow through either a porous matrix or
a fracture  system in a porous  matrix. The dominant
mechanical  processes   are  advection,   dispersion
(hydrodynamic dispersion, channeling) and diffusion.
The  chemical   processes  potentially   affecting
radionuclide  transport   include  radioactive  decay,
adsorption on  mineral   surfaces (both internal and
external  to   the   crystal  structure),   speciation,
precipitation, colloidal transport, radiolysis,biofixation,
natural organic matter interactions, anion exclusion, and
complexation.

Spatial dimensionality.    Ground-water  flow  and
contaminant transport are seldom constrained to one or
two dimensions.  However, in some instances, it may be
appropriate to  restrict  the analysis  to  one  or two
dimensions.  The particular number  of  dimensions
should be chosen based on the modeling objectives and
the availability of field and/or laboratory data.

Temporal  dimensionality.   Either  steady-state  or
transient flow simulations can be performed. At steady-
state, it is assumed that the flow field remains constant
with time,  whereas  a transient system changes with
time. Steady-state simulations produce average or long-
term  results  and   generally  require  that  a true
equilibrium case be physically possible.   Transient
analyses are  typically  performed  when  boundary
conditions  vary through time or when study objectives
require answers at more than one time.   It  is also
possible to  mix  temporally  dimensionality  in  a
modeling study.   A common  technique  is to use a
steady-state flow model and a transient transport model.

A conceptual model  describes the present condition of
the system. To predict future behavior, it  is necessary
to develop a dynamic model,  such as physical scale
models, analog models,  or  mathematical models.
Laboratory sand tanks are physical scale  models that
simulate ground-water  flow directly.  The flow of
ground water can also  be implied using  electrical
analog  models.   Mathematical models,  including
analytical and numerical methods, which are discussed
below, are more widely used because they are easier to
develop and manipulate.

Model application.  The model  application is the
process of  choosing and applying the  appropriate
software algorithm,  or   other  analysis  techniques,
capable of simulating the characteristics of thephysical
hydrogeologic system, as identified in the conceptual
model.   To enhance understanding  and  facilitate
implementation of  the  model  application  criteria
developed in this report, the evolution of the computer
model is traced from the inception of the conceptual
model, its  progression through to the  mathematical
model, and finally to the development of the computer
code where computer instructions for performing the
operations that are specified in the mathematical model
are programmed.

Mathematical  Model.   A mathematical  model  is
essentially a mathematical representation of a process
or  system  conceptual  model.    For   example, the
mathematical model for ground-water flow is derived
by applying principles of mass conservation (resulting
in  the  continuity   equation)  and  conservation  of
momentum (resulting in the equation of motion). The
generally applicable equation of  motion in ground-
water flow is  Darcy's Law for laminar flow, which
originated in the mid-nineteenth century as an empirical
relationship. Later, a mechanistic approach related this
equation to the  basic laws of fluid dynamics. In  order
to solve the flow equation, both initial and  boundary
conditions are necessary.

Solution Methodology. Solution methodology refers to
the strategy and  techniques used to solve a set of
mathematical equations. In ground-water modeling, the
equations   are  normally  solved  for  head  (water
elevations  in  the  subsurface)  and/or  contaminant
concentrations.

Mathematical methods developed to solve the ground-
water flow  and transport equations can  be broadly
classified   as   either  deterministic  or   stochastic.
Deterministic methods assume that a system or process
operates  such that the occurrence of a given set of
events leads to a uniquely definable outcome, while
stochastic methods  presuppose the outcome  to  be
uncertain  and  are  structured   to  account for this
uncertainty.

Most stochastic methods  are not completely  stochastic
in that they often utilize a deterministic representation
of soil processes and  derive their stochastic nature from
their representation of inputs and/or spatial variation of
soil characteristics and resulting chemical movement.
While the deterministic approach results in  a specific
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value of a soil variable (e.g., solute concentration) at
pre-specified points  in the  domain,  the stochastic
approach provides the probability (within a level of
confidence) of a specific value occurring at any point.
The  development  of stochastic methods  for  solving
ground-water flow is a relatively recent endeavor.  It
occurred as a result of the growing awareness of the
importance  of  the  intrinsic   variability   of  the
hydro geologic  environment and the fact that the
variability  cannot  be fully characterized.   Stochastic
methods are still primarily research tools; however, as
computer speeds  continue to increase,  the  use of
stochastic  methods  will  spread  from the research
community into mainstream management applications.
This discussion focuses  primarily on deterministic
methods, due to their more widespread use.

Deterministic Methods.  Deterministic methods may
either  be broadly classified as  either analytical or
numerical.    Analytical  methods  usually   involve
approximate or exact solutions to simplified forms of
the differential  equations for  water movement and
solute transport. Simple analytical methods are based
on the  solution of  applicable differential equations
which make a simplified idealization of the field and
give qualitative estimates  of the extent of contaminant
transport.   Such  methods  are  simpler  to use than
numerical methods and can generally be solved with the
aid of a calculator, although computers are also used.
Analytical   methods are  restricted  to   simplified
representations of the physical situations and generally
require only limited  site-specific  input data. They are
useful  for screening  sites  and scoping the problem to
determine  data needs or  the  applicability of more
detailed sophisticated methods.

Analytical   methods  are  used  in  ground-water
investigations  to  solve  many  different kinds  of
problems.   For example, aquifer parameters  (e.g.,
transmissivity,  storativity) are obtained from  aquifer
tests through the use of analytical methods, and ground-
water flow and  contaminant transport rates can also be
estimated by analytical methods.

Analytical  methods that solve ground-water flow and
contaminant transport equations  in porous media are
comparatively  easy  to use.   However,  because the
governing  equations are relatively simple, analytical
solutions are generally restricted either to radial flow
problems or to cases  where velocity is uniform over the
area of interest. Except for some radial flow problems,
almost all available analytical solutions are developed
for systems having a uniform and steady flow. This
means  that the magnitude  and direction of the velocity
throughout the system are uniform with respect to time
and   space,  which  requires   the   system  to   be
homogeneous  and  isotropic  with   respect  to  the
hydraulic conductivity.

Unfortunately, the equations of flow and continuity in
the form of partial differential  equations do not lend
themselves easily to rigorous analytical solutions when
boundaries  are  complex.  Therefore,  if  a  realistic
expression for  hydraulic head  or  concentration as a
function of space cannot be written from the governing
equations  and  boundary and initial conditions, then
analytical methods are generally abandoned, and more
sophisticated numerical methods are used to solve the
set of equations.

Numerical methods provide solutions to the differential
equations   describing  water  movement  and  solute
transport using  approximate methods such as finite
differences and finite elements. Numerical methods can
account for complex geometry and heterogenous media,
as well as  for  dispersion, diffusion, and chemical
retardation  processes  (e.g.,  sorption,  precipitation,
radioactive decay, ion exchange, degradation).  These
methods always  require a digital computer,  greater
quantities of data than analytical modeling,  and an
experienced modeler.

A numerical model for ground-water  flow  consists of
the mathematical  framework for the  solution of the
material balance equations that govern laminar flow
through porous media. These mass balance equations
depend on  physical  constraints  and constitutive
relationships.  The constraints simply state conditions
that components  of the mass balance equations must
satisfy, whereas the constitutive relationships describe
the dependence of parameters, in the  mass balance
equations, on other physical processes.  Furthermore,
the mass  balance equations are composed  of both
spatial and temporal terms, both of which  require
discretization within the  model domain.  These terms
describe the head or concentration in space and time.
The numerical methods  mentioned above  (i.e., finite
element and finite difference) are used as discretization
methods for the spatial term, whereas  finite-difference
methods are generally used to discretize the temporal
term.

The mass  balance equations, physical constraints, and
constitutive relationships lead to a series of equations
that must be solved in space and time. The means by
which the  equations are discretized,  linearized (e.g.,
Newton-Raphson), organized (i.e., matrix construction),
and solved via either direct or iterative methods are all
part of the numerical model.
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Following the formulation of the numerical model, the
computer pro gram is developed. The program consists
of the assembly of numerical techniques, bookkeeping,
and control language  that represents the model from
acceptance of input data and instructions to delivery of
output.

In summary, the conceptual model is an interpretation
or working  description of the  characteristics  and
dynamics of a physical system.  Model construction is
the process of transforming the conceptual model into
a simplified, mathematical description of the physical
system, coded  in computer programming language,
together with a  quantification of the simulated system
(in the form of boundary and initial conditions, system
and process  parameters,  and  system stresses).   An
intermediate step  in the model transformation process
is the mathematical  model which consists  of two
aspects: a process equation and a solution technique to
solve  the process equation.  An analytical solution
solves a very simple process equation analytically by
hand calculations. An analytical model solves a more
complex, but still relatively simple, process equation
analytically with  a  computer program.  A numerical
model solves a simple  or complex process equation
numerically with a computer program. In the context of
this document,  mathematical model refers to all three
solution  techniques  of a process equation.    The
complexity of the process equation dictates the solution
technique required.  The model formulation process
concludes with the coding of the mathematical model
into computer programming language for performing a
specified set of operations.

1.4  Conceptual Approach

One of the primary goals of mathematical modeling is
to synthesize the conceptual model into mathematical
expressions, which,  in turn, are solved by selecting and
applying an appropriate computer code.  This section
discusses  how  the  different  components  of  the
conceptual model, in  conjunction with the modeling
objectives, influence the model selectionand ultimately
the model application.

The underlying premise of model application is that the
various aspects of the  conceptual  model may be
simulated in a variety of ways,  but the selected
approach must  remain consistent with the objectives.
That is, the physical system cannot be overly simplified
to meet  ambitious  objectives, and less  demanding
objectives  should  not  be addressed  with  highly
sophisticated modeling approaches.

Table  1-1 presents  an  overview  of how the overall
approach to modeling a site differs as a function of the
stage of the remedial process. The most common code
application mistakes are applying codes that are more
sophisticated than are appropriate for the available data
or the level of the result desired, and the application of
a code that does not account for the flow and transport
processes that dominate the system.  For example, a
question that  often arises is:   when should three-
dimensional  codes be used as  opposed to two-
dimensional or one-dimensional codes?  Inclusion of
the  third dimension requires substantially more data
than  one- and  two-dimensional   codes.    Similar
questions involving underlying assumptions  need to be
considered in the selection of a modeling approach and
the physical processes which are to be addressed. If the
modeler is not practical, sophisticated approaches may
be used too early in the problem analysis.  In other
instances,  the  complexity of  the  modeling  is
commensurate with the qualifications  of the modeler.
An  inexperienced modeler may take an unacceptably
simplistic approach.   One  should  begin  with  the
simplest code  that will  satisfy the  objectives and
progress toward the more sophisticated codes until the
modeling objectives are achieved.

1.5   Standardization in Ground-Water Modeling

On  October 26, 1993, the Office of Management and
Budget  (OMB)  issued  a  revised  version  of  OMB
Circular  A-119,   "Federal  Participation  in  the
Development and Use of Voluntary Standards." The
revised  circular  encourages greater  agency  use  of
voluntary standards.  It reaffirms  the basic federal
policy  that voluntary  standards  should  be  given
preference over nonmandatory government standards
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unless  the use of such voluntary standards would
adversely  affect  performance  or  cost,   reduce
competition, or have  significant disadvantages. Even
before this circular was revised, the American Society
for Testing  and Materials  (ASTM),  U.S. EPA, the
USGS, and the U.S. Navy entered into a cooperative
agreement  in  1988  (the Navy joined in 1990)  to
accelerate the development of voluntary consensus
standards by ASTM. The cooperative agreement funds
eleven task groups  within ASTM's  Subcommittee
D18.21   on  Ground-Water  and   Vadose  Zone
Investigations. Task Group 10 (D18.21.10) was formed
to develop standards on subsurface fluid-flow modeling
and has produced a total of seven standards to  date,
with  numerous  standards  in draft form.    The
information presented in this report is consistent with
these  recent standards  on  ground-water modeling
published by ASTM.   These standards have  been
written in the form of guides (not rigid standards) and
include the following publications:

D-5447 Standard Guide for Application of a Ground-
        Water Flow Model to a Site-Specific Problem

D-5490 Standard Guide for Comparing Ground-Water
        Flow Model  Simulations  to  Site-Specific
        Information

D-5609 Standard  Guide   for  Defining  Boundary
        Conditions in Ground-Water Modeling

D-5610 Standard Guide for Defining Initial Conditions
        in Ground-Water Modeling

D-5611  Standard Guide for Conducting  a Sensitivity
        Analysis for a Ground-Water Flow Model
        Application

D-5718 Standard Guide for Documenting a Ground-
        Water Flow  Model Application

D-5719 Standard Guide for Simulating Sub surface Air
        Flow using  Ground-Water Flow Modeling
        Techniques
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Table 1-1. General Modeling Approach as a Function of Project Phase
Attributes
Accuracy
Temporal
Representation of
Flow and Transport
Processes
Dimensionality
Boundary and Initial
Conditions
Assumptions
Regarding Flow and
Transport Processes
Lithology
Methodology
Data Requirements
Scoping
Conservative
Approximations
Steady-State Flow
and Transport
Assumptions
1 -Dimensional
Uncomplicated
Boundary and
Uniform Initial
Conditions
Simplified Flow
and Transport
Processes
Homogeneous/
Isotropic
Analytical
Limited
Characterization
Site-Specific
Approximations
Steady-State
Flow/Transient
Transport
Assumptions
1 ,2-Dimensional/
Quasi-3 -Dimensional
Nontransient
Boundary and
Nonuniform Initial
Conditions
Complex Flow and
Transport Processes
Heterogeneous/
Anisotropic
Semi-
Analytical/Numerical
Moderate
Remediation
Remedial Action
Specific
Transient Flow and
Transport
Assumptions
Fully 3 -Dimensional/
Quasi-3 -Dimensional
Transient Boundary
and
Nonuniform Initial
Conditions
Specialized Flow and
Transport Processes
Heterogeneous/
Anisotropic
Numerical
Extensive
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        CHAPTER 2 -^MODELING OBJECTIVES AND DATA REQUIREMENTS
Successful ground-water modeling must begin with an
approach  that is consistent  not only with  the  site
characteristics but also with the modeling objectives,
which  depend strongly  on the  stage of the remedial
process (i.e., scoping vs.  site characterization vs. the
selection and implementation of a remedy).

The most common mistakes in applying models are in
using models that  are  more  sophisticated than are
appropriate  for the  available data or the level  of the
result desired,  and in using a  model that does not
accurately account for the flow and transport processes
that dominate the system. The simplest model that will
satisfy the objectives should be used first, progressing
toward  more sophisticated ones as understanding of
the system improves and objectives change.

The remedial process is generally structured in a way
that  is  consistent with  this philosophy (i.e., as the
investigation  proceeds,  additional  data  become
available to  support more sophisticated ground-water
modeling).   The data available in the early  stage of
remediation  may limit  the modeling to one or  two
dimensions.  In  certain cases, this may be sufficient
to  support   decision-making.     If  the  modeling
objectives cannot be  met in this manner,  additional
data  will be  needed to support more complex models.
The  selection of more  complex models in the later
phases  often depends on the  results  obtained with
simpler models during the early phases.

Generally, in the  later phases  of the investigation,
enough data  have  been  collected to  meet  more
ambitious   objectives   through   complex   three-
dimensional  modeling.   The  necessary  degree of
sophistication of the modeling effort can be evaluated
in terms of both site-related issues and objectives, as
well as the  qualities inherent  in the  computational
methods available for solving ground-water flow and
transport.

Modeling objectives  for  each  stage of the remedial
investigation must be very specific and well-defined
early within each phase.   All  too often modeling is
carried out  without  a  clear rationale to meet the
objectives, and only after modeling  is completed are
the weaknesses in the approach discovered.

The  objectives must  consider  the decisions  that the
results are intended  to support.  The selected approach
should not be driven by the availability of data, but by
the modeling objectives  which should be defined in
terms of what can be accomplished with the available
data;  also,  the  objectives should be reviewed  and
possibly  revised  during  the  modeling  process.
Furthermore, ground-water modeling should not be
thought of as static or linear process, but rather one
that can be continuously adapted to reflect changes in
modeling  objectives, data needs, and available data.

2.1 Scoping Phase

A large part of  ground-water modeling in this early
phase is understanding the decisions that need to be
made  and determining which of these, which can be
assisted by using specific calculations when the data
are  limited  and  the  controlling  hydrogeologic
processes  at the  site are not completely understood.

In the scoping phase, the objectives generally focus on
establishing order-of-magnitude estimates of the extent
of  contamination   and  the  probable   maximum
radionuclide concentrations  at actual  or  potential
receptor locations.  At most sites, the migration rates
and contaminant concentrations are influenced  by
several parameters and flow and transport  processes
that typically are not fully characterized in the early
phase of the investigation.   The parameters include
recharge,  hydraulic  conductivity,  effective porosity,
hydraulic   gradient,    distribution   coefficients,
thicknesses of the  aquifer and confining  unit,  and
source  concentrations.   During  this  early  phase,
questions  pertaining to flow  and transport processes
typically are limited to general considerations, such as
whether flow and transport are controlled by porous
media or  fractures,   and whether  the wastes are
undergoing transformations from one phase to another
(e.g., liquid to gas).

At this point in the remedial program, one of the most
useful analyses  is to evaluate the potential  effects of
the controlling parameters on flow and transport. One
objective  of the  early  analyses is to  assess the
relationships among the parameters.  How do changes
in one parameter affect the others and the outcome of
the modeling exercise? A better under standing of such
interdependencies assists in properly focusing the site-
characterization activities and ensuring that they are
adequately scoped. Also, it is desirable to evaluate the
effects  that various   processes have on   flow  and
transport; however, this generally has to be deferred
until  additional  information  is  obtained  during site
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characterization.    Furthermore,  some caution  is
needed:  if simplistic assumptions have been made in
the  model,   the  results  may  not be valid  (i.e.,
transferable) to a more refined model that incorporates
more realistic or complex boundary conditions, initial
conditions, or variations in parameters.

In general, the uncertainty associated with each of the
parameters is expressed by a probability distribution,
which  yields  a  likely range  of values  for  each
parameter.   At  this early  phase in  the  modeling
process,  it is important to use a modeling approach
where values for individual parameters can be selected
systematically  from  the  probable range and easily
substituted into the governing mathematical equations
describe  the dominant flow and transport processes at
the site.   In  this manner,  the  effects that a single
parameter, or a multitude of parameters, have on the
rate of movement and concentrations of contaminants
may be evaluated.  This technique  of substituting one
value for another from within  a range of values is
called a sensitivity analysis.  It is important to ensure
that the range of individual values and combinations of
parameters selected allow for a  conservative analysis
of the flow and transport processes.

In  many cases,  the potential  range  of  values  of
important parameters  is  unknown or very  large.
Consequently, the analyst has little alternative but to
evaluate  the  sensitivity  of the results to a very broad
range of possible values for the parameters.  Many of
these results will be unrealistic but cannot be ruled out
until  reliable  site  data  are  obtained during  site
characterization.   These types of analyses are useful
because they help to direct the field work.  However,
they also can be used incorrectly.    For  example,
individuals not familiar  with the scoping process could
come reach grossly inappropriate  conclusions about
the potential public health impacts of the site based on
these results.  Accordingly,  care  must be taken  to
assure that the results of scoping analyses are used to
support the decisions for which they were intended.

An alternative to a detailed sensitivity analysis is a
conservative  bounding  approach.    In   this  less
demanding  analysis, values  are selected  from  the
range of parameters to provide the highest probability
that the  results   are  conservative  (i.e.,   that  the
contaminant migration rates and concentrations would
not be underestimated).  For example,  high values of
hydraulic conductivity  combined with low effective
porosities and low  distribution coefficients  would
maximize  the  predicted  migration   rates  of  the
contaminant, although the higher flow rates may dilute
the concentrations predicted to reach the receptors.
Even though efforts are made to ensure a conservative
analysis, natural as well as anthropogenic influences
may adversely affect the migration of radionuclides.
For  instance,  published distribution  coefficients  are
frequently determined at neutral pH values. However,
even values conservatively selected from  the low
range could be too  high  if acidic wastes were also
discarded with the radioactive material.  Burrowing
animals  and construction activities  also have been
responsible  for moving radioactive wastes beyond the
boundaries  predicted by  ground-water  flow  and
transport models.

Other processes that  could  invalidate an otherwise
conservative analysis include facilitative transport and
discrete features, such as soil macropores. Facilitative
transport is  a term used to describe the mechanism by
which radionuclides  may couple with either naturally
occurring material or other contaminants and move at
much faster rates  than would otherwise be predicted
by   their  respective   distribution  coefficients.
Furthermore, discrete features are rarely considered in
early analyses,  even  though it is well known that
some,   such  as   soil macropores,   can  allow  the
movement of contaminants on the  order of meters per
year in the vadose zone.  Such features can result in a
gross underestimate  of  the time   of arrival and
concentration   of   contaminants    downgradient.
Nonetheless,  the  lack  of  site-specific  data  will
generally preclude  the mathematical modeling  of
anomalous  flow and transport processes during the
project'  s scoping phase.  Therefore, it' s possible that
what normally would be  considered  conservative
modeling results actually underestimate the velocities
and   concentrations  of  the  contaminant.     This
possibility highlights the need to confirm the modeling
results  with site-specific  field data, even when  a
conservative approach has been taken.

In the scoping phase, the data generally available have
been collected   over relatively  short   intervals.
Therefore,  modeling objectives would be limited to
those  which   could  be  met  without  a  detailed
understanding of the temporal processes affecting flow
and  transport. For example, a typical analysis that
may not require detailed  knowledge of the temporal
nature of recharge,   source release rates, and other
flow and transport mechanisms would be an estimate
of the distance that radionuclides  have traveled since
the beginning of waste management  activities.  This
analysis would use yearly average values for the input
parameters, such  as infiltration and source release
rates.     However,   without  accommodating  the
transience  of  these  processes,  predictions of peak
concentrations   of  contaminants   arriving   at
                                                     2-2

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downgradient receptors would be  associated with a
high degree of uncertainty.

Site-specific information is often limited in the scoping
phase. Therefore, modeling during the early planning
phase of  most remedial  investigations  generally  is
designed to support relatively  simple  objectives that
can  be  easily linked with more  ambitious  goals
developed during later phases of  the  investigation.
The iterative process of data collection, analysis, and
decision-making  itself dictates that the preliminary
objectives must evolve to meet the needs of the overall
program.   That  is, it would    be unreasonable to
assume  that initial modeling based upon limited data
would do  little more than direct future activities.

2.2  Site Characterization

In the site characterization phase, the plans developed
during  the scoping phase  are  carried  out.    The
collected field data are used to characterize more fully
the nature and extent of the  contamination at the site,
to   define   environmental   and   demographic
characteristics, and to support  assessments of the
actual or  potential impacts.  The results of the site
characterization are analyzed to determine compliance
with  applicable regulations and to begin to define
strategies for remediation.

The  site characterization phase typically provides the
first opportunity to gain a detailed understanding of the
overall  behavior  of the system.   This improved
understanding leads to a refinement of the conceptual
model and, in turn, allows more ambitious objectives
to be entertained.

The primary reasons for ground-water modeling in the
site characterization phase of the remedial process are
to:  (1) refine  the existing conceptual  model; (2)
optimize the effectiveness of the  site characterization
program;  (3) support the baseline  risk assessment; and
(4) provide  preliminary  input  into   the  remedial
approach.  To accomplish these goals, it is generally
necessary to apply relatively complex ground-water
models  to simulate flow and transport in the saturated
zone and, in some instances, the  unsaturated zone.

A properly designed site characterization program will
expand  the data base to  address  very  specific,  often
demanding objectives.  Consequently, the simplified
modeling approaches undertaken  in the scoping phase
give way to  more sophisticated means of evaluating
the data,  but also convey far more complications  in
developing the proper approach.
In many instances,  several  different  approaches to
modeling will be taken to accomplish these objectives.
For example, the output of analytical modeling of the
unsaturated  zone,   in  the  form   of radionuclide
concentrations at the interface  between the saturated
and  unsaturated  zone,  may  be  used as  input to
numerical models of the saturated zone. Regardless of
the phase  of  the  remedial  process,  the simplest
modeling approach that meets the objectives should be
taken.

The site characterization program is the first time in
the investigation that  detailed flow  and  transport
processes are identified and investigated.  Before site
characterization, the investigator could only evaluate
the effects of various parameter values on flow and
transport.  In the scoping phase, the modeling focused
on estimating the dominant parameters rather than on
the effects that more complex  chemical and physical
flow mechanisms have on the  fate and transport of
contaminants. Examples of these mechanisms include
fractures,  time-dependence of  physical and chemical
processes,  phase transformations, and changes in the
geochemical  environment.

It is  important  to  gain  an  appreciation  for the
governing geochemical processes, as they may have a
significant impact on the transport of radionuclides,
and can  be  simulated indirectly in the analysis by
assuming  a specified retardation of the contaminant.
Direct  means   (computer   codes)  for   simulating
geochemical  processes  are available;  however,  a
detailed discussion  of these methods  is  beyond the
scope of this  report.

As additional  data  are  acquired  during the  site
characterization program and  the  system  boundary
conditions   and   hydrogeology   become   better
understood,  the modeling  approach becomes  more
involved.  Without the data limitations that constrained
the choice of methods in  the scoping  phase, the
number  of  possible alternatives  in  the  modeling
approach increases  dramatically.

2.3  Data Requirements

At most sites, the parameters that influence migration
rates and concentration, flow, and transport processes
of  the  contaminant would  not  have  been  fully
characterized in the early phase of the investigation.
These parameters are the basis upon which the early
conceptual model is formulated, and include variables
such as recharge,  hydraulic conductivity, effective
porosity, hydraulic  gradient, distribution coefficients,
aquifer thicknesses, and source  concentrations.  As the
                                                     2-3

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site  characterization proceeds additional  data  are
obtained to support more  advanced modeling.   The
following information is generally required to estimate
the concentrations of contaminants released, although
the precise  data needs will depend on the  modeling
objectives:

Release Concentration
  1.   Curies of radionuclide(s)
  2.   Water solubility of radionuclide(s) (optional)
  3.   Half-life of the radionuclide
  4.   Distribution coefficient(s) of radionuclide(s)
  5.   Saturated hydraulic conductivities of soil
  6.   Source dimensions
  7.   Soil bulk densities
  8.   Total porosities
  9.   Volumetric water content(s)
 10.   Infiltration rates
 11.   Soil-specific moisture-release curve

Volumetric Release Rate
      Percolation    rate    (evapotranspiration,
      precipitation, runoff)
      Area of contributing source
      Water solubility of radionuclide(s)
      Hydraulic conductivities
      Hydraulic gradient
Table  2-1  shows  the data  typically required  for
ground-water modeling at each stage in the remedial
process.  For convenience, the data have been grouped
into   three  general  categories:      the   Physical
Framework,  the  Hydrogeologic  Framework,  and
Source   Characteristics.     Data  in  the   physical
framework category  define the  geometry  of  the
system,  including the thickness  and areal  extent  of
each  hydrostratigraphic  unit.   Hydrogeologic data
include  information  on   the  system's   boundary
conditions as well as the properties of the aquifer.
Source  characteristics  pertain to  the contaminated
zone, which is the below-ground region within which
radionuclides  are  present  in   above-background
concentrations.  Sometimes referred to as the  source
term, it serves as  the starting point for all pathways.

The following is a brief discussion of the relevance of
the individual parameters to the  overall conceptual
models.
To estimate the velocity of ground water through the
unsaturated zone, the following information is needed:

 1.    Average percolation or recharge rate
 2.    Average volumetric water content

To estimate the velocity of ground water through the
saturated zone, the following information is needed:

 1.    Hydraulic    conductivities    (vertical    and
      horizontal)
 2.    Hydraulic gradient
 3.    Effective porosities

To  estimate  migration of radionuclides through the
saturated   or  unsaturated  zones,  the  following
information is needed:

 1.    Pore-water velocity
 2.    Concentration in the liquid phase (optional)
 3.    Dispersion   coefficients  in  the  x,  y,   and z
      directions (optional)
 4.    Decay coefficients (half-life)
 5.    Retardation factors (bulk density,  distribution
      coefficient, effective porosity)
                                                     2-4

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Table 2-1.  Data Requirements
TYPICAL SOURCES OF INFORMATION

Scoping Calculations
Site Characterization/
Remedial Design
PHYSICAL FRAMEWORK
Depth to Ground Water
Areal Extent and Thickness of Aquifer(s)
Areal Extent and Thickness of Confining
Unit(s)
Elevation of Unsaturated Zone Base
Elevation of Top and Bottom of
Aquifer(s) and Confining Units
Areal Extent and Thickness of Stream and
Lake Sediments
Location and Orientation of Discrete
Features
Topographic Maps
Literature Values
Literature Values
Literature Values
Literature Values
Literature Values
Literature Values
Well Logs/Water -Level Data
Monitoring Well Logs/Geophysics
Monitoring Well Logs/Geophysics
Soil Borings/Elevation Survey
Monitoring Well Logs/Elevation
Survey /Geophysics
Soil Boring
Surface Mapping/Aerial Photo
Interpretation
HYDROLOGIC FRAMEWORK
UNSATURATED ZONE
Hydrodynamic Dispersion
Infiltration Rate
Moisture-Release Curve Parameters
Saturated Hydraulic Conductivity (ksat)
Soil Water Content
Gradient
Total Porosity
Bulk Density
Distribution Coefficients (kj)
SATURATED ZONE
Gradient
Hydraulic Conductivity
Storage Properties
Effective Porosity
Literature Values
Literature Values
Table C-2
Table C-3
Table C-l
Unit Gradient Assumed
Table C-9
Literature Values
Table C-5
Topographic Map
Table C-4
Literature Values
Table C-10
Literature Values
Field Measurements
Laboratory Test
Laboratory Analyses
Laboratory Analyses
Unit Gradient Assumed
Laboratory Analyses/ Field
Analyses
Laboratory Analyses/Literature
Values
Laboratory Analyses/Literature
Water Level Measurements/
Elevation Surveys
Aquifer Stress Tests
Aquifer Stress Tests
Field Tracer Tests/Laboratory
Analyses/Literature
             2-5

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Table 2-1 (Continued)
TYPICAL SOURCES OF INFORMATION

Scoping Calculations
Site Characterization/
Remedial Design
HYDROGEOLOGIC FRAMEWORK
Bulk Density
Dispersivity
Distribution Coefficients
Diffusion Coefficients
Receptor Location(s)
HYDRAULIC BOUNDARIES
Precipitation
Evapotranspiration/Runoff
Surface- Water/Ground- Water
Interactions
Ground- Water Pumping
Literature Values
Table C-ll
Table C-5
Literature Values
Literature Values
Literature Values
Literature Values
Literature Values
Assumed Rates
Laboratory Analyses/Literature
Values
Literature Values/Field Tracer
Tests
Laboratory Analyses/Literature
Values/Field Tracer Tests
Literature Values/Laboratory
Experiments
Field Survey
Field Measurements/Literature
Values
Independent Calculations/
Literature Values
Field Measurements
Field Measurements
SOURCE CHARACTERISTICS
Areal and Vertical Extent
Composition
Release Mechanism
Concentration
Radioactive Decay
Assumption Guidelines
Historical Site Activities
Calculations (Appendix C)
Assumption
Literature Values
Radiation Surveys/ Soil Borings/
Immunoassays
Chemical Analyses
Soil Borings/Ground- Water
Monitoring Data/Site History
Field Data
Literature Values
         2-6

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Physical Framework

The  physical  framework of the system  defines the
geometry of the system and includes the depth to
water, areal extent of hydrostratigraphic units and
fluvial deposits, and discrete features.  The relevance
of each of these  data to ground-water flow  and
contaminant transport is discussed below.

Areal Extent and Thickness of Hydrogeologic  Units.
In heterogeneous  formations,  hydraulic  properties
change spatially.  These properties may  include the
aquifer and/or confining unit (i.e., aquitard) thickness.
The thickness  of the units directly impacts the volume
of flow  and therefore,  mass  transport through the
system.  Furthermore, areas where the confining units
are thin  or discontinuous would provide avenues for
radionuclides  to move  more freely among aquifers.
For  these  reasons,  the determination of the  areal
extent and thicknesses  of the hydrogeologic units is
one  of  the  primary   objectives   during the  site
characterization program.

The thickness  of the aquifer is generally not a required
parameter  for  the  scoping calculations,  although  it
does set upper bounds  on the maximum  amount of
vertical  mixing that could  potentially occur  as is
discussed in Appendix B.

Areal  Extent  and  Thickness  of Stream  and  Lake
Sediments.   The physical properties (e.g., hydraulic
conductivity, sorption properties) of fluvial  deposits
are typically different  from  the underlying  aquifer.
Therefore,   ground-water  flow   and radionuclide
transport into and out of the ground-water system may
be very sensitive to the degree of interconnection of
the aquifer system with surface-water bodies.

Location and  Orientation of Discrete Features.  The
presence of discrete features, such as fractures, faults
and macropores could have a significant effect on the
ground-water  flow and  radionuclide transport.

Modeling  flow  through  the   unsaturated  zone is
generally based on the  assumption that the  soil is a
continuous unsaturated  solid matrix that holds water
within the pores. Actual soil, however, has a number
of cracks, root holes, animal burrows,  etc., where the
physical properties  differ  enormously  from  the
surrounding   soil   matrix.     Under   appropriate
conditions, these flow channels have the capacity to
carry immense  amounts of  water at velocities that
greatly  exceed those in  the  surrounding matrix.  At
present, there is no complete theory describing water
flow through these  structural voids or macropores.
There  is  uncertainty regarding  the  significance of
subsurface voids in  water  flow,  since,  if large, they
should fill only when the  surrounding soil matrix is
close to saturation.  Nonetheless, studies have shown
that contaminants can migrate to  substantial depths
with only a small amount of water  input.

Ground-water flow  and radionuclide transport in  the
saturated  zone  may be  strongly influenced  by  the
presence  of  fractures.   When  a  radionuclide  is
introduced into a fractured porous medium,  it migrates
through the fracture openings by means  of advection
as well as hydrodynamic dispersion. The radionuclide
may also  diffuse  slowly  into   the porous matrix.
Molecular diffusion dominates  flow  and transport
within the porous matrix because the fluid  velocity in
the porous matrix  is  usually  very small.   Upon
introduction  of  the radionuclide  into  a  fractured
aquifer,  the  radionuclide  moves rapidly  within  the
fracture  network.  As time  progresses, the zone of
contamination  will  diffuse farther into the  porous
matrix.    Since  the  porous matrix  has a  very  large
capacity to store the  contaminant, it plays a significant
role in retarding the advance of the concentration front
in the  fractures.  If the source  of contamination is
discontinued and the aquifer is flushed by fresh water,
the contaminant mass in the fractures will be removed
relatively quickly, whereas  the  contaminant in  the
porous  matrix  will be removed  very  slowly  via
diffusion back to the fracture openings.

Hydrogeologic Framework

The hydrological  data have  been divided  into those
associated with the  unsaturated  zone and saturated
zones.   These data include  information on aquifer
properties, hydrologic stresses, and hydraulic heads.
The relevance of each of these to ground-water flow
and contaminant transport  is  discussed below.

Unsaturated Zone

The unsaturated zone is the zone  between the land
surface  and  the water table including the capillary
fringe.  In the subsurface environment, contaminants
migrate through this partially saturated zone  (i.e.,
unsaturated zone) prior to reaching  the saturated
zone. In this zone,  flow is usually assumed to be in
the vertical direction.   The flow  is generally one-
                                                     2-7

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dimensional: therefore, scoping calculations are also
performed in one dimension. Generally, water in this
zone  is under  less  than  atmospheric pressure, and
some of the voids may contain air or other gases at
atmospheric pressure.  Beneath  flooded areas  or  in
perched water bodies the water pressure locally may
be greater than atmospheric.

The volumetric flux of liquid moving under isothermal
and isosmotic conditions through a partially saturated,
natural hydrogeologic unit, regarded as an equivalent
porous-medium continuum system, is determined by
the  spatial  gradients  of matrix  and  gravitational
potentials and  by  the  hydraulic properties.    This
functional dependence obeys "Darcy's  Law" for
unsaturated  liquid flow (Appendix B).

The  means  by  which water transports radionuclides
through the unsaturated zone is  a complex  process.
The  passage of water  is dynamic  and  depends on
detailed variations of the hydraulic properties of the
soil through which the water passes. Water storage by
a  soil  profile   is  characterized  by  water  content
distribution, which ultimately depends on the detailed
spatial variability of hydraulic properties.  Infiltrating
water that exceeds the soil water-holding capacity will
contribute to  the net  recharge  of  the  underlying
aquifer.

A rigorous analysis of the flow and transport processes
through  the unsaturated zone is accompanied by
demanding data requirements. However, rarely in the
scoping phase of the investigation would detailed data
be available.  Even during the site characterization
phase, these data are rarely available.  A discussion of
the data that are required for  both scoping and site
characterization modeling of the unsaturated zone are
presented below.

Infiltration  Rate   (Recharge).    Water  from   a
precipitation event moves downward through the soil
under  the influence  of gravity and matric pressures.
Water is extracted from the unsaturated  zone  as
surface evaporation and as plant transpiration; together
these processes  are  termed evapotranspiration.  The
rates of both extraction processes depend primarily on
available  solar  energy,  surface winds,  and plant and
soil type.

A number of simple methodologies are available  to
estimate the fraction of precipitation that recharges
into    the  aquifer   (i.e.,    precipitation   minus
evapotranspiration and runoff).  Recharge estimates
are described by DAS77, FEI75, andTHOSS,  and 57.
In areas drained by perennial streams, recharge may
be estimated by base-flow separation methods.

A   somewhat  more   sophisticated   method   is
incorporated in the Hydrologic Evaluation of Landfill
Performance (HELP) model (SCH83 and 84). HELP
is a quasi-two-dimensional model that computes the
daily water budget for a landfill represented as a series
of horizontal layers.

As a first, rough approximation, net recharge can be
estimated  by  subtracting  pan  evaporation  from
precipitation rates, both of which are generally readily
available.   This approach  would  overestimate net
recharge because runoff is assumed to be negligible.
Typically,  higher infiltration rates  result in greater
health risks, but there are exceptions to this guideline.
When radium is a concern, the risk associated with
direct exposure to radium is generally greater than the
radium risk associated with the ground-water pathway.
Therefore, higher infiltration rates  tend  to flush the
radium from the source and, in turn, reduce the direct
exposure.

Soil Type.  The soil type (e.g., sand,  silt,  clay) may be
used to  obtain qualitative  estimates  of saturated
hydraulic conductivities, porosities,  and the moisture
release information.   In conjunction with infiltration
rates, the soil type  can be used to make preliminary
estimates of moisture content.  The  moisture content
is assumed to fluctuate between field capacity and
saturation  with the  effective  hydraulic  conductivity
based on an empirical equation (Appendix B).  Typical
values for these parameters are presented in Appendix
C.   Appendix B describes how these parameters are
used to solve radionuclide transport.

Hydraulic  Gradient.  After water infiltrates  beneath
the  ground surface,  it generally travels vertically
downward under the influence of gravity and matric
(i.e., suction) forces until it reaches the water table.
The gravity and capillary forces make up the hydraulic
gradient.  Under partially saturated conditions, liquid
water is bound to the solid within the pore and fracture
openings  either by  surface-tension (capillary) forces
or, at very low saturations, by physical  or chemical
adsorption.  The  strength  of the bonding  force  is
measured in terms of an equivalent negative pressure,
or pressure head, designated as the matric potential.
                                                     2-8

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Since the gravitational head gradient has the value of
unity,  it follows that scoping calculations  will  not
require  site-specific  information pertaining to  the
partially saturated zone hydraulic gradient. For more
complex site characterization modeling, however,
capillary pressure relationships are used to determine
hydraulic gradients.

Matric   potential is  a  function  of  liquid-water
saturation.     Typically,  an  analytic  or graphical
representation of the functional relationship defines the
moisture-retention curve for  the  porous  medium.
Moisture-retention  curves for most media  are  not
unique; they display  hysteresis in which the precise
relation  between matric  potential  and  saturation
depends  on  the  wetting  and  drying  history of  the
medium.

Standard  techniques,  using  mercury  intrusion,
pressure-plate apparatus, thermocouple psychrometers,
and  centrifuges are  used to  measure the moisture-
retention curves for small soil and rock samples.

Thickness.   The thickness of the  unsaturated zone or
depth to  water affects the travel time of radionuclides
leached  from  the  surface  to  the  ground water.
Typically, very little dilution occurs in the unsaturated
zone   and   radionuclide  concentrations   will  be
diminished   only through  radioactive  decay  and
volatization. The depth to ground water has no direct
influence on transport mechanisms other than  to create
a relatively thin region known as the capillary fringe
which is above  the  water table and  has  a higher
moisture content, and therefore, a  higher relative
hydraulic conductivity.

Depth to ground water can also influence the  extent of
upward water flow occurring to a surface layer which
has  been evaporating without water  input for  an
extended period  of time.   It  has been shown both
theoretically and experimentally that finer  textured
soils can move water and radionuclides upward from
much greater depths than can  coarse textured soils.

If site data  are  unavailable,   approximate  depth to
water estimates may  be made based  on land surface
topography,  the  elevation of nearby surface water
bodies,  and the tendency of the shallow water table to
mirror   the  land  surface  topography.     Detailed
modeling,  however,  cannot be performed without a
good understanding of the vadose zone geometry.
Distribution Coefficient.  A distribution or partitioning
coefficient (designated Kj), which describes the degree
of sorption,  is used to  calculate  the  partitioning  of
species such  as  radionuclides  between  the  ground
water and aquifer and, thereby,  calculate the sorption
capacity or retardation.  The standard  convention for
recording concentration units for soil samples is  to
express the  concentration in mass of  constituent per
dry  mass of soil.   Based on  this convention, the
dissolved liquid and absorbed-solid concentrations can
be expressed as follows:
                  C=-
                s_
in which

and
where:
 C  =
 CSTOT-
 S =
                          -
                           C
dissolved-liquid phase concentration,
expressed  as  mass  per  volume  of liquid
(Ci/ml or g/ml)
 total contaminant concentration,  expresse
                                 d     in
                                 weight
                                 of  dry
                                 soil
                                 (Ci/g  or
                                 g/g)
bulk density of the soil (g/cm3)
moisture content
equilibrium    (partition   of distribution)
coefficient (ml/g)
particulate concentration, expressed in weight
of dry soil (Ci/g or g/g)
This expression assumes that there is a direct, linear
relationship between the  amount of a solute sorbed
onto soil, S, and the concentration of the solute, C.
Therefore, the adsorption isotherm of C as a function
of S will graph as a straight line.   The assumptions
regarding  this linear  relationship  are  presented  in
                                                     2-9

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Appendix A.

If the soil contaminant concentrations are presented on
a per unit volume basis (i.e.,  mass of contaminant per
total volume  of sample), the dissolved liquid and
absorbed-solid concentrations  can  be  expressed as
follows:
                   C=
                   S=
where:
 CT   =  total contaminant concentration, expressed in
         activity or mass per unit volume (Ci/cm3 or
         g/cm3)
These relationships are used in Appendix B to estimate
the radionuclide release leaching into the subsurface
environment and migrating with the ground water.

In the literature,  distribution coefficients measured
from adsorption conditions abound; however, the Kd
values depend not only  on the  soil's physical and
chemical properties but also on the chemical properties
of the  ground water.  Because of its dependence on
many  site-specific  properties,  the  value  of  the
distribution coefficient  for a specific radionuclide in
soils can range over several orders of magnitude under
different conditions.

Of particular  significance in the unsaturated  zone is
that sorption,  rather  than  being  dependent  upon
effective  porosity  as  in  the  saturated  zone,  is a
function of the moisture content as described by  the
following:
because moisture  content  is transient  in  space and
time, the retardation factor will also  exhibit  these
characteristics.

Unless  data  are  available to the contrary,  scoping
calculations will  generally use the same distribution
coefficient for the unsaturated zone and for the source
term.   Whereas  the distribution coefficient in  the
source term is used to predict leaching concentrations
and rates, the distribution  applied to the unsaturated
zone dictates the rate at which the radionuclide will be
transported as described in Appendix B.   Typical
distribution coefficients are presented as Table C-5 in
Appendix  C.  However,  the  modeling  results  are
typically very sensitive to the distribution coefficient,
and caution should always be used when applying non-
site-specific data.

Hydrodynamic Dispersion.   Since  soil water flux is
represented as a continuous quantity which is volume-
averaged over many pores, the individual travel paths
around  soil grains are mathematically replaced by an
equivalent one-dimensional  flow.   When  this one-
dimensional  flow  of water is multiplied by  the
dissolved solute concentration, the resulting mass flux
does not take into account the additional spreading of
solute which occurs by three-dimensional mass flow at
the pore scale in  the actual system.   This  apparent
solute  spreading  arising from the mass flux effects
which are obscured by mathematical volume averaging
is  called hydrodynamic dispersion.

Saturated Hydraulic Conductivity. Saturated hydraulic
conductivity  is the proportionality coefficient between
the  saturated water flux  and  the  hydraulic  head
gradient.  In cases where water  is ponded on the soil
surface, either through irrigation, rainfall or natural
lakes  or   man-made  storage  ponds  or   lagoons,
hydraulic  conductivity will have a dominant influence
on the amount of water infiltrating into the  soil and,
therefore, will strongly affect mass flow and transport.
where:
 Rj-   =  Retardation Factor
 Kd   =  Distribution Coefficient
 8    =  Moisture Content
 p    =  Bulk Density
This  relationship  indicates  that  retardation  will
increase as moisture content decreases.  Furthermore,
Hydraulic conductivity and permeability are often used
synonymously  in  ground-water modeling;  however,
they have different meanings.  Hydraulic conductivity
combines the properties of the aquifer and of the fluid,
while permeability is a property of only the aquifer
material.   The two parameters are related by  the
following equation:
                                                    2-10

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where:
 K    =
 k
 P
hydraulic conductivity (m/s)
permeability (m )
fluid (water) density (kg/m3)
acceleration due to gravity (m/s )
fluid (water) viscosity (Pa-s)
Most saturated  ground-water  flow  models  require
hydraulic conductivity as input,  while  multi-phase
models  require permeability data.

Soil Water Content. Volumetric soil water content has
a  significant  influence  on  the  flow  and transport
mechanisms.  The curies of radionuclide moved per
unit time from  one  point  to  the next  is  inversely
proportional to the distance  between the two points.
The  actual  path  length in  soil   followed  by   a
radionuclide is  strongly  affected by water content.
Therefore, water content increases, the cross-sectional
area for flow increases, and the path  length decreases
as liquid replaces air  in the medium.  Since flux  of
radionuclide is proportional to water flux multiplied by
the  dissolved radionuclide  concentration,  it  is not
directly affected by water content. However, because
increasing the water content of a given soil will result
in  a higher mass flux,  some correlation between
radionuclide movement and water content may be
found.

The soil water content can influence adsorption in two
ways: it can modify the solution  pathway leading  to
the adsorption sites and thus increase or decrease the
accessibility of the surface to the solute, and it may
also affect  the  physical-chemical properties  of the
adsorbent by increasing or decreasing the hydrolysis of
the clay lattice.  However, the  influence of soil water
content  on  adsorption  is  slight  until  the  soil  is
extremely dry.  In dry soil, the preferential coverage
of water molecules on the soil' s adsorbing surfaces is
removed, and solute adsorption increases dramatically.
Total Porosity.  The porosity of a rock or soil is  its
property of containing interstices or voids.  This may
be expressed quantitatively as the ratio of the volume
of its interstices to its total volume.
Flow and transport are indirectly affected by porosity
since regions of low porosity are likely to have lower
permeability to transport water. Although no reliable
models exist to  describe  the  relationships  between
porosity and permeability, permeability of a given soil
type strongly decreases as porosity decreases because
the pore sizes contract.  However, finer-textured soils
such  as clays generally have  a higher porosity and
lower permeability than sandy soils.

Porosity  is an  important  parameter  in  computing
ground-water  velocity in  both  the  saturated and
unsaturated zones.  Velocity is inversely proportional
to  porosity.   Another way  that  porosity affects
transport is that decreasing soil porosity increases the
density of mineral adsorption sites and  thus causes
increased   adsorption  of  radionuclides  with   a
corresponding decrease in solution concentration.

Bulk Density.   The soil or dry density is the ratio of
the mass of the solid phase of soil (i.e, dry soil) to its
total volume (solid and pore volumes together).

The influence of increasing bulk density on adsorption
is to  increase the density of adsorption sites per unit
volume  which   will  directly  increase  adsorption
capacity.     However,   the   correlation  between
adsorption and bulk density for a group of soils will be
small because clay and organic soils tent to be found
at lower bulk density than coarser textured soils which
are  low  in organic  matter.    Thus,  the effect  of
increasing  bulk density  on  adsorption refers  to
compressing a given soil volume.

Saturated Zone

The saturated zone is that part of the earth' s crust
beneath the regional water table  in which all  voids,
large and small,  are filled with water under pressure
greater than atmospheric.  The  saturated zone may
depart from the ideal in some respects. A rising water
table may cause entrapment of air in the upper part of
the  zone  of  saturation.   The  shallowest  aquifer
typically would be under unconfined conditions or  a
water-table aquifer.  The ground water flowing within
a water-table surface is in immediate contact with the
atmosphere and is directly  recharged through the
overlying unsaturated zone. This water-table surface
is free to rise and fall within the aquifer in response to
varying amounts of recharge (e.g., rain).   The water-
table   aquifer   generally   follows    land-surface
                                                     2-11

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topography and is frequently revealed in the form of
surface-water bodies such as lakes and rivers.  This
connection between the ground water and the surface
water also creates potential surface-water pathways.
Scoping calculations generally focus on contaminant
releases  to  the shallowest  aquifer,  whereas   site
characterization modeling would tend to include all
aquifers  and  aquitards  in the  hydrogeologic flow
system.  The data required to describe ground-water
flow and radionuclide transport through the saturated
zone are presented below.

Potentiometric Surface Maps.   The potentiometric
surface is a  way of depicting the static head in an
aquifer.  It is defined by the levels to which water will
rise in tightly cased wells. In cases  where the head
varies  appreciably   with  depth  (i.e.,   upward   or
downward gradients) in the aquifer, a potentiometric
surface is meaningful only if it describes  the static
head along a particular specified surface or stratum in
that aquifer.  More than one potentiometric  surface is
then required to describe the distribution of head.  The
water table is a particular potentiometric surface  for
an unconfined aquifer.

With respect to ground-water  flow and contaminant
transport,  the  potentiometric  surfaces  define  the
hydraulic gradients, which  in  turn,  are  used  to
calculate the direction and volume of flow through the
system, as well as the ground-water and contaminant
velocities.

Hydraulic Gradient.  The hydraulic gradient will play
a significant  role in estimating the velocity at which
the radionuclides are migrating (Appendix B). If site-
specific  data  are   not  available for  the  scoping
calculations, hydraulic gradients maybe approximated
from the land-surface topography.  However, in  the
site characterization modeling, water levels from at
least three wells screened in the aquifer are needed to
determine the direction and magnitude of the gradient.

Hydraulic Conductivity. The hydraulic conductivity of
a soil  or  rock is a measure  of  the  soil's  ability to
transmit water under a hydraulic gradient. The values
of hydraulic  conductivity in  soils and  rocks vary
within a  wide range of several orders of magnitude,
depending on the grain size, the  structure of the soil
matrix, the type of soil fluid, and the relative amount
of saturation present in the soil or rock matrix.

Aquifer tests are often performed for the purpose of
determining   field  values  of   aquifer   hydraulic
conductivities.  Analyses  of the  field test data  are
based upon analytical solutions for radial flow towards
wells under a variety  of conditions.  The  analytical
methods used are very straightforward and generally
do not require the use  of a computer.

Before  site  characterization,  only the most general
assumptions  can be  made about  the  relative flow
properties of the aquifers.  For example,  as a rule of
thumb for sedimentary deposits, it is often assumed
that  the hydraulic  conductivity  in  the  horizontal
direction is ten times greater than that  in the vertical
direction.   In the absence  of site-specific values,
literature values  may  be  used  for the scoping
calculations  (Table  C-6,  Appendix C).    For  site
characterization  modeling,  hydraulic  conductivity
values should be site specific.

Storage  Properties.    The  storativity  of  a  saturated
confined aquifer can be defined as the volume of water
that an aquifer releases from storage per unit surface
area of aquifer per unit  decline in the  component of
hydraulic head normal to that surface.

The storage term for unconfined aquifers  is known as
the specific yield.  It is defined as the volume of water
that an unconfined aquifer releases from  storage  per
unit  surface  area  of aquifer per  unit  decline in  the
water table.

Storage  properties are  required  only for  transient
ground-water flow simulations.  If flow is assumed to
be  steady  state,  the  storativity  of the  aquifer is
assumed to be zero: in flow is equal to outflow with
no change in storage.

Effective Porosity.  The  effective porosity is the ratio
of the volume of interconnected pore spaces available
for transport to the total system volume.  It is used to
estimate the  velocity at  which  ground water  and
radionuclides travel  through  a  porous   medium
(Appendix B). The smaller the effective porosity the
higher the ground-water  velocity and the more rapidly
the transport of radionuclide(s)  or other   solubles.
Total porosity is the ratio of the total pore volume to
the total system volume and includes dead pore space.
Therefore, it is  important not to confuse effective
porosity with total  porosity,  as  total porosity will
always be greater  than effective porosity.

In natural porous systems, such  as subsurface soil,
                                                     2-12

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where the  flow of  water is caused by  capillary,
molecular,  and  gravitational forces,  the  effective
porosity can be approximated by the specific yield,
which is defined as the ratio  of the volume of water
drained by gravity from a saturated sample of soil to
the total volume of soil.

The  most  accurate  means  of  obtaining  effective
porosity data is by conducting  site-specific field tracer
tests.  These tests, however, are time consuming and
may not significantly reduce the uncertainty associated
with the effective porosity. Since the greatest source
of uncertainty relative to transport is  typically  the
distribution coefficient, it is generally best to estimate
effective porosities from  the literature (Table C-10).
An  analysis  can  be  performed  to  evaluate  the
sensitivity on  flow  and  transport  results  (Section
4.1.4).

Bulk Density.  The bulk density of the soil or rock is
used to determine the retardation factor  as derived in
Appendix B. The soil or dry density is the ratio of the
mass of the solid phase of soil  (i.e, dry soil) to its total
volume (solid and pore volumes together).  The  dry
density of most soils  varies within the range of 1.1 -
1.6 gr/cm . In sandy soils, dry density can be as high
as 1.6 gr/cm3,  in clayey  soils  and aggregated loams,
it can  be as low  as 1.1 gr/cm3. Although laboratory
measurements  may be made  to obtain accurate bulk
density values, it is rarely worth  the  effort as  the
potential range is relatively narrow, and the modeling
results are typically insensitive to bulk density.

Dispersion  Coefficients.   The equations  of solute
transport  that  are  solved in contaminant-transport
codes  are derived assuming that the solute migration
is  due  to  advection  and hydrodynamic dispersion.
Hydrodynamic dispersion is caused by the tendency of
the solute to spread out from the path that it would be
expected to follow  if transported  only by advection.
This  spreading of  the contamination over  an ever-
increasing area is called hydrodynamic dispersion and
has  two  components:    mechanical  dispersion and
diffusion. Hydrodynamic dispersion causes dilution of
the solute and occurs because of spatial variations in
ground-water flow  velocities  and  mechanical mixing
during fluid advection. Molecular diffusion, the other
component of hydrodynamic dispersion, is  due to the
thermal kinetic energy of solute molecules and also
contributes to  the  dispersion process.    Thus,  if
hydrodynamic  dispersion is factored into the solute
transport processes, ground-water contamination will
cover a much larger region than in the case of pure
advection,  with  a  corresponding reduction  in  the
maximum   and   average   concentrations   of  the
contaminant.   Typical dispersivity values,  obtained
from tracer tests, are presented in Table C-ll.

Because  hydrodynamic  dispersion  is  the   sum  of
mechanical dispersion and diffusion, it is  possible to
divide the hydrodynamic dispersion term into the two
components  and  have two  separate  terms  in  the
equation.   Under most conditions of ground-water
flow, diffusion  is  insignificant and  is  frequently
neglected in many of the contaminant transport codes.
However, this artificial exclusion of the diffusion term
may create problems in certain instances (see Section
3.3 under the topic of matrix diffusion).

Representing dispersion adequately in computer codes
is  difficult, because dispersion  is related to spatial
scale  and  variations in  aquifer properties  that  are
generally not explicitly simulated in the code  (e.g.,
tortuosity). Furthermore, dispersion coefficients are
very difficult to measure in the  field and have been
shown generally to increase with scale of observation.
These difficulties are generally addressed by using
dispersivity values from  the published literature and
refining these estimates during the model  calibration
process.

Distribution  Coefficient.    As with  the  unsaturated
zone, the  distribution coefficient assigned  to  the
saturated zone will  help determine the rate  at which
the radionuclides migrate.  This distribution coefficient
should be  consistent with the rock or soil types that
make up the  aquifer or water-bearing unit.

A  detailed discussion  of distribution coefficients is
presented in Appendix A.  The use of literature values
for site characterization modeling is rarely  defensible.
Furthermore,  modeling  results  are  typically very
sensitive to the magnitude of the
distribution  coefficients.    Therefore, site-specific
distribution coefficients should be obtained during the
site characterization program.

The two most common experimental techniques for the
determination of the distribution coefficient are the
batch and column methods. The batch method is used
to  measure the distribution coefficient under saturated
equilibrium conditions. The column method is used to
obtain a more representative value as the soil has not
been altered (e.g., grinding, agitated)  as much as in
                                                     2-13

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the batch experiments.

Precipitation/Irrigation.  The characteristics  of the
precipitation or rainfall  events  (i.e.,  intensity and
distribution) greatly affect the extent of radionuclide
transport.    Precipitation  will  have  a  dominant
influence on flow because the rainfall rate is directly
related to the water flow rate in the soil.  Therefore,
soils that receive intense, frequent rainfall  will have
high water fluxes and hence high radionuclide activity
fluxes. Furthermore, extremely intense rainfall might
induce saturation which  could  result in  a  greatly
enhanced mass  transport   through  soils   of  high
permeability.    That  is,   the  saturated  hydraulic
conductivity   may   be  reached.      These   same
characteristics may be observed in aquifers underlying
irrigated fields.

Evapotranspiration. Evapotranspiration represents the
amount of applied water which is removed by plants
or water loss from surfaces via evaporation and hence
is  unavailable  for  drainage.  Thus,  the  extent of
evapotranspiration will strongly affect the water flux
below  the root zone and  therefore,  the  extent of
radionuclide leaching by mass flow.   For soils not
receiving  water input  by irrigation,  rainfall  minus
evapotranspiration  and runoff  determines the net
amount of water infiltrating beyond the root zone.

Surface-Water/Ground-Water  Interactions.    Water
resource development has frequently been based on the
predominant use of either surface or ground  water.
These  two components of  the total water  resource,
however,  are   interdependent.    Changes in  one
component can have significant effects on the other.
In streams that are termed "gaining," stream flows are
sustained  by ground water  influx, whereas "losing"
streams replenish the ground water by seepage through
the stream bed.  The  hydraulic  conductivity  of the
stream bed sediments will be a contributing factor to
the rate at which water moves into or out of a stream.

Ground-Water Pumping/Injection.   The injection or
withdrawal of water into or out of an aquifer can have
a pronounced effect on the hydraulic gradients.  In the
case of withdrawal wells, capture  zones are created
which will not allow contamination to migrate beyond
this zone.

Source Characteristics
The accurate portrayal of the contaminant source term
is  one of the most difficult  tasks  in  the  modeling
process.    All too  often,  there are  no  data  that
characterize the nature and extent of the contamination
or the release  history.

Some knowledge of the history of the waste disposal
activities can  often provide valuable insight into  the
probable nature of the contaminant  source  term.  In
general, the longer the site has been active, the more
likely it is that the wastes have been discarded in many
different forms and dispersed over a larger area.  The
presence  of product  and waste lines  immediately
suggests   that   line-type  sources   are   present.
Absorption beds  and storage  tanks indicate potential
point sources, whereas mill tailings,  large lagoons,
and  air  emissions  that  carried and  subsequently
deposited contaminants  in the  site vicinity  would
generally represent area  sources.

The distribution of measured contaminants in the soil
and ground water will also provide clues as to their
source.   Contaminants that are  wide-spread and of
similar concentrations  suggest an areal source (or non-
point), while narrowly defined areas of contamination
indicate a more localized or point source.

As a general rule,  it is  best to keep initial assumptions
regarding the  source term as simple as possible.  The
large uncertainties of the initial scoping phase dictate
that  the   sensitivity  analysis   become  a  critical
component  of the  analysis  to  quantify  associated
uncertainties.  As more data become available during
the site characterization,  source term characteristics
can be more accurately modeled.  The characteristics
typically associated with the source term are discussed
below  and include:   source  dimensions,  release
mechanisms, radionuclide concentrations, and leaching
rates.

Areal and Vertical  Extent.   The vertical  and areal
extent  of contamination  is  a  site-specific parameter
that will potentially have a high  degree of associated
uncertainty for the scoping calculations. In practice,
scoping calculations often assume the source to be  a
point source that includes  1  m  of material.  This
volume is subsequently  scaled  upwards to analyze
larger areas.

One  of   the  primary   objectives   of  the  site
characterization program is to define the geometry of
                                                    2-14

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the contaminant source. Most numerical models allow
the source geometry to be accurately portrayed to the
degree desired.

Release Mechanism.  Computer codes can simulate the
introduction of contaminants to the ground water as an
instantaneous  pulse  or as a  continuous  release over
time. A continuous  release may either be constant or
vary with time.  The two most common means of
simulating continuous or pulse releases are by either
specifying release concentrations or by specifying the
contaminant mass entering the system.   In  general,
both approaches have drawbacks and limitations and
require considerable thought and possibly a number of
independent   calculations  prior  to  selecting  and
implementing the most  appropriate method for the
modeling exercise.   Furthermore, most ground-water
flow and transport codes do not explicitly account for
the physical  degradation of waste containers,  and
therefore, anticipated release rates must be estimated
through other means (e.g., waste package codes) and
input  as  boundary   conditions  into  the  flow  and
transport model.

Concentration. The source term  concentration is one
of the most critical  parameters.  It is recommended
that  site-specific  data be obtained because the initial
concentration  will  directly  impact  the  predicted
concentration  at   a  receptor.     Source  term
concentrations should also be varied as an integral part
of the  sensitivity analysis.   Frequently, the source
concentration is normalized:  that is, the concentration
is set to one.  This practice allows the predicted results
presented in  terms  of percentages  of the  actual
concentration.

Radioactive Decay.    Radionuclides either decay to
stable products or to  another radioactive species called
a  daughter.    In some  species,  several  daughter
products may be produced before the parent species
decays to a stable element.  In considering this process
over the transport path of radionuclides, one transport
equation must be written for each original species and
each daughter product to yield the concentration of
each  radionuclide   (original  species  and   daughter
products) at points of interest along the flow path.

Radioactive   source  terms   present    special
considerations in that the activity of the parent isotopes
will  diminish with  time due to radioactive decay.
However,  if  the radionuclide  release  is  solubility
controlled, or if the half-life is extremely long, the
concentration of the leachate may remain  constant
despite  the decay of the source term.  The release
concentrations may remain constant until  the source
term has decayed to concentrations where solubility
limits no longer dictate  the amount of radionuclides
that may go into the solution.

Distribution Coefficient.  As mentioned previously, the
distribution  coefficient  describes  the  soil-water
partitioning for a given compound.  This relationship
is   frequently used  to  predict  the rate  at  which
radionuclides will leach from  the source term, as
described in Appendix B.

2.4   Remedial Design and Implementation Phase

As the site  characterization process  ends  and the
Remedial Design and Selection Phase is entered,  data
that will assist in defining the  remedial alternatives
have been acquired. The various remedial alternatives
can be conveniently grouped into the following three
categories:

 •    Immobilization
 •    Isolation
 •    Removal
This section briefly describes each category, the types
of processes that need to be modeled to  support each
category, and the special information needs for each of
these categories.  The information is required not only
for implementation of the remedial design but also to
evaluate its effectiveness through numerical modeling.

Immobilization

Immobilization of  the radioactive wastes refers to
physical,  chemical, and/or biological processes used
to  stabilize the  radionuclides  and  preclude  their
transport. A number of treatment options  exist, each
having its own associated modeling needs, including:

 •    Physical
      •   vapor extraction
      •   in-situ coating
      •   grouting of fissures and pores
      •   in-situ freezing
      •   in-situ vitrification
                                                    2-15

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 •    Chemical
      •  induce secondary mineralization
      •  induce complexation
      •  alter oxidation-reduction potential

 •    Biological
      •  in-situ microbial activity

 •    Physical/Chemical
      •  alter surface tension relationships
      •  alter surface charges
      •  in-situ binding
      •  adsorbent injection
      •  radionuclide  particle  size  augmentation
        through clay flocculation

The following are the types of physical, chemical, and
biological processes that may need to be modeled to
support alternative remedies based on immobilization:

 •    Physical Properties and Processes
      •  unsaturated zone flow and transport*
      •  heat energy transfer*
      •  multiple layers*
      •  vapor transport*
      •  extreme heterogeneity*
      •  temperature-dependent flow and transport*

 •    Chemical Properties and Processes
      •  density-dependent flow and transport*
      •  oxidation-reduction reactions
      •  system thermodynamics
      •  chemical speciation*
      •  ion-exchange phenomena
      •  precipitation
      •  natural colloidal formation
      •  radiolysis
      •  organic complexation
      •  anion exclusion
 •    Biotic Properties and Processes
      •  biofixation

 * indicates modeling codes are readily available

It would be  ideal if these processes and  properties
could  be  reliably  described  and  modeled  with
conventional and available models.  However, many
of  these  properties  and  processes  are  not  well
understood, and, in these  instances, models  do not
exist that yield reliable results.

The specialized data required to support ground-water
modeling of immobilization techniques  include:

 •    Determination of temperature-dependent  flow
      and transport parameters

 •    Characterization    of   the    geochemical
      environment

 •    Determination  if  the  physical  rock
      properties that govern flow and transport
      have been altered

 •    Characterization of the microbial environment

Isolation

A common  remedial  alternative  is  to  emplace
protective  barriers either to prevent  contaminated
ground  water  from  migrating   away  from   a
contaminated  site or to  divert incoming (i.e., clean)
ground water from the source of contaminants. These
barriers include walls, caps and lines.   Several types
of materials are being used to construct  such barriers,
including  soil and  bentonite,  cement and bentonite,
concrete,  and  sheet piling.   An alternative to the
physical emplacement of protective barriers is the use
of hydraulic containment  which involves controlling
the hydraulic  gradient through the  use of injection
and/or withdrawal wells  or trenches  in  order  to
contain and treat the contaminant plume.  Examples of
potential barriers include the following:

 •    Physical
      • hydraulic containment
      • grout curtains, sheet piling, bentonite slurry
        walls
      • low permeability caps (clay and/or synthetic)
      • liners
 •    Chemical
      • ion-exchange barriers

 •    Biological
      • microbial barriers

If properly designed and emplaced, such barriers can
last  for  several  decades,  barring any  geological
disturbances,   such as  tremors,  ground  settling,
significant  changes  in  hydraulic  gradients,  etc.
                                                    2-16

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Accordingly, such barriers can be useful in mitigating
the impacts of relatively short-lived radionuclides, or
to control the migration of long-lived radionuclides
until a more permanent remedy can be implemented.

Several mechanisms or processes can affect the long-
term integrity of such barriers.  Once  the installation
is complete, failures   can  occur  due to cracking,
hydrofracturing, tunneling and piping, and chemical
disruption.   Changes  in the  site's  geological or
hydrological  characteristics   can  also   lead  to
catastrophic failures, such as partial collapse, settling,
and  breaking.   If a  barrier should  fail following
installation,  water  may  infiltrate   the  site,  and
contaminated leachates may move beyond the  site.
This type of failure  could result in the dispersion of
contaminants in the environment.

The modeling approaches to simulating the effects of
flow barriers on the fate and transport of radionuclides
are  closely  tied  to  the  ability  of  the code to
accommodate factors,  such as:   high permeability
contrasts, transient boundary conditions, and possibly
chemical  and   biological  reactions.      These
considerations will be discussed in greater detail in the
following sections.

The following are the types of physical, chemical, and
biological processes that may need to  be modeled to
support alternative remedies based on isolation.  Many
of these processes are  very complex, and attempts at
modeling will meet with varying degrees of success.

 •    Physical Properties and Processes
      •  unsaturated zone flow and transport*
      •  runoff*
      •  multiple layers*
      •  vegetative cover*
      •  transient  source term*
      •  extreme heterogeneity*
      •  areal recharge and zero flux capability*

 •    Chemical Properties and Processes
      •  localized ion exchange phenomena

 •    Biotic Properties and Processes
      •  localized biofixation
      •  microbial population modeling

 * indicates modeling codes readily available
Typical characterization data needs related to barrier
emplacement include:

 •    Barrier dimensions
 •    Barrier hydraulic conductivity
 •    Geochemical environment
 •    Structural    integrity    of   barrier/barrier
      degradation
 •    Microbial environment
 •    Detailed hydrogeology

Removal

Radioactively contaminated soil can result from the
disposal of both solid and liquid waste.  Solid wastes
may have been  buried in the past without sufficient
integrity  of   containment   so  that,   eventually,
radioactivity intermingled with the  contiguous soil.
Percolation of rain water through shallow burial sites
can contribute further to the migration of radionuclides
to lower depths as well as to some lateral movement.
Wider areas of contamination have occurred when
waste, stored temporarily  at  the surface,  has  lost
containment and has been dispersed by the wind.  The
most common technologies for removing radionuclides
in solid, liquid, and vapor (e.g., tritium) form include
the  following:

 •    Physical
      •  soil excavation (solid)
      •  pump and treat (liquid)
      •  in-situ vaporization (vapor)

 •    Biological
      •  injection and  removal of biomass foam

The following are the types of physical, chemical, and
biological  processes may need to   be  modeled to
support alternative remedies based on removal. Most
of these processes and properties are readily described
in mathematical terms  and can be modeled reliably.
Obviously, modeling the biological activity associated
with the injection of a biomass will have the same
limitations  that  are  common  to  other types  of
biological modeling.

 •    Physical Properties and Processes
      •  transient source term*
      •  unsaturated zone flow and transport*
      •  matrix  diffusion*
      •  desaturation and resaturation of the  aquifer*
                                                    2-17

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     •  vapor transport*                                   Typical characterization needs related to radionuclide
                                                         removal include:
•    Biological Properties and Processes
     •  physical injection  and  withdrawal  of the         •    Air permeability of the unsaturated zone
       biomass                                           •    Unsaturated zone flow and transport parameters
     •  microbial population modeling                      •    Areal extent of contaminated wastes
                                                          •    Depth to ground water
* indicates modeling codes readily available                 •    Saturated zone flow and transport properties

                                                         The degree to which these factors are addressed in the
                                                         modeling relies heavily upon the objectives as well as
                                                         the availability of the required data.
                                                   2-18

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                  CHAPTER 3 —CONCEPTUAL MODEL DEVELOPMENT
3.1   Preliminary Conceptual Model

In the scoping phase, site-specific information is often
limited.  Therefore, the modeling performed  during
the  early   planning   phase   of   most   remedial
investigations  is   generally  designed  to  support
relatively simple objectives which can be easily tied to
more ambitious  goals  developed  during  the  later
phases of the investigation.  The very nature of the
iterative process of  data  collection,  analysis, and
decision  making  dictates  that  the   preliminary
objectives will need to evolve to  meet the needs of the
overall program.  That is, it would be unreasonable to
assume that  simplified  modeling based upon  limited
data would do little more than provide  direction for
future activities.

An important issue that often arises during the scoping
phase is whether remediation and  decommissioning
strategies can be selected  during the scoping phase
based on limited data and  simple screening models.
Such decisions can be costly at  complex sites where
the  nature  and  extent of the contamination and
transport processes are poorly understood.  However,
at relatively simple sites, early remediation decisions
can  help avoid  the  unnecessary delays  and costs
associated   with   a   possibly   prolonged  site
characterization and modeling exercise.

The  formulation of a  conceptual model  is an integral
component of the  modeling  process.   Sometimes,
components of the conceptual model may be simplified
to meet either limited objectives or limitations in the
data. That is, it is often  useful to simulate only certain
components of the  conceptual model.  For instance,
even if there  are data  that indicate separable property
zones in the aquifer, it is common during the scoping
phase to evaluate ground-water flow and contaminant
transport as   a function  of  average values  using
homogeneous  soil  and  rock   properties.    This
simplification  of the conceptual model  is a valid
approach because, in practice, early modeling focuses
upon assessing the  significance of specific parameter
values and their effects  on flow  and transport, rather
than on modeling  specific hydrogeologic  transport
processes.  Figure 3-1  illustrates typical conceptual
models in the early phase of the investigation.

While  different aspects  of  the conceptual  model may
be  simulated  in  a variety  of ways,  the selected
approach must remain consistent with the objectives.
That  is,  the physical  system  cannot  be  overly
simplified  to  meet  ambitious  objectives,  and less
demanding objectives  should not be addressed with
sophisticated models.  Hence,  the  development and
acceptance of a  conceptual model is an evolutionary
process that  depends upon the modeling  goals and
availability of data.   An  important  part of model
application in the early phase of the investigation is
understanding the project decisions that  need to be
made, and identifying which of these decisions can be
supported by the use of specific codes when limited
data and the controlling hydrogeologic processes at the
site are incompletely understood.

Because general  trends, rather than accuracy, are most
important during the scoping phase, the ground-water
modeler  typically makes the following simplifying
assumptions early in the investigation:

   •     Steady-State Assumptions
   •     Restricted Dimensionality
   •     Uncomplicated Boundary and Initial
        Conditions
   •     Simplified  Flow  and  Transport
        Processes
   •     System  Homogeneity

These  conceptual assumptions,  discussed  in greater
detail  below,   generally  translate  into   modeling
approaches that  are consistent with the available data.
They are discussed in greater detail next.

Steady-State Solutions

In the scoping phase, the data generally available have
been collected over relatively short time intervals.
Therefore,  modeling objectives would be limited to
those  that  could  be  met  without   a  detailed
understanding of the  temporal nature  of processes
affecting flow and transport. For example, a typical
analysis  not requiring  detailed knowledge  of the
temporal nature  of recharge, source release rates, and
other flow and  transport mechanisms would be the
estimation  of the distance that  radionuclides  have
traveled  since the beginning  of waste management
activities. This analysis would use yearly average
                                                    3-1

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                            Conceptual Model
                  Cross-sectional Conceptual Model



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                              3-2

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values for the input parameters,  such  as  ambient
recharge,  stream flow stages, and source concentration
release rates.  However, without accommodating the
transient nature of these processes, predictions of peak
contaminant concentrations arriving at downgradient
receptors  would have a  high  degree of uncertainty.
The conceptual model could, therefore, be simplified
to a translation of the  physics  of the  system into
relatively  simple mathematical  terms such as those
described  by analytical expressions.

Restricted Dimensionality

Ground-water flow  and  contaminant transport  are
seldom  constrained  to   one  or  two  dimensions.
However,  during  scoping,  modeling objectives  and
conceptual model development must take into account
that  information  is  rarely  sufficient  to  describe
mathematically  the  controlling  flow and  transport
processes  in three dimensions.  In reality, most of the
modeling  analysis in the preliminary investigation will
focus upon centerline plume concentrations which are
essentially one- and two-dimensional analyses.  One-
dimensional analyses  of the unsaturated  zone  are
customarily performed in a cross-sectional orientation
because   flow  and  transport   are predominantly
vertically  downward.  Similarly, in the saturated zone,
vertical gradients are generally much smaller than
lateral gradients  and,  as a result,  vertical transport
need not always be explicitly modeled. Therefore, the
assumption that  flow is  two-dimensional  may  be
appropriate for areal analyses.

Uncomplicated   Boundary  and   Uniform   Initial
Conditions

Boundary conditions  are  the  conditions  that  the
modeler specifies as known values in order to solve
for the unknowns. Ground-water boundaries may be
described in terms of where water is flowing into the
ground-water  system  and where water is flowing out.
Many different types of boundaries exist, including:
surface-water  bodies,  ground-water divides, recharge,
wells, and geologic features such as faults and sharp
contrasts in lithology. Initial conditions are defined as
values of ground-water elevation,  flow  volumes, or
contaminant concentrations initially assumed  to  be
present  in the  area of interest.

Because of the lack of site-specific data in the scoping
phase,  the  system boundary and  initial  conditions
usually cannot be accurately defined; only very limited
calculations  of approximate travel  distances  and
contaminant concentrations can be made.

Uniform Properties

Homogeneity describes  a system  where  all of the
characteristics spatially are uniform within the aquifer,
whereas isotropy means  that the hydraulic properties
are identical in all directions. A homogeneous system
may have anisotropic flow properties; for example, an
otherwise homogeneous sandstone aquifer may have a
greater  hydraulic  conductivity   in  the  horizontal
direction   than  in   the   vertical.     Therefore,
hydrogeologic units may have anisotropic qualities but
still be considered spatially homogeneous throughout,
provided the  anisotropy does not vary within the unit.

Before  site characterization, only the most  general
assumptions  may be made  about  the relative flow
properties  of the aquifers.  For example,  it is  often
assumed  that  the   hydraulic  conductivity  in the
horizontal direction is ten times greater than that in the
vertical direction for  sedimentary deposits.   These
types of simplifying assumptions regarding the aquifer
properties  would form the  basis of  the conceptual
model.

Simplified Flow and Transport Processes

Site-specific  information describing  the flow  and
transport processes  that dominate the migration of
radionuclides would not be available before detailed
site characterization  occurs.  Therefore,  modeling
objectives would need to be limited to those that can
be addressed with only limited knowledge of the site
hydrogeology and  geochemistry.   In  practice,  this
means   that uniform  porous media  flow would be
assumed in  the conceptual model,  and  all of the
geochemical reactions that  affect  the  radionuclide
transport  would be  lumped together as  a  single
parameter  termed the distribution coefficient.

Discrete features, such as macropores, fractures, and
faults,  would generally have to be excluded from the
mathematical expression of the conceptual model, and
conservative distribution coefficients would be selected
from  conservative  values  found  in  the  literature.
Movement through  the  unsaturated  zone would be
simulated with simplified versions of more complex
equations  describing  the   unsaturated   flow  and
transport.
                                                     3-3

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To  demonstrate the potential effects that simplifying
assumptions  may have  on modeling  results,  the
discussion  in Appendix B outlines the physical  and
chemical processes that may affect the transport of
radionuclides (estimates of moisture content).
3.2
Evolution of the Conceptual Model
The  conceptual model is based  on the modeler's
experience and technical judgment and represents the
modeler' s understanding of the system framework and
behavior.   The conceptual  model will  naturally
become  more  complex   as  more  processes  are
identified   and  interrelationships  of   important
components within  the systems are considered.  The
transformation  of  the  conceptual  model  into  a
mathematical  model  which,  in reality,  is  only  an
extrapolation of a basic understanding of the system,
will result  in  intrinsic simplifications of the system.
For example,  the mathematical models assume that
there is a direct scaling between the model simulations
and the scale at which the data are collected. The lack
of knowledge  about the system resulting from limited
information   also   contributes   to   inevitable
simplifications   between  the    conceptual  and
mathematical  models.

Besides the simplifications inherent in the process,
there   are  deliberate  simplifications  in  which  the
modeler  selects the  physical  characteristics  and
processes  relevant   to   the  model's  application.
Examples of these simplifying assumptions  include:

   •  Flow  through the unsaturated zone is vertical and
     in one dimension.
   •  Chemical   reactions    are   reversible   and
     instantaneous.
   •  Soil  or   rock  medium is   isotropic  and/or
     homogeneous.
   •  Flow   field is uniform  and  under steady-state
     conditions.

As more and  more of these simplifying assumptions
are found  to  be significant,  the  complexity of the
model increases. Thus, the development of a dynamic
model allows for  the neglected components of the
conceptual model to be integrated  systematically.
Components  of  the  conceptual  model  may  be
simplified,  either because  of limited  objectives or
because of constraints on data availability. Even when
the  available  data  support  the  use  of a  more
sophisticated model,  simplifications  are sometimes
advisable.   For  instance, the  site characterization
modeling described in  Section  4.2  discusses  the
application of complex numerical models.  However,
after applying these complex models, it is frequently
possible to simplify the assumptions again and use less
sophisticated models to meet the objectives of the risk
assessment.   This iterative process ensures that the
mathematical model is consistent with the  modeling
objectives.

As discussed in Chapter 1, formulating a conceptual
model is an  integral  component  of the  modeling
process.       The   data   obtained  during   site
characterization provides an opportunity to remove
some of the simplifications made in the scoping phase.
Generally, in the site characterization phase,  sufficient
data are collected to formulate relatively complex
conceptual models.  Therefore, the degree to which
the conceptual model is simplified frequently depends
more on the objectives, than on limitations in the data.
Figures  3-2  and 3-3  illustrate typical  conceptual
models  in the  site characterization  phase  of the
investigation.

The   following  assumptions  are  typical  of  the
conceptual model in the site characterization phase:

   •   Steady-State Flow/Transient Transport
   •   Multi-Dimensionality
   •   Steady-State Boundary and Non-uniform Initial
      Conditions
   •   Complex Flow and Transport Processes
   •   System  Heterogeneity

These  conceptual  model  assumptions   generally
translate into modeling approaches that are consistent
with the data available during the site characterization
phase. They are discussed in greater detail next.

Steady-State Flow/Transient Transport

The  data obtained during the site characterization
program are generally collected over a relatively short
time and frequently do not reflect the temporal nature
of  the  hydrogeologic   system.    Unfortunately,
objectives  in the site characterization  phase often
involve the prediction of temporal trends in the data.
                                                     3-4

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                          -.7
                                                          _
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                rr-Ai.•.!!•> t. n.'..-4:i 111  nri
                           !      i
               Figure 3-2.  Representative conceptual model of the unsaturated zone.
WEST

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                                        AHBIEk'3
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                Figure 3-3.  Representative conceptual model of the saturated zone.
                                                3-5

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For instance, the risk assessment generally includes an
analysis of the peak arrival times of radionuclides  at
downgradient receptors.  This incompatibility between
the objectives and the data available gives rise to some
of the greatest uncertainties associated with the entire
remedial investigation. However, one of the principal
utilities of mathematical models is  their ability  to
extrapolate unknown values through time.

The  modeling approach during site characterization
generally assumes  a  steady-state  flow  field  and
accommodates the transient  nature of the  system
through the contaminant transport analysis. Steady  or
transient leaching  rates are used in conjunction with
the existing plume concentrations for initial conditions.
Therefore, the system is actually modeled as a steady
flow system with possibly a transient or pulse-like
source term.  However,  the transient  nature  of the
plume is  generally  used  as  a model   calibration
parameter and  is not  carried  forward  into the
predictive   analysis    for   future   radionuclide
concentrations.  That is, rarely are there sufficient
data to describe the  temporal nature of the source
release.   Exceptions to this occur when records are
available  pertaining to the volumes of radioactive
liquids that were dumped over time into infiltration,
recharge or evaporation trenches or when correlations
between rainfall events and source leaching rates may
be extrapolated.

The validity of the steady-state assumption depends on
the features  of the flow pattern, which are  in turn
dictated by the nature of boundary conditions and sinks
or sources existing in the flow domain.  Whether  or
not such an assumption is justified also depends on the
time scale of interest and, perhaps most important, the
conservative objectives of the modeling study.

For example, as mentioned above, ground-water flow
modeling performed in conjunction with contaminant
transport  modeling is usually based on an assumption
of steady-state  flow.  This  is  done to  reduce the
complexity and cost of the time-dependent transport
simulation.   Indeed, all analytical solutions and most
of the numerical solutions of the contaminant transport
equation likely to be used in the  modeling study will
be based  on the assumption of a  steady-state velocity
field.  Such an assumption is  valid,  provided that
during the time period of the transport simulation the
flow pattern or velocity distributions do  not  change
significantly.  A common pitfall is a situation where
the modeler deals  with the ground-water flow system
containing internal sinks or sources (e.g., pumping or
injection wells) but ignores drastic  changes  in the
velocity  distribution due  to  changes in  the well
operation or flow rates.  Another situation involves
gradual or sudden changes  in  conditions  at the flow
boundaries which lead to reversal of flow directions
during the period of the transport simulation.   Such
changes must be taken into  account to obtain reliable
predictions of contaminant migration.

As a cautionary note, one modeling report  identified
in the EPA  CSMoS study (LEE95) assumed steady-
state  conditions  based on  only  several  months of
ground-water monitoring  data.   This  assumption
resulted in a predicted ground-water gradient  to the
west,  whereas contaminant data indicated that the
plume was migrating northward.  Obviously, steady-
state  assumptions  must  be based on  a  sufficient
monitoring period.

Multi-Dimensionality

The site characterization program should be designed
to gather sufficient data to develop a three-dimensional
conceptual  model.    It  is  only after  the  three-
dimensional system  is relatively well understood that
it can be  determined whether  one-,  two-,  or  three-
dimensional  modeling is necessary.   If one or two
dimensions are eliminated from the analysis, careful
consideration needs to be  given to  what impact
restricting the dimensions will have  on the model' s
capability to  simulate existing field conditions.

The magnitude of flow and transport in any direction
relative to the other directions provides the criteria for
which dimension(s)  should be  included or  excluded.
In  most  instances,  flow  and   transport in the
unsaturated zone are  assumed to be  predominantly
downward with smaller horizontal components.  If the
flow components are found to have two dominant flow
directions, a two-dimensional cross section may allow
for an adequate representation  of the  flow field.

Modeling and field validation studies of the vadose
zone (the unsaturated zone) have yielded mixed results
both in model calibration and in the comparison of
transport predictions against measured field values. In
modeling the vadose zone, as well as the  saturated
zone, the question is always how much uncertainty in
the results is acceptable, considering the objectives.

Two-dimensional simulations of the saturated zone are
                                                     3-6

-------
usually   performed  when  the   horizontal   flow
components are far greater than the vertical  flow
components, allowing the vertical components to  be
ignored.    However,  in  much  of the  modeling
performed for  site  characterization,  the  vertical
components of  flow are important because  many
natural features, such as surface water bodies, often
have strong vertical flow components associated with
them.  Furthermore, particular care must be taken in
eliminating the third dimension because attempts  to
simulate    three-dimensional   processes   in   two
dimensions can  lead   to   difficulties   in  model
calibration, as  well  as in  producing  defensible
modeling results.

Water-level data collected from closely spaced wells
that penetrate  the  same aquifer and are  screened at
different  depths  provide excellent information  on
vertical hydraulic gradients.  This information may be
used  during  the  site  characterization  program  to
determine  the effective  hydraulic  basement of any
contamination  present,  as  well  as  recharge and
discharge areas.  If there are strong vertical gradients,
the capability  to  simulate the vertical movement  of
ground  water  within   the  hydrogeologic  system
becomes very important in defining the nature and
extent of the contaminant plume.

It  should  also  be kept in mind that two-dimensional
planar  modeling   will  average   the   contaminant
concentrations over the entire thickness of the aquifer,
and the vertical definition of the contaminant plumes
will be lost. This vertical averaging of contaminants
will result in lower downgradient concentrations and
may not provide a realistic  or  conservative baseline
risk assessment.  Again, this example illustrates that
the decision as to how many dimensions to include in
the modeling must be related to the objectives and the
need to be aware of the limitations in the results if one
or more dimensions are eliminated.

The recent development of more sophisticated pre- and
post-processors  greatly  facilitates  data entry and
processing. These advances, in conjunction with the
rapid increase in computer speeds over the past several
years,  have greatly reduced  the  time  involved  in
performing three-dimensional modeling.  In general,
it  is better to include the third  dimension,  even if
many of the parameters in the third dimension have to
be estimated than to constrain the analysis to two
dimensions.
Two-dimensional   analyses   during   the   site
characterization  program  are  most  valuable  for
modeling  the  unsaturated  zone  and for performing
sensitivity analyses of selected cross-sections through
a  three-dimensional  model.      Two-dimensional
approaches are also useful for  performing regional
modeling  from which the boundary conditions for a
more site-scale modeling study may be extrapolated.

Steady-State and Non-uniform Initial Conditions

In  general,  boundary   conditions  are  known  or
estimated  values  that are  assigned to  surfaces and
planes that either  frame the perimeter of the modeled
area  or  define  the  nature  of release  from  the
contaminant source.   The different types of  flow
boundary  conditions  are:   (a)  head (ground-water
elevation) is known for surfaces or planes bounding
the modeled region; (b) ground-water flow volumes
are  known for  surfaces  or planes bounding  the
modeled region; and (c) some combination of (a) and
(b) is known  for surfaces or planes bounding the
region.  Boundary conditions could also be assigned to
interior features of the modeled region where ground-
water elevations or flow volumes are known, such as
lakes, rivers, canals, lagoons, or marshes.

The   most common  types of  contaminant  source
boundaries either specify the source concentration or
prescribe the mass flux  of contamination entering the
system.  The  concentration is  generally prescribed
when the solubility limits of the contaminant largely
controlled the  release.   The mass flux type boundary
is  typically used  when  a leaching  rate is known  or
estimated.  Specialized source boundaries have also
been formulated which  allow for radioactively decay
in the source.  The ability  of the code to treat source
decay may not  be important  if  the  parents and
daughters have a relatively long half-life compared to
the expected travel time to the nearest receptor.

One  of   the  primary   objectives  of  the  site
characterization program is to identify the presence
and  location of ground-water flow and contaminant
source boundaries so that  they may be incorporated
into  the conceptual model.  These boundaries are
generally quantified in terms of the  volume of ground
water and contamination moving through the system.
The   physical  boundaries  are  then translated into
mathematical terms as input into the computer model.
                                                    3-7

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Initial conditions are defined as values of ground-water
elevation,   flow   volumes,    or   contaminant
concentrations, which are initially assigned to interior
areas of the modeled regions.   At least for  the flow
modeling  performed during the  site characterization,
initial conditions are generally set to uniform values.
This is because the temporal nature of the flow system
is  usually poorly defined.  In  addition,  if  the flow
analysis is performed to steady-state, which is usually
the case,  the initial conditions assigned to the  model
domain are irrelevant as identical  solutions will be
reached for  these  values regardless  of the  values
initially assigned.  This occurs because these steady-
state values depend solely on the  values assigned to the
boundaries of the model.

Non-uniform   initial   values   (i.e.,   contaminant
concentrations) are  routinely used in the contaminant
transport analysis to depict the geometry and varying
contaminant concentrations within the plume, as well
as to define the contaminant concentrations  leaching
from the contaminant source.  The ability of a code to
allow non-uniform initial conditions would be essential
to a full description and simulation of the contaminant
plume(s).

Complex Flow and  Transport Processes

Site-specific  information describing  the flow  and
transport  processes  that  dominate  the migration of
radionuclides is not available during the scoping phase
of the  investigation.   As  the  site  characterization
activities progress,  greater attention is focused on the
physical, chemical,  and biological processes that affect
ground-water flow and contaminant transport.   Up
until  this  time, attention  has been paid  primarily to
estimating parameter ranges and variance s within these
ranges via sensitivity  analyses.   This  approach has
limitations and needs to be broadened during the site
characterization  phase  if  ground-water  flow  and
contaminant transport are to be  well described. This
parameter-based  approach  is  expanded by  using
computer codes that mathematically accommodate the
dominant flow and transport   processes.    These
processes could include flow and transport through
fractures,   density-driven flow,  matrix  diffusion,
fingering,  surface-water/ground-water  interactions,
and  geochemical  reactions.   If  active, each of these
processes can invalidate the output of models  based on
the assumption that uniform flow and transport  are
occurring through a homogeneous porous media.
Even at  this stage, all  of the geochemical reactions
that  affect  radionuclide  transport are likely to be
lumped together into a single parameter, termed the
distribution coefficient.  However, a better delineation
of any  geochemical  facies  would allow  for  the
distribution coefficient to vary from layer to layer as
well as within the units themselves.  If this simplified
means of simulating geochemical processes is found to
be   inadequate,   it  may  be   necessary  to   use
thermodynamically based geochemical models in order
to address specific geochemical  reactions.

Movement  through  the  unsaturated   zone can be
simulated in a number of different ways, depending
upon the objectives.   If the  unsaturated  zone is
relatively thin  and travel times  are short, simplified
versions of more  complex  equations  describing the
unsaturated flow and transport may suffice. However,
if the travel time through the unsaturated zone is
significant and accurate flow and transport predictions
are  required,  then  mathematical  methods,  which
account  for complex processes  associated with flow
and  transport through the unsaturated  zone, may be
necessary.

The  modeling objectives  need to be defined prior to
the characterization; only then can the modeler be sure
that  data are sufficient to perform modeling at the
necessary  level  of  complexity.    All  too  often,
limitations  in  the  data,  rather than   the  modeling
objectives, drive the sophistication of the modeling.

System Heterogeneity

One   of  the   primary   objectives   of  the   site
characterization program is to identify heterogeneity
within the system and to delineate zones of varying
hydraulic properties.  System heterogeneity is one of
the leading causes of  a  poor understanding  of the
physical system controlling flow and transport.

If an accurate  simulation of  heterogeneous rocks is
required to meet the modeling objectives, a modeling
approach which allows for zones with different porous
rock properties is  required; however,   relatively few
codes can simulate discrete features,  such as  faults,
fractures, solution features,  or macropores.
                                                     3-8

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3.3  Remedial Design and Implementation

As  the site  investigation proceeds  into the remedial
phase, data  are  acquired  that  will be  useful in
identifying  feasible   remedial  alternatives.     In
combination with models,  these  data  are  used to
simulate   flow and  transport.   By predicting the
behavior of ground-water flow and the transport of
radionuclides the data and models in the selection and
design of the remedy and can be used to demonstrate
that the  chosen  remedy will  achieve  the  remedial
goals.

Once remedial action alternatives have been identified,
their design may be refined as part of the development
of a conceptual design.  Optimizing a design involves
evaluating alternative screen depths, pumping rates,
and well locations  to identify  the most  effective
configuration.

Numerous studies have demonstrated the benefits of
using models to evaluate the flow of ground water and
the transport of radioactive substances.  Models have
been used in the detailed analysis of alternative actions
to identify actions that would be ineffective or would
fail  to  meet  the site's  remediation  goals.    The
quantitative measures  of performance  derived  from
simulation provide a useful basis for comparison with
other factors  like  the  costs of  remedial  action.
However, if the  travel time  through the unsaturated
zone is significant and accurate predictions of flow and
transport  are  required,  then mathematical  methods
may be necessary to account  for the complexity of
flow and transport through the unsaturated zone.

The modeling objectives  associated with  remedial
alternative design generally are more ambitious than
those associated with the site characterization phase.
Therefore, it  often is necessary either to  select an
advanced computer  code or to modify the existing
model to simulate the more complex conditions.  The
following are specific examples of processes that may
not be important to assessing baseline risk or to site
characterization but are often essential to the remedial
design:

   • three-dimensional flow and transport

   • matrix diffusion (pump-and-treat)

   • desaturation and  resaturation  of the  aquifer
     (pump-and-treat)
   •  heat-energy    transfer
     vitrification/freezing)
(in-situ
   •  sharp contrasts in hydraulic conductivity (barrier
     walls)

   •  multiple aquifers (barrier walls)

   •  movement  from   confined  to   unconfined
     conditions (pump-and-treat)

   •  simulation of complex flow conditions (pumping
     wells, trenches,  injection wells)

From a modeling standpoint, the remedial design and
implementation is the most challenging phase of the
investigation.  Frequently, it is the first time that data
are sufficient to verify the model' s predictions.   The
many potential remedial actions (e.g., pump and treat)
provide  excellent  information   on  the  temporal
response  of  the  flow and  transport  to hydraulic
stresses.   These data  allow continuous refinement to
the  calibration,  making the  model  a  powerful
management  tool.

The  modeling  approaches  taken  at various  sites
generally would have the  following  characteristics of
the conceptual model  in common:

   •  Transient Flow and  Transport
   •  Multi-Dimensionality
   •  Prescribed  Boundary and Non-uniform Initial
     Conditions
   •  Specialized  Flow and Transport Processes
   •  System  Heterogeneity

Transient Solutions

By the time of the remedial design phase, the available
data usually span  a relatively long period,  which often
allows the temporal  nature  of  the  hydrogeologic
system to be well defined.  The objectives of remedial
design can involve many criteria that could not be met
during the site characterization phase.  Many of these
additional criteria may require that the code simulate
transient  flow  and transport  which is necessary to
evaluate  the  effectiveness of remedial  alternatives.
One such alternative  is the placing of earthen covers
and  a  broad range  of natural and synthetic barriers,
which are  engineered  to  cap  the  surface   and
subsurface soil.  The cover prevents rainwater from
percolating through contaminated soil and carrying
                                                     3-9

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radionuclides
to the ground water.   In the  site characterization
program, the objectives could probably have been met
by  assuming  a  constant  areal  recharge  over  the
modeled area.  However,  this steady-state  approach
would not account for varying recharge rates, which
would be needed to  simulate the deterioration of the
cap and the subsequent effect on the leaching rates of
radionuclides.

Excavation of radioactively contaminated  soil  will
leave some residual radioactivity in the soil contiguous
to the removal operations.  It also  could  redistribute
contaminants in the  unsaturated zone.  Without the
ability to perform  transient  simulations,  with  the
source now largely removed, it would not be possible
to determine how long it would take for the remedial
actions to have a noticeable effect on downgradient
receptors.

Multi-Dim ensionality

The  need  to  perform three-dimensional  modeling
during the remedial  phase will largely depend on the
remedial alternatives being considered and how their
effectiveness will be evaluated.

The  remedial alternatives that are most commonly
supported  by  three-dimensional  and  quasi-three-
dimensional modeling  are those that impart a strong
artificial stress to the hydraulic  flow  field, such as
pumping wells and extraction trenches. Often, before
these  stresses  are  imposed,  vertical ground-water
gradients are up to several orders  of magnitude  less
than the  horizontal gradients  and,  therefore, can be
ignored;  this simplification allows the system to be
modeled  using a  one-  or  two-dimensional  flow
analysis.     However,   when   imposed   stresses
significantly alter on the  hydraulic gradients, three-
dimensional flow fields generally develop.  Without
the ability to simulate a three-dimensional flow field,
it would be very  difficult to determine capture zones
and   influent   contaminant  concentrations largely
because vertical leakage from units above and below
the  screened interval of the extraction well  would be
ignored, as would vertical concentration gradients.

Another  remedial alternative that  generally creates
three-dimensional flow fields is installation of physical
barriers to ground-water flow. Whether  the barriers
consist of grout injection techniques, sheet pile cutoff
walls,  or bentonite slurry walls,  all have a common
problem:   the  hydraulic head builds up behind the
structures  and  induces vertical  gradients,  allowing
ground water to  flow under the barriers.  In these
cases,  the analysis  of vertical  flow  component is
essential in determining probable leakage rates and the
volume of water  that would potentially flow beneath
the structure.

Transient  Boundary   and   Non-Uniform   Initial
Conditions

Most of the analysis up until the remedial phase can be
modeled with steady-state boundary conditions; i.e.,
physical features, such  as  the water  elevations of
surface water  bodies  and  areal recharge,  can  be
simulated with  values that are constant  in time.   The
objectives  of the remedial  phase, however,  may
demand that the  transiency  of these boundaries be
considered in the analysis. Time-weighted averages
may no longer apply.  For  instance,  water bodies,
such as radioactively contaminated waste lagoons,
probably  would   have  been  treated   as  constant
boundaries, and their water-surface elevations would
have been held constant.  However,  if one  of the
remedial activities involved withdrawing contaminated
water from one or more of the lagoons, the effect that
the change in water-surface elevations would have on
the ground-water  gradients could be evaluated only by
simulating the  drop  in surface elevations with time.
This would be  simulated by prescribing progressive
changes in the lagoon water level over time.

The ability to prescribe boundaries within the model
domain also  would be important in the evaluation of
in-situ  soil flushing techniques,  which are used to
enhance the  mobility  of  contaminants  migrating
towards recovery points. In this case, recharge would
be  varied  with time to reproduce the effects  that
various rates of flushing would have on the ground-
water flow and transport of contaminants.

Protective  barriers   to   ground-water  flow  are
constructed of very low permeability material  and
emplaced either to prevent contaminated ground-water
from migrating away from a site or to divert incoming
clean  ground  water  away  from the source  of
contaminants. Potentially, barriers can last for several
decades, barring  any geological disturbances, such as
tremors, ground  settling,  or significant changes in
hydraulic gradients.  However, if a barrier should fail,
                                                    3-10

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water  may  infiltrate  the  site,  and  contaminated
leachate may move beyond the  site.  Therefore, the
effects of failure of a barrier to ground-water flow and
transport  should be evaluated.   The failure of the
barrier can be simulated in several ways.   The  most
straightforward method is to use transient boundaries
to simulate additional flow through the barrier as well
as a reduction in the difference between water-level
elevations  in  front  of  and  behind  the  barrier.
Therefore,  the  selected  code  should  be  able  to
incorporate transient boundaries.

Specialized Flow and Transport Processes

The design and evaluation of remedial alternatives
frequently involve consideration of flow and transport
processes that probably were not  explicitly modeled
during site characterization.  These processes include
complex geochemical reactions, matrix diffusion, heat
flow, and possibly, biological reactions.

As  discussed,  few  numerical models satisfactorily
couple ground-water flow and contaminant transport
to complex  geochemical  reactions.   The complex
geochemical models are  based upon the  laws  of
thermodynamics, so they predict  the potential  for a
particular reaction to occur within a closed system.
Consequently,  it  is  important  that  the controlling
geochemical reactions  are  examined,  possibly  in
laboratory benchscale  or  field  studies.    This  is
particularly  significant   when  physical/chemical
stabilization  processes  are considered as a remedial
alternative.  In these processes,  physical or chemical
agents are added to and mixed with a waste (typically
sludge in pits,  ponds, and  lagoons), to improve the
handling  or leaching  characteristics of  the  waste
destined for land disposal.

A detailed understanding of geochemistry also can be
very useful in estimating leach rates for uranium mill
tailings which  otherwise might be  associated with
unacceptably high uncertainties.

Matrix diffusion is the process by which concentration
gradients cause contaminants either to move into or be
drawn out of low-permeability areas  where diffusion
rather  than  advection  and  dispersion  governs
contaminant  transport.  Pump-and-treat systems tend
to draw water from the more permeable units, which
may leave large volumes of contaminants stored  in the
clays and  other fine-grained materials,  which will
eventually diffuse out.  Many computer codes do not
adequately simulate this very slow process.  If matrix
diffusion is not  accounted for, the movement of the
contaminant  will  be  based solely on ground-water
velocities rather than the diffusion term.  Ground-
water velocity generally  will move the  contaminant
much more rapidly than diffusion, and clean-up times
may be dramatically underestimated.

In-situ  vitrification (ISV) of soils is a destructive
thermal treatment that converts contaminated soil and
waste  into  a  chemically  inert,  stable  glass  and
crystalline product that resembles obsidian. Predicting
the effectiveness  of  ISV  requires the modeling of
several specialized processes.   One such process
would be vapor  transport of radionuclides, such as
tritium,  which  would  be  an   important  health
consideration if the media was heated.

Microbial fixation appears to affect the transport of
radionuclides under some conditions.  Radionuclides
may be either immobilized or mobilized by organisms
or plants. Immobilization may occur if radionuclides
are incorporated in the cells of microorganisms or
plants  that are relatively  stationary.  On  the other
hand,  radionuclides  may  be  mobilized  by forming
biocolloids   with bacteria,   spores,  and  viruses.
Modeling microbial processes requires a code that, at
a bare  minimum, allows a degradation  rate to be
assigned to the contaminant(s).

System  Heterogeneity

The ability of a code to accommodate severe contrasts
in the  properties of  soils and rocks  is  particularly
important in designing and evaluating physical barriers
for protecting  ground water.    If  the  application
involves  extending   the  barrier  down  to a  low-
permeability strata to  form a seal and deter underflow
leakage, it is important that the code can incorporate
multiple stratigraphic  layers, as well as sharp contrasts
in hydraulic  conductivity. Only in this  way can the
modeler show how contaminant flow and transport
affects leakage through the barrier wall and basement
strata.
                                                    3-11

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                             CHAPTER 4 -^MODEL APPLICATION
Figure 4-1 shows the three primary sources of ground-
water contamination by radioactivity that lead to four
possible contamination scenarios: (1) placing wastes
beneath the water  table in direct  contact  with the
ground  water,  (2)  placing  wastes  above the water
table, (3) disposing of wastes in surface impoundments
and  seepage basins, and (4) recharge from surface
water bodies (steams, rivers, lakes) to  the ground
water.  Once the radioactivity  reaches  the ground
water, it may be reintroduced to the ecosystem in the
following ways:  (1)  discharge to rivers, lakes, and
other surface water bodies, (2) pumped to the surface,
(3) brought to the surface through plant transpiration
(phreatophytes),  and  (4)  transport  of vaporized
radionuclides undergoing phase transformations (e.g.,
3H, 14C, 85Kr, and222Rn).

The  complexity  of the  analysis  of  the   fate  and
transport  of radionuclides  will depend upon  the
objectives  of the  evaluation  as  well  as  on  the
availability of the necessary data.  It is important to
understand the uncertainty associated  with  the  data
used for the analysis because this uncertainty will play
a role in evaluating the results of the analysis.  As a
general rule, it is best to start with the simplest means
of evaluating  the data and progress towards  more
complex techniques.  Appendix B presents simplistic
but useful calculations that may be made for release
rates, and the fate and transport of ground water and
radionuclides.  Appendix B also gives some examples
of problems where common analytical methods, which
are less complex than numerical methods, have been
used  to   estimate  the  fate   and   transport   of
radionuclides.
Prior to scoping calculations, the appropriate release
mechanisms for the movement of radionuclides to the
ground water must be determined.  If it is relatively
certain that one or more components of the conceptual
model (e.g., unsaturated zone) is unimportant, then it
may  be  neglected.   The  physical and chemical
processes  affecting  the  fate   and  transport  of
radionuclides  at the site (e.g., fracture flow, vapor
transport) also needs to  be  determined.  An  earlier
report issued  as part of this interagency agreement
outlines   how  to  determine   what    site-related
characteristics may be important (EPA94a).

After these determinations have been made,  it must
then be decided how accurate the results need to be
and what level of analysis is appropriate to obtain the
desired results. If the physical and chemical processes
at the site  are too complex to  be  satisfactorily
predicted by simplistic data  analysis,  then experts in
the  field  should  be consulted  regarding how to
proceed.    It  is not practical to perform complex
analyses  without the use of computer programs and
considerable expert help.

The  calculational methods presented in this  chapter
and Appendix B are focused on scoping level analyses.
They have been divided  into two parts:   the release
analysis and the fate analysis.  The equations given in
the release  analysis section  are used  to  estimate
contaminant release concentrations  and  volumetric
release rates.  The fate analysis section deals with the
processes influencing radionuclide transport and how
to estimate radionuclide concentrations in the ground
water.
lie-low Winer Tiibk1
1

CVnlJiuiiiiiiiiun
t-


S'Urf;icc: Water Rndy
fLakc. River or Streams)
1
                                                        V
                                              Ground Wni
        Figure 4-1. Modes in which ground water may become contaminated
                                                    4-1

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4.1
Scoping Calculations
One of the primary goals of mathematical modeling is
to synthesize the conceptual model,  as  discussed  in
Chapter  3, into mathematical expressions,  which  in
turn are solved with  either  a hand  calculator or a
microcomputer.  However, accurate  modeling of all
aspects   of  the  conceptual  model  is  not  always
necessary; only certain components require modeling.
In practice, early modeling focuses upon assessing the
significance of  specific  parameter values and their
effects on flow  and transport, rather than modeling
specific  hydrogeologic  transport  processes.    For
instance,  it  is common during the scoping phase  to
evaluate transport as a function of a range of hydraulic
conductivities;  however,  it  is unlikely that more
complex processes, such as flow and transport through
fractures, would be considered.

This  section,  in  conjunction  with  Appendix  B,
describes methods used to calculate the volume and
concentration of radioactivity that may be expected to
reach  the ground  water  from  several  types   of
contaminant sources (Figure 4-1).  Also described are
methods for estimating transit times and concentrations
of  radionuclides.    To   impart   a   sense   of the
uncertainties inherent in the calculations, the primary
mechanisms  that affect  the  fate  and  transport  of
radionuclides  are discussed.    In particular,  it  is
important to keep in  mind that all of  the complex
geochemical reactions that  influence  radionuclide
transport generally are lumped into a single parameter
termed the distribution coefficient (Kd). Without a
basic understanding of how these processes can affect
radionuclide  transport,   even  the  most  simplistic
analysis may have fundamental flaws.  Therefore, the
geochemical processes affecting radionuclide transport
are discussed briefly in Appendix A.  In Appendix B,
a series   of screening  calculations are given with
several   examples  of   problems  illustrating  the
mathematical methods that may be used to estimate
radionuclide transit times and concentrations.

4.1.1  Release Analysis - Ground Water

When  analyzing a  radionuclide  release to  ground
water, the potential release mechanisms  should be
evaluated first.   This evaluation involves a qualitative
screening approach aimed at determining the sources
of release.  The factors  and mechanisms  that may
significantly affect the potential for release are then
analyzed;  this  may  require  more  detailed  field
investigations or numerical modeling.
Several mechanisms may release radionuclides to the
ground water either directly or indirectly, as follows:

  •   Direct discharge  (e.g.,  on-site  release  from
     treatment processes)

  •   Generation of leachate (e.g., from buried wastes,
     surface impoundments,  and absorption beds)

  •   Overland   flow   (e.g.,   from   impoundment
     overflow or failure, drum leakage)

Generation of leachate  and direct discharges are the
mechanisms  most likely  to  affect  ground  water
directly.  Overland  flow might  affect  ground water
indirectly, and is discussed in Appendix B.

Several factors affect leachate release:

  •   Physical/chemical/radiological properties of the
     radionuclides;

  •   Type  of waste form and container (e.g.,  steel
     drums, wooden or cardboard boxes, plastic bags,
     absorption beds);

  •   Length of time that the wastes have been stored
     or buried;

  •   Hydrogeologic  framework of the  system (e.g.,
     depth to water table, soil/rock properties);

  •   Quantity of wastes;

  •   Climatological   considerations   (e.g.,    pre-
     cipitation).

Information  about   the  physical,  chemical,   and
radiological properties of the radionuclides  may help
to determine the associated disposal practices, which
may,  in turn, assist  in  estimating  the potential for
release.   Furthermore,  the physical  and  chemical
properties of a particular radionuclide will dictate its
fate and transport processes.

A clear understanding of the physical  system (e.g.,
climatology,  hydrogeology)  is  necessary as a  basis
from  which to predict migration rates  and exposure
pathways.

Information about when the  wastes were disposed or
emplaced and the quantities involved is important
                                                     4-2

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when estimating concentrations of radionuclides that
could potentially reach sensitive receptors.

Ground-water   contamination   results   from
radionuclides  leaching  from  surface  or subsurface
soils; from treatment, storage, and disposal areas; and
from  the  direct   migration  of  liquid  wastes.
Radionuclides can be leached from disposal areas by
precipitation and runoff that percolates through the soil
or by direct submersion of the waste in ground water.
Unlined  lagoons  and  surface impoundments  may
introduce contaminants directly into ground water.
The  containers for radioactive materials  stored above
ground may leak and percolate to ground water.  The
potential for release from  all of these sources must be
evaluated;  any that are  significant generally undergo
a more quantitative assessment.

Estimation of release involves two quantifications:  (1)
of  radionuclide  concentrations  in  waste  and/or
leachate,  and  (2)  of the  volume  of the leachate or
direct-discharge release rates.  The procedures vary,
depending upon the characteristics of the release site.
Section B.I of Appendix  B describes procedures to
calculate  steady-state  releases of  radionuclides to
ground  water.  The calculations  focus on release
concentrations and  volumetric release  rates.   For
ponds or lagoons, the concentration of the radionuclide
in the lagoon or impoundment is considered to be the
concentration of the leachate. This assumption ignores
the geochemical reactions that may be occurring at the
base  of the pond where  sediments  may tie up high
concentrations  of  radionuclides   when   oxidizing
conditions  prevail  (summer)  and  release  pulse
concentrations  of  contaminants   when  reducing
conditions  are  favored   (winter).    Methods  for
estimating volumetric release rates are presented for
both solid  and liquid wastes.

4.1.2    Fate Analysis - Ground Water

The nature of  the ground-water environment restricts
the number of  processes that control  the fate of
radionuclides as they are transported from their source
to the receptor area.  These processes fall into two
categories: transport processes and radioactive decay.
Transport-related   processes   (i.e.,   sorption,   ion
exchange,  and precipitation of solids) can facilitate or
retard the  movement of ground-water contaminants,
but  radioactive  decay  always  results  in a loss of
activity (disintegrations or decays per  second) of the
original  radionuclide.    However,  as   the  parent
radionuclide  disintegrates, radioactive or chemically
toxic daughter products can increase.

Calculational screening  methods  do  not  directly
simulate fate processes that influence the transport of
radionuclides.    Generally,  the  effects   of these
processes on transport are combined  into a  single
term,  designated the  distribution  coefficient.   In
Appendix  A,  these   fate  processes  are   discussed
qualitatively  to  provide a general understanding of
distribution  coefficients,   which  are  later used in
Section B.2  (Appendix B) to determine quantitative
retardation factors.   Fate processes  associated with
radionuclide  transport must be explicitly  simulated,
geochemical  and/or hydrochemical computer  models
will be needed.

4.1.3    Analytical Methods  for Aquifer  Flow  and
         Transport

Analytical ground-water transport models can be used
for certain analyses where the available data do not
warrant a more complicated numerical analysis. Such
models are useful for scoping the transport problem
and may frequently be adequate for regulatory needs
if the model and corresponding input data are chosen
conservatively.

Analytical  transport  solutions  are  generally able to
simulate  only systems that assume steady-state flow
conditions.   However,  because the available data
rarely support transient simulations during the scoping
phases, common analytical methods may often be used
more effectively than numerical methods.  It is much
easier  to conduct bounding and sensitivity analyses
with   analytical  rather   than  numerical models.
Examples  of  such   calculations  are  presented  in
Appendix B.

4.1.4    Uncertainty Analysis

In the  scoping phase, the uncertainty in the analysis
should be  emphasized.   Uncertainty  is inherent in
models of  the behavior of a hydrogeologic  system
because  our  knowledge   is   incomplete.    Many
parameters used as inputs to a model are obtained by
data collection. Investigators knowledgeable about the
data they collect make a finite number of observations,
choosing the  parameters, and,  how, where,  and when
to measure them.  However, the collection process
itself  can  introduce  uncertainty  through   errors in
measurements, the system's inherent randomness, and
                                                     4-3

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limited sampling of the variable physical,  chemical,
and  biological properties  of the  system.   In  many
aspects of data collection, the professional judgment of
an analyst with expertise in the area of investigation
often enters into the scientific process. For example,
selecting methods to collect  data, interpreting data,
developing conceptual models, and selecting model' s
parameters all  require  professional  analysis and
judgment.     Therefore,  the  uncertainty   in  input
parameters used in predictive models may result from
several sources,  including incomplete data, intrinsic
spatial  variability  of  the   property  in  question,
uncertainties  in  measurement,  and  uncertainties
resulting from differences in scale between acquisition
of the data and application of the model.

In practice, much of the early modeling focuses  on
assessing the significance of the uncertainty  associated
with specific parameters and their effects on flow and
transport, rather than on modeling specific processes
of  hydrogeologic  transport.   For instance,   it  is
common during the scoping phase to evaluate transport
as a function of a range of hydraulic conductivities;
however, it is unlikely that more  complex processes,
such as flow and transport through fractures, would be
considered.

In general, the uncertainty associated with each of the
parameters is expressed by a probability distribution,
which  yields  a likely range  of  values  for  each
parameter.  It is important to select a model where
individual  parameter  values   can   be   selected
systematically from the range and  easily substituted
into  the   governing  mathematical  equations that
describe the dominant flow and transport processes at
the  site.   In this  manner,  the  effects  of a  single
parameter or  a multitude of parameters on the rate of
contaminant  movement and  concentrations may  be
evaluated. This technique of substituting one value for
another from within  a range of values is called a
sensitivity analysis.

In  many  cases, the  possible range  of  values  of
important  parameters  is  unknown  or very   large.
Consequently, the analyst has little  alternative  but to
evaluate the sensitivity of the results to a very broad
range of possible values.  Many of these early results
will be unrealistic but cannot be ruled out until reliable
site  data are  obtained.  These types of analyses are
useful because they help to direct  the  field  work.
However,  they also can be  used incorrectly.  For
example,   individuals   unfamiliar with the  scoping
process could reach grossly inappropriate conclusions
about the potential public-health impacts of the site
based on these scoping analyses.  Accordingly,  care
must be taken to assure  that the results  of scoping
analyses are used for their intended purpose.

Sensitivity analyses identify the main contributors to
the observed variation in the results. These techniques
typically are applied iteratively.  The first iteration can
include  rather   general   assumptions   leading   to
preliminary results that help focus these techniques in
subsequent iterations.  Thus,  the resources required
for the  uncertainty  reduction  techniques can  be
directed at the areas of the site characterization where
the benefits of understanding uncertainty and reducing
it (where possible) are greater.

However, sensitivity analyses alone will rarely identify
a flawed conceptual model. For example, the failure
to identify and  include a fault(s)  in the conceptual
model subsequently would not account for preferential
pathways  that   could,   potentially,  underestimate
receptor concentrations.

An alternative to the  detailed  sensitivity analysis is a
conservative   bounding  approach.    In  this  less
demanding analysis,  values  are  selected from  the
range of parameters to provide the highest probability
that  the  results  are  conservative,   i.e.,  that  the
migration rates and concentrations of the contaminant
would  not be underestimated.   For example, high
values of hydraulic conductivity combined with low
effective porosities and  distribution coefficients would
maximize  the  predicted migration rates  of  the
contaminant  although its  concentrations  at receptors
may be underestimated.

Tables 4-1 and 4-2 give preliminary  guidance  on the
general effects that various parameters have on the
modeling results. Table 4-1 indicates  whether the high
end or low end of the parameter's distribution should
be used if a  conservative estimate  (i.e., maximum
value)  of the extent of contamination is desired.  The
same concept has been used in Table 4-2 to  show the
effect  of  various  parameters  on   the  maximum
concentrations arriving at a downgradient receptor.
As shown  in  these tables,   when   estimating  the
maximum  extent of  contamination,  the dispersivity
should be maximized.   The  opposite is true  when
estimating maximum  concentrations;  in this  case
dispersivity should be minimized.
                                                     4-4

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Table 4-1. Bounding Analyses: Extent of Contamination
Parameter
Maximum
Minimum
Source Term
Constant Concentration
Mass Flux
Insensitive
Insensitive
Unsaturated Zone
Infiltration Rate
Moisture Content
Total Porosity
Bulk Density
Distribution Coefficient
High
Low
Low
Low
Low
Low
High
High
High
High
Saturated Zone
Aquifer Thickness
Gradient
Distribution Coefficient
Dispersivity
Effective Porosity
Hydraulic Conductivity
Well Location and Intake Depth
Insensitive
High
Low
High
Low
High
Shallow/Plume Centerline
Low
High
Low
High
Low
Deep/Off Plume Centerline
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               Table 4-2.  Bounding Analyses:  Concentration of Contaminants
Parameter
Source Term
Highest
Constant Concentration
Lowest
Mass Flux
Unsaturated Zone
Infiltration Rate
Moisture Content
Total Porosity
Bulk Density
Distribution Coefficient
High
Low
Low
Low
Low
Low
High
High
High
High
Saturated Zone
Aquifer Thickness
Gradient
Distribution Coefficient
Dispersivity
Effective Porosity
Hydraulic Conductivity
Well Location and Intake Depth
Thin
Low
Low
Low
Low
Low
Shallow/Plume Centerline
Thick
Low
High
High
High
High
Deep/Off Plume Centerline
4.2  Site Characterization Modeling

In  the  scoping  phase of the investigation,   data
limitations impose a simple modeling approach which
uses conservative  parameter estimates.  One  of the
primary objectives of the site characterization program
is to obtain sufficient data to enable the conservative
modeling approach to be replaced by a defensible and
more realistic  approach  which incorporates  site-
specific data.

Conservative analysis by itself cannot  meet many of
the objectives  defined for  the  site characterization
phase of the investigation.  If parameter values are not
known,  it may be necessary to make conservative
estimates; however, the effects that  a conservative
approach may have on other aspects of the remedial
program must be considered. For example, if, during
the baseline  risk assessment,  conservatively  high
hydraulic  conductivities are used in order to ensure
that the downgradient contaminant  arrival times are
not underestimated, several problems  may occur.
First,  it would be difficult to calibrate the model to
known parameters (e.g., potentiometric surface), and
adjustments to other parameters would be required in
order  to match measured field values. The end result
would be a  model  that poorly  predicts  system
responses to hydraulic stresses (e.g.,  extraction wells).
A   second  problem  would  involve  contaminant
concentrations. A conservative increase in hydraulic
conductivity would predict more ground-water flow
through the system than is actually  occurring,  which
might result in an underestimate of the contaminant
concentrations  at downgradient receptors.   More
problems may arise during the remedial design. If the
modeling  results are used  to estimate clean-up  times,
the model may predict that water and contaminants are
flowing faster  than they  actually are and at lower
                                                    4-6

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concentrations. This would result in an underestimate
of both the amount of time required for remediation as
well as the contaminant breakthrough concentrations.

The  major  impact that  a more specific conceptual
model of the site will have on model application is that
now  parameter  ranges  have  been  narrowed  by
additional data acquisition, and sensitivity analyses can
become more focused.  Refinement of the parameter
values diminishes  the  need to perform  so  many
sensitivity analyses.  In view of the increased demand
for  more accurate simulation of the controlling flow
and  transport processes,  the advantages of scoping
type  analyses are outweighed  by their  inability to
simulate more complex conditions.  Therefore,  model
application  in the site  characterization  phase  will
generally be performed with numerical models.

After the  conceptual model is  formulated and  the
modeling objectives are clearly defined in terms of the
available data, the investigator should have a good
idea of the level of sophistication that the anticipated
modeling will require.  Now, one or more  computer
code(s)  can  be  chosen  that  have  the  attributes
necessary to describe mathematically the conceptual
model at the desired level of detail.  Selecting the code
requires a detailed analysis of the conceptual model to
determine the degree to which specific waste and site
characteristics need to  be explicitly modeled.   The
selection process and evaluation criteria are  described
in a joint agency publication (EPA  94).

During the site characterization phase, application of
the model is generally quite sophisticated and typically
experienced modelers are  in charge of the  modeling
process.

Therefore, this section will not describe the modeling
process step-by-step,  but,  rather, will  provide  the
Remediation  Manager  and  support  personnel with
sufficient information to allow  the remedial team to
make   informed   decisions  about   ground-water
modeling.

Accordingly,  this section has three goals:

  1. to impart a general understanding of how ground-
     water  modeling   is  carried  out  in  the  site
     characterization phase  and what objectives  are
     achievable.
  2. to outline the topics that should be covered in the
     application  report  and how results  should be
     presented to facilitate peer review.

  3. to provide relatively simple methods that can be
     used as reality checks on modeling performed by
     others.

This section is organized into subsections that follow
a path typical of model application strategies.  Specific
guidance for each subsection is tabulated in Table 5-1.

4.2.1   Code Selection

After formulating the conceptual model, it is necessary
to select one or more computer  code(s).  Three basic
choices are available:  analytical, semi-analytical, or
numerical  codes.   Analytical  and   semi-analytical
methods,   which   are   limited   to    simplified
representations of the physical  setting and flow and
transport processes, are ideally suited  for performing
sensitivity and conservative bounding analyses because
they are  computationally efficient (i.e.,  fast)  and
require relatively little data  as input.  As discussed in
Section 4.1.3, analytical models  are typically designed
for easy  performance of sensitivity analyses.   In
contrast, numerical methods do not lend themselves to
the same kind of  "simplified" applications.  Primarily
because numerical models are difficult to  set up and
require substantial data input to  calibrate the model,
and multiple parameter substitutions are generally very
cumbersome.  However, as the modeling objectives
become more complex and can no longer be addressed
by simple bounding and sensitivity analyses, additional
field data  and  more  sophisticated  analysis  methods
(e.g., numerical  models) become necessary.

The  greatest  difficulty   in   selecting  the  most
appropriate computer code is not in determining which
codes have specific  capabilities, but rather, which
capabilities are required to support remedial decision-
making during each  phase of the  remediation  at a
specific site.  The necessary degree of sophistication
of the modeling can be evaluated in terms of both  site-
related issues and objectives, as well  as the  qualities
inherent  in the  computational  methods for  solving
ground-water flow and transport equations.
A contaminant fate and transport model results from
the  application  of a  previously written  or  new
                                                     4-7

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computer code to a specific problem via the collection
of  input  data  and  the  parameterization  of  site
characteristics.  The resultant model is, therefore, a
merger  of a  mathematical  formulation,   solution
methodology,  data, and ancillary information  which
enhances or controls the use of the model. In addition
to selection criteria for the modeling objectives  which
were presented in the  previous section, the  code
evaluation  process must also consider attributes that
are  integral components  of the computer code(s)
including;

  •  Source Code Availability
  •  History of Use
  •  Code Documentation
  •  Code Testing
  •  Hardware Requirements

The development of selection criteria presented  in this
section takes  an  approach consistent with  industry
standards by relying on published reports pertaining to
the  quality assurance  and  quality  control in the
development and application of computer codes.

Source Code Availability

To facilitate a thorough review of the generic code,
detailed  documentation   of  the   code  and   its
developmental history is required. Also, the source
code must be available for inspection.  In addition, to
ensure independent evaluation of the reproducibility of
the verification  and validation  results,  the computer
source code as  well as the compiled version  of the
code (i.e., computer code in machine language) should
be  available to  the  reviewer,  together with files
containing  the  original test data used  in the code's
verification and validation.

History of Use

Much of the information needed for a thorough code
evaluation  can  be  obtained  from  the author  or
distributor  of the code.  In fact, inability to obtain the
necessary publications may indicate that the code is
either  not  well  documented or that  the  code  is not
widely used. In either case, the inaccessibility  of the
documentation and related  publications should be
strong  grounds  for  deciding  that  the   code  is
unacceptable.

The  acceptance and evaluation process should rely on
user opinions and published information in addition to
hands-on experience and testing.  User opinions are
especially valuable in  determining whether the code
functions as documented or has significant  errors or
shortcomings.  In some instances, users independent
of the developer have performed extensive testing and
bench-marking or are  familiar with published papers
documenting the use of the code. Users will also have
first-hand knowledge about how easy it is to use the
code and what level of experience is required.

Quality Assurance

Code  selection should be closely  tied to  the quality
assurance criteria followed during the development of
the  computer code.  These  criteria will determine the
adequacy of the code testing and documentation.

Quality assurance in modeling is the procedural and
operational framework put in place by the organization
managing the modeling  study,  to assure technically
and scientifically  adequate execution of all project
tasks  included  in the  study,  and to assure that  all
modeling-based analysis is verifiable  and defensible
(TAY85).

The two  major elements  of quality assurance are
quality control and quality assessment. Quality control
refers to the procedures that ensure the quality of the
final product.   These  procedures  include the use of
appropriate methodology in developing and applying
computer  simulation codes, adequate verification and
validation procedures, and proper usage of the selected
methods and codes (HEI92).  To monitor the quality
control procedures and to evaluate the quality  of the
studies, quality assessment is applied (HEI89).

Software  quality  assurance  (SQA)  consists  of the
application  of  procedures,  techniques,   and  tools
through the software  life  cycle,  to  ensure that the
products  conform  to  pre-specified  requirements
(BRY87). This requires that in the initial stage of the
software  development  project,  appropriate   SQA
procedures (e.g.,  auditing, design  inspection,  code
inspection, error-prone  analysis,  functional testing,
logical testing, path testing, reviewing, walk-through),
and tools  (e.g.,  text-editors,   software  debuggers,
source code comparitors, language processors) need to
be  identified  and  the software  design  criteria  be
determined (HEI92).
                                                     4-8

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Quality  assurance   for   code  development   and
maintenance implies a systematic approach,  starting
with the careful formulation of code design objectives,
criteria, and standards, followed by an implementation
strategy.  The  implementation strategy includes the
design of the code structure and  a description of the
way in which software engineering principles  will be
applied to the code.  In this planning stage, measures
are to be taken to ensure complete documentation of
code design and implementation, record keeping of the
coding  process,  description  of the  purpose  and
structure   of  each  code    segment   (functions,
subroutines),  and   record  keeping   of  the  code
verification process.

Records for the coding and verification process may
include:  a description of the fundamental algorithms
describing  the physical process(es) which are to be
modeled;  the  means  by  which the mathematical
algorithms have been translated  into  computer  code
(e.g.,  Fortran); results  of  discrete  checks  on the
subroutines for accuracy;  and comparisons between
the codes' numerical solutions and analytical or other
independently verified numerical solutions.

Code verification or testing ensures that the underlying
mathematical algorithms have been correctly translated
into computer code.  The verification process varies
for different codes and ranges  from simply checking
the results  of  a  plotting  routine to  comparing the
results of  the  computer  code to known  analytical
solutions or to results from other verified codes.

Traceability  describes the ability of the computer
analyst to  identify  the software  which was used to
perform a particular calculation,  including its name,
date, and version number, while retrievability refers
to the availability of the same version of the software
for further use.

Code Documentation

Detailed   guidelines   for   the  preparation   of
comprehensive software  documentation are given by
the Federal Computer Performance Evaluation and
Simulation Center  (FEDSIM81).  This  publication
discusses the structure recommended for four types of
manuals providing model information for managers,
users,  analysts, and programmers.   According to
FEDSIM81,  the manager's summary manual should
contain a  model  description,  model  development
history, an experimentation report, and a discussion of
current and future applications.   Currently, ASTM
(American Society  for  Testing  and Materials) is
developing a standard ground-water code description
for this specific purpose (HEI92).

As discussed  in van der  Heijde  (HEI92),  the  code
documentation should include a  description of the
theoretical framework  represented by  the generic
model on which the code is based, code structure and
language standards applied, and code use instructions
regarding model setup and code execution parameters.
The  documentation  should also include a  complete
treatment of the equations  on which the generic model
is  based, the underlying mathematical and conceptual
assumptions,  the  boundary   conditions   that  are
incorporated in the model, the method and algorithms
used to solve the equations, and the limiting conditions
resulting   from   the   chosen  approach.      The
documentation should also include user's instructions
for  implementing  and  operating  the  code,   and
preparing data files.  It should present examples of
model formulation (e. g.,  grid  design, assignment of
boundary conditions), complete with input and output
file  descriptions,  and  include an  extensive  code
verification and  validation  or field testing report.
Finally, programmer-oriented  documentation should
provide  instructions  for  code   modification   and
maintenance.

An integral part of the code development process is
the preparation of the code  documentation.   This
documentation of QA in model development consists
of reports and files pertaining  to the development of
the model and should include (HEI92):

  •  A report on  the  development of  the  code
     including the  (standardized  and  approved)
     programmer's   bound    notebook   containing
     detailed  descriptions  of  the  code verification
     process;

  •  Verification   report   including   verification
     scenarios, parameter values, boundary and initial
     conditions,  source-term   conditions,   dominant
     flow and transport processes;

  •  Orientation   and   spacing  of  the  grid   and
     justification;

  •  Time-stepping scheme and justification;
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  •   Changes and documentation of changes made in
     code after baselining;

  •   Executable and source code version of baselined
     code;

  •   Input and output (numerical and graphical) for
     each verification run;

  •   Notebook  containing reference  material  (e.g.,
     published  papers,   laboratory   results,
     programmer's  rationale) used to formulate the
     verification problem.

Furthermore, the software should be documented in
sufficient detail to (GAS79):

  •   record technical information that enables system
     and program changes to be  made  quickly  and
     effectively;

  •   enable programmers and system analysts,  other
     than software originators, to use  and to work on
     the programs;

  •   assist the user in understanding what the program
     is about and what it can do;

  •   increase program sharing potential;

  •   facilitate  auditing and verification  of program
     operations;

  •   provide managers with information  to review at
     significant developmental milestones so that they
     may   independently  determine  that  project
     requirements have been met  and that resources
     should continue to be expended;

  •   reduce disruptive effects of personnel turnover;

  •   facilitate   understanding   among   managers,
     developers, programmers, operators,  and  users
     by providing  information  about maintenance,
     training, and changes in and operation of the
     software;

  •   inform other potential users of the functions  and
     capabilities of the software,  so  that they  can
     determine  whether it serves their needs.
The user's manual should,  at a minimum, consist of:

  •   an extended code description;
  •   code input data description and format;
  •   type of output data provided;
  •   code execution preparation instructions;
  •   sample model runs;
  •   trouble shooting guide; and
  •   contact person/affiliated office.

The  programmer' s manual should, at a minimum,
include;

  •   code specifications;
  •   code description;
  •   flow charts;
  •   descriptions of routines;
  •   data base description;
  •   source listing;
  •   error messages;  and
  •   contact person/affiliated office.

The analyst's manual should, at a minimum, present:

  •   a functional description of the code;
  •   code input and output data;
  •   code verification and validation information; and
  •   contact person/affiliated office.

The code itself should be well structured and internally
well  documented;  where  possible, self-explanatory
parameter, variable,  subroutine, and function names
should be used.

Code Testing

Before a code can be  used as a planning and decision-
making  tool,  its  credentials  must be  established
through  systematic testing of the code's  correctness
and   evaluation   of   the   code's   performance
characteristics (HEI89).  Of the two major approaches
available,  the  evaluation or   review   process  is
qualitative in nature, while code testing results can be
expressed using  quantitative performance measures.

Code  testing  (or  code  verification)  is aimed at
detecting programming  errors,  testing embedded
algorithms,   and   evaluating   the    operational
characteristics of the code through its execution on
carefully selected example test problems and test data
sets.  ASTM84 defines verification as the examination
                                                    4-10

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of the  numerical technique in the computer code to
ascertain that it truly represents the conceptual model,
and that there are no inherent problems that prevent
correct solutions.

At this point, it is necessary to point out the distinction
between  generic  simulation  codes  based  on  an
analytical  solution  of  the governing  equation(s)
(Appendix C)  and codes  that  include  a numerical
solution.  Verification of a  coded analytical solution is
restricted to comparison with independently calculated
results using the same mathematical expression, i.e.,
manual calculations, using the results from computer
programs   coded   independently   by   third-party
programmers.  Verification of a code formulated with
numerical methods  might take  two  forms:   (1)
comparison with analytical solutions, and (2)  code
intercomparison between  numerically based codes,
representing the same generic simulation model, using
synthetic data sets.

It is important to distinguish between code testing and
model  testing.  Code testing is  limited to  establishing
the correctness of the computer code with respect to
the criteria and requirements for which it is designed
(e.g., to represent the mathematical model).  Model
testing  (or model validation) is more inclusive than
code  testing,  as  it represents the  final  step  in
determining   the   validity  of   the   quantitative
relationships derived for the  real-world system the
model  is designed to simulate.

Attempts  to validate models must address the issue of
spatial and temporal variability when comparing model
predictions  with  limited  field observations.     If
sufficient  field  data  are  obtained  to  derive  the
probability distribution of contaminant concentrations,
the results of a stochastic model  can be compared
directly.  For  a  deterministic  model, however, the
traditional approach has been to vary the input data
within  its  expected range of variability (or uncertainty)
and determine whether the  model results satisfactorily
match  historical field measured values.  This code-
testing  exercise is  sometimes referred to as history
matching.

Konikow and Bredehoeft (KON92) argue compellingly
that computer models cannot be truly validated but can
only  be  invalidated.    As reported  by  Hawking
(HAW88), any physical theory is only provisional,  in
the sense  that it is only a hypothesis that can never be
proven.  No matter how many times the results of the
experiments  agree  with some theory, there is never
complete certainty that the next test will not contradict
the theory.   On the  other  hand, a  theory  can be
disproven  by finding even  a single observation that
disagrees with the predictions of the theory.

From  a  philosophical perspective,  it is difficult to
develop  selection  criteria  for a  model validation
process which may  be intrinsically flawed. However,
the average strategy presented in this chapter provides
some assurance that the code selected has the highest
probability  of  most   accurately  representing  the
conceptual model.

Hardware  Requirements

In general, hardware requirements should rarely be  a
discriminatory factor in the selection of a  computer
code.   However,   a number  of  the  available codes
require  very sophisticated  hardware,  not  so much
because  of the intrinsic requirements of the code but
because  the simulated processes may be very complex
and  require  time-consuming  solution  methods.
Therefore, hardware requirements should be clearly
identified for the code itself and be consistent with the
hardware available to the user.

An earlier report prepared by this interagency working
group  details the  conditions  under which specific
features  and  capabilities  of the model are needed to
support remedial decision-making (EPA94).

A  final consideration,  true  for  all  phases of the
project,  is the need to select  codes that have been
accepted by  technical  experts  and  used  within  a
regulatory context.

4.2.2    Model Construction

One primary goal  of mathematical  modeling  is to
synthesize  the conceptual model into numerical terms
from  which  flow  and  transport processes may be
investigated under specified conditions. This process
entails several discrete  steps:   (1) partitioning the
conceptual model into  units of time and space;  (2)
assignment  of  boundary   conditions;   and   (3)
specification   of the values  of  parameters.    The
following sections  discuss the relevance of each of
these topics to the modeling process. Then guidelines
for modeling and, where appropriate, modeling review
                                                    4-11

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criteria are suggested.

4.2.2.1 Layering and  Gridding

In  a  numerical  model  the  region  of  interest  is
partitioned into a series  of blocks (i.e., elements)
which are arranged in layers  (Figures 4-2 and 4-3).
This  practice,   termed  discretization,  effectively
replaces the continuous problem domain with an array
of blocks  and nodes.  The basic  concept used is to
divide up  the  section  as realistically as practical.
When possible,  geologic  logs and other information
typically are  used to identify  geologic unit contacts.
Information  on formational dip,   depositional,  and
erosional features may have a pronounced effect on
unit contact elevations and, therefore,  will also have
a  significant impact   on  ground-water  flow  and
contaminant transport.  To accommodate variations in
unit thickness,  some finite element models allow the
use of curvilinear elements  to allow the model' s
planes to trace the unit contacts more precisely.

The determination of how many layers  to include
depends  on  both  the conceptual  model and the
objectives of  modeling.  Typically, multiple layers are
used  to   accommodate  the  vertical  variation of
hydrologic parameters that represent the hydrogeo logic
units  within the modeled region.

One of the critical steps  in applying a ground-water
model is  selecting the size of the nodal spacing.  The
more finely the grid is spaced, the more accurate the
numerical solution. However, the desire for accuracy
must be balanced against the impracticality of solving
for large numbers of nodes and the long computer run
times that may be involved.

The most quantitative guidance for selecting the nodal
spacing applies only to modeling contaminant transport
not to ground-water flow modeling.  These criteria are
related  to   the  fact  that  the value  of  dispersion
coefficients (Section 2.4) varies with  the  absolute
value of the Darcy velocity (Section B.3).

This  relationship,  as expressed below,  defines  a
dimensionless Pec let number.
                     p =
                           D
where:
  Pe =  Peclet Number
  V  =  Darcy Velocity
  D  =  Dispersivity

The  numerical  solution  of the transport equation
becomes unstable if the  Peclet number becomes too
large.   Price et  al  (PRI66) have shown that the
stability of the  transport solution  is  ensured if the
Peclet number is less than 2.
                              Figure 4-2.  Three-dimensional view of model grid.
                                                    4-12

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       Rawer
                                                                                              Uytr 3
                                                                                        Lr:
                               Figure 4-3.  Cross-sectional view of model grid.
4.2.2.2 Definition of Boundary and Initial Conditions

To obtain a unique solution for the governing equation
of ground-water flow  and  contaminant transport,
additional information is required about the physical
state of the ground-water system.  This information is
described   by   boundary  and   initial  conditions.
Boundary  conditions are the  conditions the modeler
specifies as known values to solve for the unknowns in
the  problem; these values may be associated with
either ground-water flow or contaminant transport.

One   of   the   primary  objectives   of  the  site
characterization program  is to  identify the presence
and location of ground-water flow and contaminant
source boundaries so that they  may be incorporated
into  the  conceptual model.    These  boundaries
generally  are quantified in terms  of the volume  of
ground water and contamination moving through the
system. The physical boundaries are then translated
into mathematical terms,  as input into  the  computer
model.  The initial conditions are simply the values of
hydraulic  head  or contaminant concentrations at a
reference initial time. For steady-state problems, only
boundary   conditions  are required,   whereas  for
transient problems, both conditions are required.

Ground-Water Flow

Boundary  Conditions

Ground-water boundaries may be described in terms
of where water is flowing into and out of the ground-
water system.   There  are many different types  of
boundaries, including:  surface-water bodies, ground-
water divides, rainfall, wells,  and geologic features,
such as faults and sharp contrasts in lithology.

In  general,  boundary conditions  are  known  or
estimated values  that  are assigned  to surfaces and
planes that either frame the perimeter of the modeled
area  or  define the  release  from  the  contaminant
source.   The  different  types   of  flow  boundary
conditions  are:  (a) head (ground-water elevation) is
known for surfaces or planes  bounding the modeled
region; (b) ground-water flow volumes are known for
surfaces  or planes bounding the modeled region; and
(c)  some combination of (a)  and (b) is known  for
surfaces  or planes bounding the region.   Boundary
conditions could also be assigned to  interior features
of the modeled region where ground  water elevations
or flow volumes are known, such as  lakes,  rivers, or
marshes.  In practice, these types of boundaries result
in three conditions including:  (1) specified value of
hydraulic head;  (2)  specified flux;  and,  (3) head-
dependent flux. Table 4-3 briefly describes the three
boundaries and their examples.

Just as the physical ground-water system is idealized
as  a  continuum  in  deriving   the  mass balance
differential equations, it also is expedient to idealize
the  conditions on the boundaries of the system so that
they  too  can be  approximated  by  a  mathematical
expression.   In nature, the boundary  conditions of
ground-water systems are of several kinds. One of the
most  common would be at a well.  Since the porous
medium  terminates at  the well face, the aquifer not
only  has a boundary  around  its perimeter, but  the
outline of each well also is considered a
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              Table 4-3.  Boundary Conditions of Ground-Water Flow Equations
                 Type
                     Description and Examples
  I.  Specified head
Value of hydraulic head is specified along the boundary.  Typical
examples include:  (1) constant head condition on the boundary in
direct hydraulic contact with a river or lake or spring outlets; and (2)
boundary condition at a pumped well operating at constant or specified
drawdown.
  II.  Specified flux
Flux or flow rate of water is specified along the boundary.  The flux is
usually expressed as qn =  -K 3h/3n, where n refers to the direction
perpendicular to the boundary.  Typical examples include:  (1)
condition of zero flow across impermeable rock boundaries or across a
water divide or a streamline; and (2) boundary  condition on the water
table receiving prescribed rate of accretion.
  III. Head-dependent flux
Flux or flow rate of water is dependent on the head difference across a
semi-impervious layer adjacent to the aquifer. This boundary
condition is encountered when the flow domain is intercepted by a
river bed clogged by a thin layer of silt or clay.  The leakage flux is
given by qn =  K/b (h-H) where K is the hydraulic conductivity, b is
the thickness of the thin layer, and (h-H) is the pressure difference
across the layer.  A similar situation is encountered when the aquifer
is  overlain by  a water table aquitard layer.
boundary to the aquifer.  The boundary conditions at
wells may  also be treated as a  constant or variable
specified flux, or constant head,  depending on which
best  describes the physical conditions.

Impermeable or nearly impermeable boundaries  are
formed by  underlying  or overlying beds of rock, by
contiguous  rock masses (as along a fault or along the
wall of a buried rock valley), or by dikes or similar
structures.   Permeable boundaries are  formed at the
bottom of rivers, canals,  lakes,  and other bodies of
surface water.  These  permeable boundaries  may be
treated as  surfaces of equal head (specified) if the
volume of  surface water is  large, so that its  level is
uniform and independent of changes in ground water
flow.  However,  the uniform head on  a boundary of
this  type  may change with time due  to  seasonal
variation in the surface-water level.  Other bodies of
surface water, such as  streams, may form boundaries
with non-uniform distributions of head which may be
either constant or variable with time. For example, a
small stream might be affected by a nearby withdrawal
of ground water if that withdrawal occurred at a rate
similar to the flow in the stream.  Then, the boundary
condition would depend on the ground-water flow; that
is, it would be a head-dependent flux.
                   In an analysis of ground-water flow, it is common to
                   assume a  simple  geometry  for sinks and  sources
                   existing at the boundary, or inside the flow system.  In
                   areal flow  simulations,   points often  are  used  to
                   represent individual wells, whereas lines are used to
                   represent  rivers,  lakes,   and   other  surface-water
                   bodies.  These representations are justified, provided
                   that  detailed information about potentiometric head
                   and velocity distributions in the immediate vicinity of
                   the individual sources or sinks  is not  a concern.  If
                   such information is required, then the actual geometric
                   features of the source or sink  must be incorporated
                   into  the flow system.  For instance, if the modeler is
                   using flow analysis to assess the performance (e.g.,
                   specific capacity or  maximum yield)  of a pumping
                   well or evaluate its drawdown versus  time data,  then
                   the well must be represented as a cylindrical boundary
                   of specified diameter and specified screened length.

                   Other assumptions related to sinks and sources are
                   variations of volumetric  flow rates of flux (flow rate
                   per unit length) distributions.  For  a point source or
                   sink, it is  common to assume a constant  flow  rate
                   unless the  field  data  indicate drastic  variations
                   necessitating a more accurate treatment.  For a line
                   source or sink, uniform flux distribution along the line
                                                   4-14

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also is assumed to  simplify the analysis.  Again,  the
justification of this assumption depends on actual field
conditions.

Initial Conditions

Initial conditions are defined as values of ground-water
elevation which are initially assigned to interior areas
of the modeled regions.   The  initial conditions  for
steady-state flow models are generally set to uniform
values because the temporal nature of the flow system
is not simulated. The initial conditions assigned  to the
model domain are irrelevant as identical solutions will
be reached regardless of the values initially assigned.
This occurs because these  steady-state values depend
solely on the values assigned to the boundaries of the
model.

The initial and boundary conditions  for the variably
saturated water flow equation  can  be stated in  the
same manner as those for the saturated ground-water
flow  equation.  The solution of the  former problem
enables the analyst to obtain the head distribution, as
well  as the  water  saturation  (or  water  content)
distribution, and details of the velocities and flow rates
for an analysis  of the migration  of  contaminants in
variably saturated porous media.

Initial conditions for a  transient flow model may be
interpolated from water-level data or may be set from
a previous steady-state  flow simulation. Ideally,  the
initial  heads  should  come  from   a  steady-state
simulation.  Interpolated initial conditions are  often
not consistent with the model boundary conditions  and
parameterization.  In this case, heads computed during
early time  steps are inaccurate.

Contaminant Source

Boundary Conditions

The most  common contaminant source boundaries
either specify the source concentration or prescribe the
mass flux of contamination entering the system.  The
former generally is prescribed when the release rate is
largely controlled  by  the solubility limits of  the
contaminant.  The mass-flux type boundary  typically
is used when a leaching rate  is known or estimated.
Specialized  source  boundaries  also  have  been
formulated which allow for radioactively decay in the
source.  The ability of the code to treat source decay
may not be important if the parents and daughters have
a relatively long half-life compared  to the expected
time to travel to the nearest receptor.

Contaminant transport  should  not be analyzed until
after the ground-water flow model has been calibrated
(Section 4.2.3).  As previously mentioned in assigning
initial and boundary conditions to problems of ground-
water flow,  the solution of a  contaminant transport
problem is not unique unless the initial and boundary
conditions associated with the governing transport
equation   are   given.      Generally,  the   initial
concentration is specified for each node in the flow
domain at some initial time, t= 0.  This results in a
concentration distribution that  forms  the basis of the
initial conditions.   In addition, boundary conditions
must also  be specified at all times.  Three types of
boundary  conditions  are commonly encountered in
practice:  (1) specified value of  concentration; (2) zero
normal concentration gradient;  and (3) specified mass
flux of solute.  Table 4-4 briefly  describes the three
boundary  conditions and gives  examples.

In simulating areal transport,  it also is common to
assume a  simple geometry for a contaminant' s  source
(or sink).   As in the areal simulation of ground-water
flow, points are used to represent  individual injection
and pumping wells and waste disposal areas, such as
landfills  or  recharge  ponds.    Lines are  used  to
represent   rivers,   creeks,   and  leaking  sewer   or
pipelines.   Again,  it is emphasized that point and line
representations of sources  are justified as long  as
attention is focused on contamination  over an areal
scale that  is much larger than the  area of the sources
(greater than 10 or 100 times). If local information
very near the  sources  is required, then  the  source
geometry  must be described more accurately as  part of
the flow  region  under  consideration.   Also, when
analytical methods such as those given in Appendix B
are used to simulate the transport problems, one of the
following assumptions often is  made about the  source
input:   (1) the assumption of  constant concentration
during a continuous injection period or during a finite
injection  period;   (2)  the  assumption of  constant
injection rate during a continuous  injection period; or
(3) the assumption of instantaneous injection of a slug
of contaminant.   The validity of these assumptions
certainly depends  on field conditions.
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                Table 4-4.   Boundary Conditions of Solute Transport Equations
             Type
                         Description and Examples
  I.   Specified concentration
Value of concentration is specified along the boundary.  Typical examples
include:  (1) specified concentration condition on the boundary in direct
hydraulic contact with a surface water body that is recharging into the aquifer
system; (2) zero concentration condition on the boundary located at a great
distance from the contaminant source; and  (3) specified concentration condition
at injection wells.	
  II.  Zero concentration
      gradient, normal to
      the boundary
This type of boundary condition can be expressed as dc/dn = 0.  Typical
examples include:  (1) zero normal concentration gradient on impervious
boundaries; and (2) zero normal concentration gradient on outflow boundaries
(e.g., river and spring outlets, drains, and pumped wells) where the
contaminant leaves the aquifer system.
  III.  Specified total mass
      flux of contaminant
      normal to the
      boundary
Total (advective and dispersive) flux is specified on the boundary.  This
boundary condition is usually expressed as -(Dij5c/5Xj)ni =  qn(c(-c), where n; is
the unit vector in the direction outward and normal to the boundary,  j is the
index for the principal axis, and c is the concentration.  Typical examples
include:  (1) specified mass flux of contaminant at injection wells (in this case,
qn corresponds to the volumetric fluid injection rate per unit area of the aquifer
(L/T), and c" corresponds to concentration of injected fluid); and (2) specified
mass  flux of contaminant at the boundary  receiving influx of contaminant from
sources such as landfills  and disposal ditches.
Initial Conditions

Initial conditions are defined as values of contaminant
concentrations initially assumed to  be present in the
area.  Non-uniform initial values (i.e., contaminant
concentrations) are routinely used in the contaminant
transport analysis to depict the geometry and varying
concentrations of  contaminant within the plume,  as
well as to define the concentrations  leaching from the
contaminant source.  The ability of a code to allow
non-uniform  initial  conditions is essential  to fully
describing and simulating the contaminant plume(s).

4.2.2.3  Specification of Time  Steps

Transient simulations of flow and/or transport require
the use  of time steps.  There is a direct relationship
between  numerical  accuracy  and  stability,   grid
density, and time-step size. The time-step size should
be selected to ensure that the Courant criterion is less
than or  equal to one as shown below:
                                                C =
                 vat
                 Ax
                           where:
                             Cr =
                             A*1 =
                             V
                             A*
Courant criterion
Time step interval
=       Darcy velocity
=       Grid spacing
                           That is,  the time  step should be  selected so that it
                           would take longer  than the specified time to move the
                           distance  of the grid block.

                           4.2.2.4  Specifying Parameter Values in the Model

                           Table  2-1  shows  the  data  typically  required  for
                           modeling ground-water flow and transport, which can
                           be obtained from previous and ongoing field studies.
                           Data input into the numerical model is a painstaking
                           process;  therefore,  to  identify  where a significant
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effort  should  be  made  to  ensure  accuracy,  the
uncertainties inherent in the data must be considered.
Such uncertainties will give an early indication of
which data are most likely candidates for modification.
For example,  in all likelihood, the assumed recharge
will   be   changed    considerably   from   initial
approximations   when  calibrating   the   model.
Therefore, it  would make  sense to assign uniform
values, rather than to estimate zones of recharge that
most  probably will be changed later.   Modeling
uncertainties include:

  Measurements  of flow and transport usually are
  taken at only a  few sampling points.  To obtain a
  complete  picture, it  is necessary to  interpolate
  between these  points, or make inferences from
  point  data to apply  to  conditions over a larger
  area.

  There may be an inherent difference between the
  scale on which the processes are mathematically
  described  and  the scale  at  which the  data are
  obtained.  For example, laboratory measurements
  may exhibit scale-dependence when extrapolated
  to  a field site.

  Data are never complete; in particular, those data
  pertaining   to   values  of  dispersivities  and
  contaminant input rates usually are not available.
  Therefore, the modeling discussion should include
  a data limitation section. These gaps will have  to
  be  filled   using  estimates  made   during the
  calibration and  sensitivity analyses.

  The various methods for  collecting samples and
  measuring parameters  all  have  some  error  or
  uncertainty.  Typical sources of error include  an
  improper  type  of test, poor specification  of test
  procedures,  poor   instrumentation,   incorrect
  measurement, and incorrect interpretation of the
  results.  Hence,  the  reliability of data obtained
  from various sources must be weighted.

4.2.3    Calibration of the Model

Traditionally, the term  "model calibration" is used to
refer to the trial-and-error adjustment of parameters of
the ground-water  system  by comparing the model' s
output  (calculated  values   of hydraulic  head or
concentration)  and the measured output (observed
values of hydraulic head   or  concentration).   In
essence, such a  calibration procedure involves the
following routines:  (1)  operating the model, using
initial  estimates  of the values  of parameters; (2)
history-matching or comparing computed and observed
values of hydraulic head  or  concentration;  and (3)
adjusting the values of the parameters  and repeating
the simulation.

Calibration  of the  model is aimed at demonstrating
that it can produce realistic, and to a certain extent,
accurate and reliable predictions.    The model  is
calibrated  by  determining  a  set   of parameters,
boundary conditions,  and hydraulic  stresses  that
generate simulated  potentiometric surfaces and fluxes
that match  field-measured  values  to   within  an
acceptable range of errors.

The end result of the process of model calibration is
an optimal set of values for parameters that minimize
the discrepancy between the model's output and the
observed data. Several major causes of discrepancy
should  be recognized; they are  listed below, with
general comments  on actions that  can be taken to
rectify the problem.

1.   Poor estimate  of values for flow or transport
     parameters, or incorrect assessment of initial and
     boundary conditions of the ground-water system.
     In this  case,  the  problem may be corrected by
     adjusting values of the physical parameters and
     rerunning the  model.

2.   Use  of incorrect  or  inappropriate data  on
     potentiometric head  or concentration  in the
     history-matching  or the comparison of output.  A
     common pitfall is comparing the potentiometric
     head computed for a point located at coordinates
     (x,y, z)  in a three-dimensional  flow field with
     data measured from an observation well located
     at (x,y) but screened over a significant portion of
     the aquifer thickness.   Such a comparison is not
     valid  unless  the vertical   flow component  is
     negligible because the observed head represents
     the vertically  averaged head over the screened
     length  of the observation well, and not the head
     at the point (x,y,z).

  Such a discrepancy between the model's result and
  observed head can be avoided by carefully checking
  and interpreting the  data.
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3.   Use   of  inadequate   spatial  and   temporal
     discretizations.   As pointed  out  earlier,  it  is
     important for  the user of a numerical model to
     select grid and time steps that are  sufficiently
     refined to give acceptable accuracy.

4.   Use  of an inappropriate conceptual  model.  In
     some instances, lack of information about some
     features of the  ground-water system may have led
     to the use of an oversimplified or a wrong type of
     conceptual model, or to a poor definition of the
     flow and transport problems.  Usually when this
     happens, it  is  necessary to return to the early
     stage of the  simulation process and formulate a
     new  conceptual  model,  or  alter the  existing
     model.  Alternatively,  additional  data  may be
     acquired that better define the flow and transport
     problems.

For  a cost-effective  calibration  of the  model,  a
systematic approach should be taken to the problem of
identifying parameters.  In general, a checklist should
be kept of those parameters  that are being varied and
those  that  are  being  held   constant.     Various
simplifying assumptions made in the conceptual model
and  formulation  of the problem  should  be noted,
together  with the  levels  of uncertainties  associated
with all critical input parameters.

The  iterative process  of matching calculated values
with  observed  (historical)  data  by  adjusting  the
model's   input  can  be  a  manual trial-and-error
procedure or can  be  automated.   The  calibration
process,  also known as history-matching, is closely
related to  estimating parameters. This process might
result in the refinement of initial estimates of aquifer
properties (parameters),  the  establishment  of the
location of the boundaries (areal and vertical extent of
aquifer), and the  determination of flow and transport
conditions  at  the boundaries.     Trial-and-error
calibration is a highly subjective, intuitive procedure.
As the quantity and quality  of data are often limited,
no  unique  set of  parameters  results,  leaving the
modeler with a subjective choice.  For example, the
simulated potentiometric surface could be raised either
by  increasing areal recharge  or  by increasing the
amount of leakage from a stream.

The  success of such a  procedure depends very much
on the experience  of  the analyst.   Another type of
technique is based on the use of a formal optimization
procedure   (e.g.,   Gauss-Newton   parameter
optimization algorithm),   in  conjunction with  the
ground-water flow model.  Such techniques can be
coded  into  a   computer  program  that performs
automatic history-matching, and calculates the optimal
set  of parameter  values  that  minimize  a  certain
objective function (e.g., the total sum of the square of
the  difference between computed and observed head
values  at all observation points).

Both the manual and automatic adjustment techniques
may be categorized as the  "indirect approach" to the
problem  of identifying  parameters  (See  FRE79,
pp.  357-359).  This statement implies that calibration
can be carried out via a "direct approach."  Such an
approach  requires  the inverse  formulation of the
problem  of the ground-water  flow.  In other words,
the  flow problem is set up  in such a way  that the
piezometric head and well  discharges are known, but
the  transmissivity,  storage, and recharge parameters
are unknown.    When posed in this manner,  the
identification problem is referred to specifically as the
"inverse problem." Several techniques recently were
developed to solve the inverse problem.

Automation  calibration  is  based  on  the   use  of
prescribed  algorithms, which are completed when
preset  matching  criteria are  met.   Because of the
formal approach taken in adjusting input to the model,
automatic procedures are less subjective than trial-and-
error procedures.  However,  automatic  procedures
effectively  eliminate the judgment of the modeler, and
because the calibrated solution is not unique it may not
be  the best fit  to the  overall  conceptual  model.
However,  if numerous calibrations are required,  it
would  make sense to use automated calibration tools
to obtain probability distributions.

In contrast  to the calibration of the ground-water flow
model, calibration  of a contaminant transport model
usually is more subjective using the manual procedure
of history-matching and trial-and-error adjustments of
the parameter.  There are several reasons for this; the
most  important  is  that  data  on concentration are
usually completely lacking, or insufficient to permit an
accurate calibration.  Another important reason is that
the transport equation contains more parameters and is
more complex than the ground-water flow equation.
Thus, it is more  difficult to identify the parameters by
an  automatic estimation technique or by the direct
(inverse formulation) approach.
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Calibration can  be  performed  to  steady-state  or
transient  data sets.    Although  most flow  model
calibration exercises involve steady-state data, in some
hydrogeologic  settings, assumption of steady-state
conditions  may   be   inappropriate  due  to   large
fluctuations in the water table or boundary conditions.
In this case, the model may be calibrated against long-
er short-term  trends in water levels, stream and lake
elevations,  and possibly, system  responses  resulting
from  imposed stresses such as  pumping wells.   A
transient  flow calibration is necessary  to  calibrate
values of  storage parameters,  which  are needed if
transient flow is to be modeled.

The  results of the  model  calibration  need  to  be
evaluated both qualitatively and  quantitatively.  At
present, no established protocol exists for determining
whether  a model has been  satisfactorily calibrated.
However, there are several common ways of reporting
the calibration results.  The simplest way is to  list the
measured  and simulated  heads together with their
differences and some average of the differences.

Comparison between contour maps of measured heads
versus contoured maps of simulated heads provides a
visual means  of  assessing the "goodness of fit" and
gives some idea of the spatial  distribution of error in
the calibration.

The  simulated heads  and  concentrations will have
some degree of error arising from how  the model was
discretized in both space and time. In some  instances
(e.g., if large mass balance errors  are occurring),  it
may be necessary to  perform a grid-convergence test
to determine if the grid spacings in the model are fine
enough; this can be time-consuming and painstaking
unless a  good pre-processor is available.  The ready
accessibility of high-speed  computers  may warrant
over-discretizing the model grid  at the beginning of
the project, rather than having to redesign the grid
during calibration. If a transient calibration is to  be
performed, the appropriateness of the  selected time
steps  should be checked by comparing the model' s
results against an identical simulation with the time
steps  set at very small intervals. If the results with the
large  time  steps do  not diverge  significantly from
those with the smaller steps,  the larger ones  would
provide a comparable result.

The mass balance error is calculated by comparing  all
of the water entering the modeled system with all of
the water exiting the domain.   Transient simulations
also will consider water going into and out of storage.
The mass balance error  should typically be less than
one percent.

4.2.4    Uncertainty and Sensitivity Analyses

After the model has  been satisfactorily  calibrated,
sensitivity analyses should be performed to  determine
the sensitivity of the model' s  output to variations (or
uncertainties) in physical parameters.  For instance,
what  would be the effect of  a 10  percent error in
recharge  values on  the  potentiometric   head  and
velocity distributions?

The common practice for carrying out the  sensitivity
analysis is to repeat the  simulations using a series of
selected  values for the  physical parameters and to
compare the  results with those  obtained  using the
calibrated values. Usually, the selected values of each
varied parameter are within a range that depends on
the degree of associated uncertainty. Output from the
sensitivity runs can be expressed in actual units or in
a dimensionless form. Using  dimensionless variables
often allows systematic conclusions to be drawn from
the sensitivity study.  In particular, if the model is an
analytical model, important dimensionless parameters
can often be easily identified  by carefully examining
the analytical solution.

Sensitivity analyses identify the main contributors to
the observed variation in the results.  These techniques
typically are applied iteratively. The first iteration can
include  rather  general  assumptions   leading  to
preliminary  results that help focus  the subsequent
iterations.

Uncertainty  in input parameters used  in  predictive
models may result  from several sources,  including
incomplete  data,  intrinsic spatial  variability  of a
property,   uncertainties  in    measurements,    and
uncertainties  resulting  from   differences   in  scale
between data  acquisition  and model application.
However, uncertainty in input  parameters  is not the
only  potential  source of  uncertainty  in  modeling
ground-water  flow   and  contaminant   modeling;
additional uncertainty may enter the analysis through
the choice of conceptual models used  to represent the
system.

The  following  definitions will  be  useful in  this
                                                     4-19

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discussion of uncertainty and sensitivity analyses.

  Conceptual Model:  A set of qualitative assumptions
  used to describe a system or subsystem for a given
  purpose.  At a minimum, these assumptions concern
  the geometry and dimensions of the system,  initial
  and boundary conditions, time-dependence, and the
  type of physical and chemical  processes.   The
  assumptions should be consistent with one another
  and with existing information within the context of
  the purpose.

  Alternative Conceptual Models: Alternative sets of
  assumptions that describe the  same system for the
  same purpose,  where each set of assumptions is
  consistent with the existing information.

  Conceptual  Model  Uncertainty:    The  lack  of
  knowledge about  the system  resulting from the
  limited information available  to  support or refute
  alternative conceptual models.

Uncertainty also  may  exist  in the  computational
models used for  quantitative analyses,  based on the
chosen conceptual  models.    In   this  discussion,
computational models refer to mathematical models
used to represent the physical processes,  numerical
models used to solve the mathematical models, and
computer codes used to implement the solution.

The  selection of scenarios  to be analyzed also may
introduce uncertainty into the estimated performance.
Still more uncertainty may exist in the completeness of
the  scenarios  considered,  in  the way  in  which
computational results are aggregated to represent the
consequences  of scenarios, and in the  probabilities
associated with their occurrence.

Sensitivity analyses identify the main contributors to
the observed variation in the results.  These techniques
typically are applied iteratively. The first iteration can
include  rather   general  assumptions,  leading  to
preliminary results that  help focus these techniques in
subsequent  iterations.  In this manner,  the resources
and techniques required to reduce the uncertainty can
be directed  at the areas of the modeling study  where
the benefits  of understanding uncertainty and reducing
it (where possible) are greater.  However, sensitivity
analyses alone will rarely identify a flawed conceptual
model.  For  example,  the failure to identify and
include a fault(s) in the conceptual model would lead
to an analysis that would not account for preferential
pathways that potentially could  result in higher than
predicted risks.

Modeling the behavior  of a hydrogeologic  system
necessarily will be uncertain because knowledge about
its real behavior is limited. Many of the parameters
used as inputs to a model of the system are obtained
only by collecting data.  Investigators knowledgeable
about the data they collect make a finite number of
observations, choosing which parameters to measure
and  how,  where,  and  when  to   measure  them.
However, the collection process itself can introduce
uncertainty  through  errors  in  measurement,  the
system's inherent randomness, and limited sampling of
the  variable  physical,   chemical,   and  biological
properties of the system.  The professional judgment
of an expert in the area  of investigation often enters
into  the  scientific process.  For  example,  selecting
methods to collect data, interpreting data, developing
conceptual  models,  and  selecting  parameters  all
require professional analysis  and judgment.  The
analyst' s final data set is based on available data, use
of the parameter in the computational model, behavior
of analogous  systems, and the  analyst's  own expert
judgment.

Uncertainties arising from the numerical  solutions of
a mathematical  model are  resolved  when  verifying
(checking  for numerical accuracy)  the computer
programs.  Uncertainty resulting from the  scenarios
selected   for  modeling   is  best  addressed  by  a
systematic,  thorough examination  of a  scenario's
possible   components,    based   on   probability,
consequence, physical reasonableness, and regulatory
guidance,  and  by  assigning  probability  through
techniques used for evaluation or estimation.

Monte Carlo techniques  may  be used for uncertainty
and sensitivity analyses. Uncertainty analyses evaluate
uncertainty  in performance estimates that result both
from  the  existence of alternative conceptual  models
and  from  imprecise knowledge input  variables.
Sensitivity  analyses  determine  the  contribution of
individual input variables to the uncertainty in model
predictions.

Monte Carlo analyses involve  five steps: (1) selection
of variables to be examined  and  the  ranges  and
distributions of their values; (2) generation of the
samples to be analyzed; (3) propagation of the samples
through the analysis; (4)  uncertainty analysis;  and (5)
sensitivity analysis.
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4.3  Predictive Simulations

The final stage of the process is to perform predictive
simulations using the optimal set of parameter values
obtained from the model calibration. In general, these
simulations address  specific  issues  of the existing
problem of ground-water contamination and provide
guidance for policy decisions. Each simulation usually
corresponds to one specified set of data pertaining to
natural boundary conditions, pumping operation for
the ground-water reservoir,  or proposed remedial
measures for the contamination.  Typical objectives of
the predictive simulation study are outlined  below,
alone with pertinent comments.

1.   To learn more  about the existing contamination
     and to predict future  behavior of the ground-
     water system under natural conditions. Among
     the questions that may  be  addressed are  the
     following:   Where  is the  contaminant plume
     located presently?   In which direction  is  the
     plume moving? Will the contamination at the site
     pose serious danger to the public if no action is
     taken?  Do the contaminant concentrations pose
     unacceptable risks? If the risks are unacceptable,
     how extensive must the clean-up be to reduce the
     concentration of the contaminant to an acceptable
     level?

2.   To evaluate and compare  alternative remedial
     schemes for the existing contamination. Typical
     remedial schemes that may be considered are (1)
     hydraulic barriers  (e.g.,  pumping and recharge
     wells to flush the contaminant  out of the aquifer,
     and  (2)    subsurface  barriers  to  inhibit  the
     contaminant  from leaving   the  site.     The
     predictive simulations are also aimed at the level
     of risk reduction  offered  by  each  alternative
     measure. Results from the comparative study are
     useful  in the selection and  implementation of a
     suitable remedial  scheme for the site.  These
     decisions usually are made in conjunction with
     economic considerations. In some instances, the
     predictive   simulations   can   be   directly
     incorporated into an economic analysis, allowing
     the most cost-effective remedy to be selected.

3.   To  predict  the responses of the ground-water
     system  to   various  management  alternatives
     including, for  example,  different pumping or
     recharge operations that  may  be applied to the
     wells existing at the site or groups of wells in the
     areas  surrounding the  site.   The following are
     typical  questions:   How  will different  well
     operations affect  the contaminant plume?   Can
     the existing contamination problem be contained
     to the site  and recovery efforts maximized by
     modeling review  criteria for selecting a proper
     pumping schedule?

Modeling review criteria for the  second two topics
have been considered in previous chapters.  The first
topic  is  related  to the  baseline  risk  assessment,
discussed in the next section.

4.4  Baseline Risk Assessment

The Baseline Risk Assessment typically accomplishes
the following three  objectives:

  •  Assesses the magnitude and  sources of current
     and potential  future risks  to humans  and the
     environment.

  •  Assists   in    the   scoping   ongoing    site
     characterization.

  •  Identifies contaminants of potential  concern and
     assumptions of exposure for developing  risk-
     based preliminary remediation goals (PRGs).

As  the   remedial   investigation/feasibility  study
proceeds, action  levels will evolve from the  PRGs
which ultimately will  become   part of the  final
objectives  for remedial action.  These action  levels
will entail consideration of applicable or  relevant and
appropriate  requirements   (ARARs)  for  site-wide
baseline  risk assessments and, potentially,  operable
unit-specific risk  assessments.

Although risk assessments  generally include several
receptors  (e.g.,   future  resident  farmers,  plant
workers),  the  following discussion is  targeted  at
pathways and receptors related to  ground water.

Risk-based PRGs for  ground water are frequently
developed  in accordance  with the  Human Health
Evaluation Manual,  Part B  (EPA91). This approach
is  a  first-tier type  of  analysis and typically is very
conservative.     The   methodologies   outlined   in
Appendix B for predicting radionuclide transport rates
and  concentrations  are designed for  conservative
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analyses,  yet they  also  are  designed to  be more
realistic than the HHEM Part B approach.

In many cases, estimating flow and transport through
the unsaturated zone is an integral component of the
risk assessment, particularly if the compliance point is
relatively  near the  contaminant  source.   In these
instances,  the release rates, concentrations and hold-up
times  within  the unsaturated  zone will  influence
receptor   concentrations  far  more than  flow and
transport in the saturated zone.

Under these circumstances, a practical approach would
be to use one of the many risk-based computer models
that emphasize flow and transport in the unsaturated
zone. However, if flow and transport processes in the
saturated  zone are  deemed  very  important  to the
analysis, or if the receptor is located off the centerline
of  the plume  or  far  from the source,  it may  be
worthwhile  to  use   a  risk-based  type  code  or
calculations from Appendix B to give  a transient
source-type boundary.  This can  then be used in a
more complex numerical model to simulate the flow
and transport in the saturated zone more accurately.

One of the  primary  differences of the site modeling
with risk-based codes is that the model is not
typically calibrated.  In general, this is not a problem
because the required data from  the unsaturated zone
rarely  are  collected  during site  characterization.
Therefore, evaluation  of the parameters during the
sensitivity analysis is crucial.

The  conceptual model sub-components  of  the risk-
based codes related to ground-water flow and transport
processes consist of the following:

  •   Infiltration
  •   Source Release Rate
  •   Source and Leach Strength
  •   Fate and Transport in the Unsaturated Zone
  •   Fate and Transport through the Saturated Zone

4.5  Exposure Estimation—Ground Water

Appendix B describes methods for estimating ground-
water concentration at  the point of receptor exposure.
With these estimated concentrations, the assessor can
estimate  exposure  based  on  the  equations  and
parameter  values presented in the Exposure Factors
Handbook  (EPA89).
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                        CHAPTER 5 - SUMMARY AND  CONCLUSIONS
In this chapter, the modeling evaluation criteria and a
checklist  containing  the  major  steps  within these
procedures are reviewed.  With this checklist (Table
5-1), a person analyzing a specific project can identify
potential problems in the model application.
MODELING    OBJECTIVES
REQUIREMENTS
AND   DATA
    The purpose and scope of the modeling exercise
    should be clearly indicated.

    The purpose  of the modeling should be kept in
    mind  when reviewing the modeling report.  The
    reviewer should determine whether the analyses
    performed are consistent with the purpose of the
    project.   Common problems  are overkill (the
    modeling analyses are much too complex for the
    purpose  of the  project)  and over-simplification
    (the  modeling  analyses  are too  simplistic  to
    achieve the project objectives).

    The modeling objectives  should be identified and
    related to the decision-making needs.

    In the Summary and Conclusions of the model
    application report, each of these objectives should
    be discussed separately in the context of how the
    modeling was used to meet  the objective and the
    degree to which the objective was met.

    The data required to construct a conceptual model
    should be described, and the relevance of the data
    to ground-water flow and contaminant transport
    should be discussed.

    The data should be related to the processes being
    simulated, (e.g., groundwater flow, contaminant
    transport, variably-saturated flow and transport,
    etc.).     It is  important  to  ascertain  that  no
    important processes  are  overlooked and that all
    data   types  required   to  simulate a  particular
    process have been identified.  In addition to data
    related to the physical system,  a detailed  waste
    disposal history should be provided. The latter is
    a key element in determining the source term(s)
    for the contaminant transport modeling.
The source of the data should be presented.

Data  should  be categorized based upon source
type:  (1) site-specific data collected in the field,
(2) data obtained from the scientific literature, and
(3)  data  values   estimated   through   model
calibration.  Data obtained from literature should
be thoroughly cited and should be representative
of the same  geologic and hydrologic  conditions
found at the  site.  Data values  obtained through
calibration   should  also  be   consistent  with
anticipated  ranges  of  values  (see  the  model
calibration section).

The uncertainties associated with the data should
be discussed.

Are  some field collection methods better than
others?  How reliable are  literature values?  A
probable  range and  distribution  in which the
parameters will fall should be assigned,  prior  to
the modeling analysis.

The   general  sensitivity  of the  data  to  the
determination   of   ground-water   flow   and
contaminant  transport  calculations  should  be
discussed.

This   discussion   should   enable   the   field
characterization program to be more focused.  For
example,  bulk density is used  for the transport
calculations  although  the modeling results are
typically insensitive to their values.  Therefore,
time and resources would be better spent obtaining
site-specific distribution coefficients which may be
critical to the analysis.

Limitations  and  weaknesses in the  data base
should be presented as well  as  plans to  enhance
the data base.

Data gaps should be reviewed with the modeling
objectives  in  mind.   For  example,  scoping
calculations  may  be performed with relatively
little  site-specific  data.   Detailed  simulation  of
remedial  measures,  however,  would   require
numerous field measurements of key hydraulic
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    and  geochemical  parameters  (e.g.,  hydraulic
    conductivity,  storage  coefficient,  distribution
    coefficients, etc.).

•   Recommendations should be presented, detailing
    additional data needed to increase confidence in
    the modeling results.

CONCEPTUAL MODEL DEVELOPMENT

•   The  physical and  hydrogeologic frameworks of
    the system  should be described in detail.

    The  physical  and   hydrogeologic   framework
    includes  lithologic  contacts,  facies  changes,
    discrete features  such as fractures,  and spatial
    variations of geologic units  and their hydraulic
    properties.    The  thickness, top elevation,  and
    bottom elevation should be described in detail for
    areally   continuous   hydro stratigraphic   units
    (aquifers and  aquitards).  The rationale  for the
    variability of the properties  should be explained
    (e.g., depositional history).

    The  geometry of the system  should be presented
    in three dimensions with a rationale for possible
    simplification.  For example, the analysis of the
    unsaturated zone may be reduced toone  or  two
    dimensions.  The saturated  ground-water system
    may  also be simplified to two-dimensions in plan
    view if vertical gradients are negligible.

•   The boundaries of the system should be described
    in a water budget analysis.

    The  primary  components of the water  budget
    include  recharge,  evapotranspiration,   runoff,
    pumping rates,  and flow to other  sources  and
    sinks  including  rivers  and   lakes.      The
    methodology   for   determining   individual
    components of the water budget should  also be
    included.   Boundaries of the system should be
    identified based upon  regional hydraulic features.
    Aquifer boundaries are seldom constrained to the
    immediate vicinity of the site and may extend far
    beyond the  area  of interest.  It  is  important to
    characterize these regional features,  however.

•   The  contaminant source term should be described
    in detail.
Source  terms should be  described in terms of
geometry  (in three  dimensions),  radionuclide
concentrations leached from the source, timing of
the release, and the release mechanism.  The site
waste disposal history described in the first section
of the  modeling  report  should  be  helpful in
determining this information.

The  conceptual model should be consistent with
the field data.

One  of the fundamental problems in modeling is
a poor conceptual model.   Synthesizing the field
data   into  a  coherent  picture  of  the  relevant
physical and  chemical processes is critical to the
subsequent modeling analyses.   Errors in  the
conceptual model will propagate throughout  the
modeling.  It is important to review the conceptual
model and the raw data to determine whether
there are significant errors at this  early stage in
the project.

The  rationale for any simplifications made to the
conceptual model should be presented.

Examples of simplifications include (1) modeling
ground-water flow at steady-state conditions, (2)
simulating the unsaturated  zone in one or  two
dimensions,  and (3) approximating the source
term at  a   constant   concentration.    Each
simplification should be reviewed for consistency
with  the  conceptual  model  of  the  site,   the
availability of data,  and the potential impact on
the accuracy of the modeling results.

Uncertainties in the conceptual model  should be
presented and related to earlier discussions of data
limitations and uncertainties.

Uncertainties can be  related to the variability in
field data  or  interpretations  or  simplifying
assumptions  required to evaluate the field data.
Uncertainties  can  be   evaluated  through  a
sensitivity  analysis in subsequent model phases,
but should be discussed in the conceptual model
portion  of the report.

Are  sufficient data available to meet the modeling
objectives?

Data in  this context refer to  site-specific data.
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Data  can  always be  obtained from the  scientific
literature; however, as the objectives of the modeling
become more detailed, site-specific data requirements
increase.   It is important  to relate  the quantity and
quality of site-specific parameter values to the types of
analyses performed.

•   Have database deficiencies been  clearly identified
    and modeling implications discussed?

Figures and Tables

The following are illustrations and tables that should
be included in the conceptual modeling report.  Some
figures  may not  be required; however,  justification
should be given if figures and tables are omitted.

•   Map showing location of study area.

•   Maps and cross sections showing the thickness of
    the  unsaturated zone.
•   Maps, hydrographs, and/or tables of water-budget
    information, including evapotranspiration, runoff,
    ground-water  recharge, ground-water pumping,
    and  gains/losses  between ground  water  and
    surface water.

•   Maps,   cross   sections,  or  tables  indicating
    transportparameters, including effective porosity,
    dispersion   coefficients,   and   distribution
    coefficients.

•   Areal and cross sectional isoconcentration maps of
    primary contaminants in soil and ground water.

•   Time-series graphs of contaminant concentrations
    measured over time at monitoring wells or surface
    water locations.

•   Relevant source-term inventory information.

MODEL APPLICATION
•   Geologic map and cross  sections indicating the
    areal and vertical extent of the system.

•   Topographic map indicating surface water bodies.

•   Contour maps showing the tops and/or bottoms of
    the aquifers and confining units.

•   Isopach maps of hydrostratigraphic units.

•   Maps showing  extent and thicknesses of stream
    and lake sediments.

•   Maps  indicating  any  discrete  features  (e.g.,
    faults).

•   Maps and cross sections showing the unsaturated
    zone properties.

•   Potentiometric surface maps of aquifer(s) showing
    hydraulic boundaries.

•   Maps,  cross sections, or  tables  showing storage
    properties of the aquifers and  confining units.

•   Maps, cross sections, or tables showing hydraulic
    conductivity of the aquifers, confining units, and
    stream and lake sediments.
Scoping Analysis

•    The  results of  any  scoping analyses that are
    performed to  support the modeling  should  be
    presented.  These results should be able to support
    the approach taken for more complex modeling.

    Even  though  scoping analyses  represent  sim-
    plified  modeling  approaches  whereby  model
    parameters are chosen to be conservative. Review
    of the scoping calculations should concentrate on
    whether the chosen parameter values and models
    (or equations) are conservative from a regulatory
    perspective.

Code Selection

•    Selection criteria should be clearly presented for
    the selected code(s).

    Criteria  used   in   selecting  computer   codes
    generally include (1) degree  of code  testing and
    documentation, (2) ease of use,  (3) whether the
    code is proprietary  or public, (4) physical and
    chemical  processes  to   be  solved,  and  (5)
    application history.  Even if only one computer
    code is used  in  the  project, a  series  of  codes
    should be presented as possible candidates and
    rationale  should  be  presented  to  justify the
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selection of the chosen code.
    inaccuracies or numerical problems.
•    The  general features of  the code  should  be
    discussed.

    Code  features  include whether  the  code  is  a
    proprietary version of a publicly available code,
    solution methodologies for the flow and transport
    equations, hardware requirements, degree of code
    testing,  and availability  of  source   code  and
    documentation.

•    The code  assumptions and limitations should be
    described.

    Of  particular  interest are  those assumptions
    pertaining to the conceptual model. These would
    include  code dimensionality,  ability to simulate
    heterogeneities,  and flow and transport through
    the unsaturated zone.  The code should be capable
    of simulating all pertinent processes identified in
    the site conceptual model.

•    The basis for  regulatory acceptance  should be
    discussed.

    Regulatory  acceptance criteria  may  include  a
    history of use,  particularly  for applications in a
    similar  regulatory context  and degree  of  code
    testing.  The code should also be well documented
    and the  source code should  be  available for
    inspection. Code testing should ideally follow the
    three-level   procedures   advocated   by   the
    International Ground  Water  Modeling  Center
    (IGWMC)  or  those  used   in  the  various
    international code  testing studies (INTRACOIN,
    INTRAVAL, etc.).

•    Documentation  on the source  code  should be
    included, with an executable version of the code
    and data sets relevant to the problem. This allows
    the  reviewer to independently verify the results
    presented in the modeling report and to review
    details from the individual model output files.

Layering and Gridding

•    The rationale for the selection of the grid spacing,
    number of model layers, and the resulting number
    of nodes and elements  should be given.
•    The grid should be evaluated in terms of potential
    Common  features to  evaluate  include: (1) the
    model boundaries should not be too close  to the
    area of active remediation (wells etc.), (2)  model
    nodes  should  coincide  with  pumping centers
    otherwise the effects  of these  stresses will  be
    offset, (3) the  grid  should  be  alligned with the
    principal  axes of hydraulic conductivity,  (4) in
    finite-difference models, the grid spacing between
    adjacent  cells should not vary  by more  than a
    factor of 1.5, (5) in transport modeling, the  Peclet
    number should not  be greater than 2, (6) the
    maximum aspect ratio of the grid should not be
    greater than 100:1.

    Other aspects of grid design are more subjective.
    For example, the  degree of discretization (number
    of rows and columns)  should be appropriate for
    the problem being solved.  Areas of sharp contrast
    in hydraulic properties  should be  more  finely
    discretized.  Model layering should be consistent
    with the magnitude of vertical  gradients and the
    degree  of vertical  heterogeneity.    If  matrix
    diffusion is important,  confining units should be
    discretized into multiple layers.

Figures and Tables

•   The  grid should be presented as an  overlay of a
    map of the area to be modeled.

    A vertical cross section of the modeled area  which
    displays the vertical layering of the model with
    respect to its hydrogeology should be included.

    Horizontal  and  vertical  grid   coordinates  and
    elevations  should be  identified clearly  on  all
    figures.

Boundary and Initial Conditions

•   Selection  of all boundaries and  initial  conditions
    should be justified.

    The  justification  would involve a discussion of
    how a natural feature was simulated (e.g., a river
    or ground-water divide) including any assumptions
    related to the choice of bounary type and location.
    Of particular concern are boundaries that do not
    coincide with natural features but are somewhat
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arbitrary.  Careful scrutiny should be given to such
artificial boundaries.   Ideally, a sensitivity analysis
would be performed on these arbitrary boundaries.

    Descriptions of model boundaries should include
    whether the boundaries are transient or steady-
    state. For transient boundaries, the report should
    discuss how the boundary condition changes with
    time and how these changes were determined.  In
    the  natural  system, boundaries may shift with
    time, and the effect that these positional changes
    may have on the results of modeling should  be
    considered.

    Boundaries should also be chosen to ensure that
    future simulations will not be adversely effected
    by pumping wells or other features that  stress the
    system.  Justification of  the chosen boundaries
    should address this  potential problem.

•   Uncertainty surrounding  boundaries and  initial
    conditions should be discussed.

    There  is usually significant uncertainty  in the
    selection  of  boundary   conditions.      These
    uncertainties include the type of boundary chosen
    to simulate a natural  feature, the position  of the
    boundary, the value of head or concentration at
    the  boundary,  the assignment of  conductance
    properties  to  the boundary,  and  the  transient
    response of the boundary.  All of these factors
    should be  addressed  by  the model report.  A
    sensitivity analysis on boundary conditions should
    also be included.

•   The following specific examples may be useful in
    reviewing the model boundary conditions:

    Under  steady-state conditions, the areal recharge
    should  not  exceed  the  saturated  hydraulic
    conductivity of the  surficial soil through which it
    must travel; otherwise ponding would occur.

    Potentiometric  lines on streams that are gaining
    water should point upstream, whereas  the lines
    should point downstream along losing streams.

    Contaminant  source  release  rates  should  be
    discussed.

    Ephemeral  streams  generally  should  not  be
    modeled as constant head  boundaries.
    Streams are frequently modeled as ground-water
    divides, that is, all ground-water flowing towards
    the stream  is  assumed  to  be captured by the
    stream.    The  modeler   should  justify  this
    assumption, as not all streams fully penetrate the
    aquifer.

    Surface-water/ground-water interactions should be
    discussed.

    Recharge  and evapotranspiration are difficult to
    determine,  and therefore,  recharge as  a flux
    boundary is often used as a calibration parameter.
    The method for determining recharge should be
    presented.

    Interpretation  and extrapolation methods  (e.g.,
    Kriging) should be described.

    Boundaries between two types of porous  media
    should always coincide with element boundaries.

Figures and Tables

•   The  report  should  clearly  identify  assigned
    boundaries and initial conditions in figures and
    tables.   A typical figure would be a plot  of the
    model  grid for each layer clearly  illustrating
    boundary  cells.  Each  type of boundary  (e.g.,
    constant head, constant flux, and head-dependent
    flux) should be labeled using a different symbol or
    color.  For transient boundaries, multiple figures
    representing different times may be used or tables
    of values may be more appropriate.

•   The boundary condition sensitivity analysis should
    be illustrated using figures and tables.

Time Steps

•   The Courant criterion outlined in Section 4.2.2.3
    should be  satisfied for transport  simulations.

•   Even for flow  models, the time steps should be
    small at the start of the  simulation and gradually
    increase.   Time  step size should be  decreased
    when major changes in stresses are simulated.

Calibration

•   The calibration process  should  be described in
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detail,  including any assumptions and limitations.

    Proper justification should be given if the model
    was  not  calibrated.   In some cases,  such as a
    screening  analysis,   calibration  may  not  be
    required.  However,  an uncalibrated model is not
    as  reliable  a decision-making  tool  as  a well-
    calibrated model.

    Documentation of the calibration process should
    include flow diagrams  illustrating the approach
    that  was  taken to  calibrate  the model.   The
    objectives  or criteria used to  calibrate heads,
    flows,  and radionuclide concentrations should be
    presented.   The method  of calibration  (inverse
    model, trial-and-error, or a combination of both)
    should be  documented.   If  special calibration
    software is used (e.g. an inverse model),  it should
    be documented and  described under  the  code
    selection section.

    If both steady-state and transient calibrations are
    performed,   their  similarities  and  differences
    within the  results should  be discussed.  The
    rationale  and  selection of time  steps  for the
    transient calibration  should be discussed.

•   The  sources  and magnitudes of errors should be
    described.

    All calibrated models have errors. These errors
    are  often  called  residuals  and  represent  the
    difference between a model-computed value and
    a value measured in the field (usually head or
    concentration). The errors should be described in
    detail  in  the report.    The  review  should
    concentrate on potential effects on the predictive
    simulations which will  be performed later (e.g.,
    risk assessment).

•   Modifications to the parameter values, boundary
    conditions, and imposed hydraulic stresses should
    be discussed in detail.

    The calibration process is an exercise in parameter
    estimation  where  key  model  parameter  and
    boundary values  are adjusted within reasonable
    bounds to achieve the calibration objectives. The
    review  should focus on the response of the
    modeled system  to  the altered  values  and the
    rationale for the parameter changes made during
    the calibration.  The  calibrated parameter values
should be compared with the initial range of these
parameters. Particular emphasis should be placed
on parameters that  fall outside  their originally
estimated range.   The  final values  should be
compared to  those  identified in  the  conceptual
model.

The rationale for the convergence criterion for the
heads and concentrations should be presented, in
addition to a discussion  of the  overall mass
balance results.

Problems that arose due to failure of the  code to
converge or  numerical instabilities  should be
described.   The mass-balance results should be
discussed  in   relation   to   any   convergence
problems.  Overall, the water balance should be in
error by less than one percent.

The user-specified error or convergence criterion
will result in a level of accuracy that is one to two
orders of magnitude greater  than the criterion.
This difference  should be evaluated with respect
to the desired  level of accuracy.

The calibrated model should be a good match with
the conceptual model, such as flow directions and
parameter values.

Specific examples to look  for in reviewing  the
calibration include:
The  calibrated parameters, especially hydraulic
conductivity,  should not  appear  patchworked.
Unless there is evidence indicating that hydraulic
conductivity values change substantially from one
grid  block  to  the next, it should be assumed that
large  percentages   of  the  modeled  area   are
relatively homogeneous.

Areal recharge should be uniform unless  there is
sufficient justification to vary the recharge rates
locally.

Well logs and aquifer stress test  data should be
reviewed   to   ensure   that   the   hydraulic
conductivities   assigned   to  that   area   are
compatible.

The  volume of water entering or exiting  local
streams, lakes, or rivers should be consistent with
the field data.
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    It  should  be  kept  in  mind that  head  and
    concentration values computed at a  node  are
    representative  of  an area rather  than  a  point.
    Therefore, if drawdown values during aquifer
    tests are used as calibration points, even a well-
    calibrated model would not match  the  field data
    exactly  because  data  collected   from   wells
    represent points in space.

    Vertical gradients  within an aquifer in which the
    well is not fully penetrating should  be considered
    when the model is calibrated.

Figures and Tables

•   Areal and  cross-sectional diagrams of the error
    (residual)  between  computed  and   measured
    hydraulic head  and radionuclide  concentrations
    should be presented.  The errors should not show
    significant spatial bias.  For example, if all of the
    targets  in  the western  half  of the model  are
    computed too high and those in the east are too
    low, there is a bias  in the calibration.  In this
    example, the gradients would be inaccurate.

•   A list and a figure indicating  the final  calibrated
    values for  parameters and  boundary  conditions
    should be included.

•   The  match to  the calibration targets should be
    shown in figures as well as  in tables.   Sections
    within the model should be outlined and discussed
    according  to  their  "goodness  of fit"  to  the
    calibration targets.

•   Particle  tracks or calibrated  plumes  should be
    shown in planar and cross-sectional views.

Sensitivity Analysis

•   The  approach undertaken  for the  sensitivity
    analysis should be described in detail.

    There   are a  variety  of ways to  perform  a
    sensitivity  analysis.   According to ASTM,  the
    sensitivity  analysis   should   evaluate  both  the
    calibration   and  the   predictions   (if   any).
    Sensitivity of predictions to model parameters and
    boundary conditions is important in evaluating the
    degree  of uncertainty  in  the  model.    Both
    parameter values (e.g. hydraulic conductivity) and
    boundary conditions  should be evaluated in the
    sensitivity analysis.

    The  sensitivity of model calibration quality and
    model predictions  to  variations  in  parameter
    values,  including grid  spacing,  time  steps, and
    boundary  conditions,   should  be  discussed,
    emphasizing parameters in which there is a large
    degree of uncertainty  and  the  results are very
    sensitive.

•   The  rationale for selecting parameters  for  the
    sensitivity analysis  and for  determining whether
    there were  sufficient  simulations  investigating
    single or multiple parameters should be presented.

•   The  relevance of  the  overall  uncertainty and
    sensitivity with respect to  the objectives of the
    predictive simulations should be discussed.

Figures and Tables

•   The  results of the sensitivity analysis  should be
    displayed in a graph or  table.

    A  typical  sensitivity graph plots a  calibration
    statistic (sum  of  squared residuals for example)
    versus a range  in  parameter  values  for each
    parameter.  Multiple parameters may be plotted
    on one graph.  Model sensitivity coefficients may
    be computed as the change  in a model-computed
    value  (head  or  concentration)  divided  by  the
    parameter change.  These sensitivity coefficients
    may then be  contoured to  illustrate changes  in
    model sensitivity through space.  Where  many
    parameters are involved, a table may be presented
    to  identify the most sensitive parameters.

Modeling to Support Baseline  Risk Assessment

•   The  objectives of the risk assessment  should be
    stated.

•   The  modeling approach,  in addition  to any
    inherent  limitations, should be clearly indicated.

•   The  conceptual  model  should be  presented,  in
    conjunction with  the validity of and rationale for
    any simplifying assumptions.

•   The method used to calculate infiltration rates and
    other relevant parameters should be included.
                                                     5-7

-------
•    A  discussion of  the source  term  should be
    presented, including its dimensions, strength, and
    composition.

•    The means by which release rates and leachate
    concentrations are calculated should be described.

•    The treatment of daughter-ingrowth in the source
    term in unsaturated and saturated zones should be
    described.

•    The  fate and transport processes  active  in the
    unsaturated   and   saturated  zones   should be
    presented.

•    The  processes  by  which the leachate  becomes
    diluted along the transport path from the source
    term to the receptor should be discussed.

•    If the output from  the risk-based code is coupled
    to a more sophisticated code, this process should
    be described in detail.

•    The process by which remedial action goals were
    determined from the results of the risk assessment
    should be discussed.

•    The methods  of calculation outlined in Appendix
    B can be used for independent verification of the
    results of the  risk assessment.

Figures and Tables

•    An areal and  cross-sectional representation of the
    conceptual model should be shown, including the
    locations of the assumed receptor.

•    Radionuclide breakthrough concentration  plots
    should  be  included  for  each  receptor  and
    radionuclide of interest.

•    Selected areal isoconcentration plots  should be
    given.
Preliminary Remedial Design

•   The  report  should follow the guidelines  given
    earlier in this chapter and include discussions and
    similar presentations on developing the conceptual
    model,  selecting  the parameters, designing the
    grid, calibrating the  model,  and carrying out the
    sensitivity analyses.

•   The  assumptions  and calculational procedures
    used  to  determine  the  specific assumptions
    associated with the  remedial design should  be
    presented, such as the locations of recovery wells
    and failure rates for  barriers.

•   In addition to the review of the  grid design and
    time-stepping schemes previously presented, are
    there other  relevant processes  which may  be
    important and should have been considered  (e.g.
    matrix diffusion)?

•   If a pump-and-treat scenario is modeled, does the
    model accurately simulate the rise and fall of the
    water table?

•   If the model also  was used for risk assessment,
    have conservative assumptions been removed and
    the  model   recalibrated?    For  instance,   a
    conservatively low hydraulic conductivity would
    yield high well  concentrations,  which may  be
    acceptable  for  the risk  assessment,  but would
    overestimate the  capture  zones  and  influent
    concentration of the  remedial design.

Figures and Tables

•   In addition to the figures and tables previously
    discussed that are relevant to the remedial design
    presentation, additional figures such as areal and
    cross sectional views of barrier walls,  capture
    zones, and/or recovery wells should be included.
                                                    5-8

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                   Table 5-1.  Major Steps in Modeling Evaluation Procedures
MODELING AND EVALUATION CRITERIA
APPRAISAL
Yes
No
Comments
CHAPTER 2
OBJECTIVES AND DATA REQUIREMENTS
Are the purpose and scope outlined?
Are the objectives consistent with decision-making needs?
Are the objectives satisfactory?
Are a site description and waste disposal history provided?
Are the data requirements for the proposed modeling outlined?
Are the sources of data adequately presented?
Are data uncertainties discussed?
Is the probable sensitivity of the future modeling results presented for the
data?
Are the potential data limitations and weaknesses provided?
Are the plans to resolve data limitations discussed?






























CHAPTER 3
CONCEPTUAL MODEL DEVELOPMENT
Is the physical framework discussed in detail?
Both regional and local?
Is the hydrogeologic framework described in detail?
Both regional and local?
Is the nature of the contaminant source term described?
Are the hydraulic boundaries described in detail?
Are data base deficiencies clearly identified and modeling implications
discussed?
Is the conceptual model consistent with the field data?
Are the uncertainties inherent in the conceptual model discussed?
Are the simplifying assumptions outlined?
Are the assumptions justified?
Are the natural boundaries or the aquifer system described?
Are the following figures and/or tables included:
• Map showing location of study area.




































In some instances tabular representation of the data may be appropriate.





                                              5-9

-------
Table 5-1 (Continued)
MODELING AND EVALUATION CRITERIA
• Geologic map and cross sections indicating the areal and vertical
extent of the system.
• Topographic map with the surface water bodies.
• Contour maps showing the tops and/or bottoms of the aquifers and
confining units.
• Isopach maps of hydrostratigraphic units.
• Maps showing extent and thicknesses of stream and lake sediments.
• Maps indicating discrete features (e.g., faults), if present.
• Maps and cross sections showing the unsaturated zone properties
(e.g., thickness, Ksat).
• Potentiometric surface maps of aquifer(s) and hydraulic boundaries.
• Maps and cross sections showing storage properties of the aquifers
and confining units. '
• Maps and cross sections showing hydraulic conductivity of the
aquifers, confining units and stream and lake sediments.
• Maps and hydrographs of water-budget information.
• Maps and cross sections indicating transport parameters (e.g., Kd).'
• Areal and cross sectional isoconcentration maps of primary
contaminants in soil and ground water.
• Time-series graphs of contaminant concentrations.
• Relevant source-term inventory information.
APPRAISAL
Yes














No














Comments














CHAPTER 4
MODEL APPLICATION
Section
(4.1) SCOPING ANALYSIS
Are scoping analyses performed?
Do scoping results lead to proposed modeling approach?
(4.2) SITE CHARACTERIZATION MODELING
(4.2.1) Code Selection
Is the rationale for the selection clearly presented for proposed code(s)?
Are the general features of the code(s) presented?
Are the assumptions and limitations of the code(s) presented and
compared to the conceptual model?
























         5-10

-------
Table 5-1 (Continued)
MODELING AND EVALUATION CRITERIA
Is the basis for regulatory acceptance presented?
Is the source documentation for the code included?
Is an executable version of the code included?
Is the source code readily available for inspection?
Does the code have a history of use?
Is the code well documented?
Is the code adequately tested?
Are the hardware requirements compatible with those available?
(4.2.2) Model Construction
(4.2.2.1) Layering and Gridding:
Is the domain of the grid large enough so that the boundaries will not
interfere with the results?
Do the nodes fall near pumping centers on existing and potential future
wells and along the boundaries?
Is the grid oriented along the principal axes of hydraulic conductivity?
Is the grid discretized at the scale appropriate for the problem?
Are areas of sharp contrasts (e.g., hydraulic conductivity, concentration,
gradient) more finely discretized?
Is the Peclet number less than 2?
Do adjacent elements vary in size by a distance less than a factor of 1.5?
Are strong vertical gradients within a single aquifer accommodated by
multiple planes or layers of nodes?
If matrix diffusion is important, are the confining units adequately
discretized in the relevant regions of the model?
Is the grid more finely spaced along the longitudinal direction of
simulated contaminant plumes?
Is the aspect ratio less than 100:1?
Are the following figures included:
• Grid presented as an overlay of a map of the area to be modeled.
• A vertical cross section(s) which displays the vertical layering of the
model grid.
(4.2.2.2) Boundary and Initial Conditions
APPRAISAL
Yes

























No

























Comments

























         5-11

-------
Table 5-1 (Continued)
MODELING AND EVALUATION CRITERIA
Is justification provided for the selection of all boundary and initial
conditions?
Are model boundaries consistent with natural hydrologic features?
Are the boundary and initial conditions consistent with the conceptual
model?
Are the uncertainties associated with the boundaries and initial conditions
addressed?
Are the boundaries far enough away from any pumping/injection centered
to prevent "boundary effects"?
Are transient boundaries discussed?
Is the rationale given for simplifying the boundaries from the conceptual
model discussed?
Are the values for the assigned boundaries presented?
(4.2.2.3) Specification of Time Steps
Is the Courant criterion satisfied?
(4.2.2.4) Model Parameterization
Are data input requirements fully described?
Is the discussion of the data well founded with respect to Objectives and
Data Review Section?
Are the interpretation and extrapolation methods (e.g. , Kriging)
adequately presented?
Do the figures and tables completely describe the data input with respect
to discrete components of the model?
Are the model parameters within the range of reported or measured
values?
(4.2.3) MODEL CALIBRATION
Has calibration been attempted?
Is the rationale for model calibration approach presented?
Are the calibration procedures described in detail?
Are the calibration criteria presented?
Does the calibration satisfactorily meet specified criteria?
Is the rationale presented for selecting convergence criteria?
Are code convergences and numerical instabilities discussed?
Do the calibrated parameters fall within their expected ranges?
APPRAISAL
Yes

























No

























Comments

























         5-12

-------
Table 5-1 (Continued)
MODELING AND EVALUATION CRITERIA
Are discrepancies explained?
Has the calibration been tested against actual field data?
Are the differences between steady-state and transient calibrations
presented?
Could other sets or parameters have calibrated the code just as well? Is
this discussed?
Are areal and cross-sectional representations of the final calibrated
results included for both hydraulic heads and radionuclide plume(s)?
Does calibration of the model take into account the inconsistency between
point measurements at wells and areal averages of model output?
Is the match between the calibration targets and final parameters shown
diagrammatically?
Were calibrating errors presented quantitatively through the use of
descriptive statistics?
If particle-tracking was performed, are these results shown?
Is the calibrated model consistent with the conceptual model?
Are any changes to the conceptual model discussed and justified?
Is non-uniform areal recharge applied? Is this approach justified?
Does the calibration properly account for vertical gradients?
Is the calibrated hydraulic conductivity field consistent with the geologic
logs and aquifer stress tests?
Are the convergence criteria appropriate?
Was a mass balance performed?
Is the water-balance error less than 1%?
Are the mass balance results for the calibrated model discussed?
Is the model's water balance consistent with known flows of rivers and
levels of lakes?
APPRAISAL
Yes



















No



















Comments



















         5-13

-------
Table 5-1 (Continued)
MODELING AND EVALUATION CRITERIA
(4.2.4) SENSITIVITY ANALYSES
Was a sensitivity analysis performed?
Is the approach to the sensitivity analysis detailed?
Were all input parameters selected for investigation?
If not, was rationale presented for excluding parameters?
Was a sensitivity analysis performed on the boundary conditions?
Are the ranges of parameters appropriate?
Were sufficient simulations performed? Was justification provided?
Was the relevance of the sensitivity analysis results to the overall project
objectives discussed?
Are the results presented so that they are easy to interpret?
Were sensitivity analyses performed for both the calibration and the
predictive simulations?
APPRAISAL
Yes










No










Comments










         5-14

-------
                                  6.  REFERENCES

ASTM84     Am. Soc. for Testing and Materials (ASTM), 1984. Standard Practaices for
             Evaluating Environmental Fate Models of Chemicals. Annual Book of ASTM
             Standards, E 978-84, Am. Soc. for Testing and Materials, Philadelphia,
             Pennsylvania.

BRY87      Bryant, J.L., and N.P. Wilburn, 1987. Handbook of Software Quality Assurance
             techniques Applicable to the Nuclear Industry.  NUREG/CR-4640, Off. of
             Nuclear Reactor Regulation, U.S. NUclear Regulatory Commission, Washington,
             D.C.

D-5447      Standard Guide for Application of a Ground-Water Flow Model to a Site-Specific
             Problem. ASTM (in preparation).

D-5490      Standard Guide for Comparing Ground-Water Flow Model Simulations to Site-
             Specific Information. ASTM (in preparation).

D-5609      Standard Guide for Defining Boundary Conditions in Ground-Water Modeling.
             ASTM (in preparation).

D-5610      Standard Guide for Defining Initial Conditions in Ground-Water Modeling.
             ASTM (in preparation).

D-5611      Standard Guide for Conducting a Sensitivity Analysis for a Ground-Water Flow
             Model Application. ASTM (in preparation).

D-5718      Standard Guide for Documenting a Ground-Water Flow Model Application.
             ASTM (in preparation).

D-5719      Standard Guide for Simulating Subsurface Air Flow using Ground-Water Flow
             Modeling Techniques.  ASTM (in preparation).

DAS77      Dass, P., G.R. Tamke, and C.M. Stoffel.  1977.  "Leachate Production at Sanitary
             Landfills,"  J. Environ. Eng. Division.. Proc. ASCE 103  (EEG).

EPA87       Environmental Protection Agency, 1987. The Use of Models in Managing
             Ground-Water Protection Programs, EPA 600/8-87/003, January 1987.

EPA88a      Environmental Protection Agency, 1988. Selection Criteria for Mathematical
             Models Used in Exposure Assessments: Ground-Water Models, EPA/600/8-
             88/075,  May 1988.

EPA88b      Environmental Protection Agency, 1988. Groundwater Modeling: An Overview
                                         6-1

-------
EPA89
and Status Report, EPA/600/2-89/028, December 1988.

Environmental Protection Agency, 1989. Exposure Factors Handbook,
EPA/600/8-89/043.
EPA91       Environmental Protection Agency, 1991. Risk Assessment Guidance for
             Superfund. Volume 1, Human Health Evaluation Manual. Part B, Development
             of Risk Based Preliminary Remediation Goals, PB92-963333.

EPA94a      Environmental Protection Agency, 1994. Report of the Agency Task Force on
             Environmental Regulatory Modeling, EPA 500-R-94-001, March 1994.

EPA94b      Environmental Protection Agency, 1994. Assessment Framework for Ground-
             Water Model Applications, EPA 500-B-94-003, July 1994.

EPA94c      Environmental Protection Agency, 1994. Ground-Water Modeling Compendium
             - Second Edition. Model Fact Sheets, Descriptions, Applications and Cost
             Guidelines, EPA 500-B-94-004, July 1994.

EPA94d      Environmental Protection Agency, 1994. Guidance for Conducting External Peer
             Review of Environmental Regulatory Models, EPA 100-B-94-001, July 1994.

FEDSIM81   Federal Computer Perfromance Evaluation and Simulation Center (FEDSIM),
             1981. Computer Model Documentation Guide.  NBS Special Publ. 500-73, Inst.
             for Computer Science and Technology, Nat. Bur. of Standards, U.S. Dept. of
             Commerce, Washington, D.C.

FEI75        Fein, D.G., K.J. Hanley and T.V. DeGeare.  1975.  Use of the Water Balance
             Method for Predicting Leachate Generation from Solid Waste Disposal Sites.
             SW-168, U.S. Environmental Protection Agency, Washington, D.C.

FRE79       Freeze, R.A. and J. Cherry, 1979. Groundwater. Prentice-Hall, Englewood Cliffs,
             N.J.

GAS79       Gass, S.I., 1979. Computer Model Documenation: A Review and an Approach.
             NBS Special Publ. 500-39, Inst. for Computer Science and Technology, Nat. Bur.
             of Standards, U.S. Dept. of Commerce, Washington,  D.C.

HEI92        van der Heijde, P.K.M., and O.A. Elnawawy, 1992. Compilation of Ground-
             Water Models.  GWMI 91-106. International Ground Water Modeling Center,
             Colorado School of Mines, Golden, Colorado.

HEI89        van der Heijde, P.K.M., 1989. Quality assurance and Quality Control in Ground-
             Water Modeling GWMI 89-04. Internal. Ground Water Modeing Center,
                                        6-2

-------
             Holcomb Research Inst, Indianapolis, Indiana.

KON92      Konikow, L.F., and J.D. Bredehoeft, 1992.  Ground-Water Models Cannont be
             Validated. Advances in Water Resources SWRENI 15(1): 75-83.

LEE95       Lee, Sang B., V. Ravi, J.R. Williams, D.S. Burden, 1995 "Evaluation of
             Subsurface Modeling Application at CERCLA/RCRA Sites," Subsurface Fluid-
             Flow (Ground-Water and Vadose Zone) Modeling. ASTM STP 1288. Joseph D.
             Ritchey and James O. Rumbaugh, Eds., American Society for Testing and
             Materials, Philadelphia, 1996.

PRI66        Price, H.S., J.C. Cavendish, and R.A. Varga, 1966. Numerical methods of higher
             order accuracy for diffusion convection equations. Society of Petroleum
             Engineers Journal pp. 293-303.

SCH83       Schroeder, P.R., A.C. Gibson, and M.D. Smolen, 1983. The Hvdrologic
             Evaluation of Landfill Performance (HELP) Model. U.S. Environmental
             Protection Agency, Cincinnati, Ohio.

SCH84       Schroeder, P.R., A.C. Gibson, and M.D. Smolen, 1984. The Hvdrologic
             Evaluation of Landfill Performance (HELP) Model. U.S. Environmental
             Protection Agency, Cincinnati, Ohio.

TAY85       Taylor, J.K., 1985. What is Quality Assurance? In: J.K. Taylor and T.W. Stanley
             (eds.), Quality Assurance for Environmental Measurements, pp. 5-11. ASTM
             Special Technical Publication 867, Am. Soc. for Testing and Materials,
             Philadelphia, Pennsylvania.

THO55       Thornthwaite, C.W., and J.R. Mather, 1955. "The Water Balance." Publications
             in Climatology. Vol. VIE, No. 1. Drexel Institute of Technology, Laboratory of
             Climatology, Centerton, New Jersey.

THO57       Thornthwaite, C.W., and J.R. Mather, 1957. "Instructions and Tables for
             Computing Potential Evapotranspiration and the Water Balance." Publications in
             Climatology. Vol. X, No. 3. Drexel Institute of Technology, Laboratory of
             Climatology, Centerton, New Jersey.
                                         6-3

-------
             APPENDIX A




FATE AND TRANSPORT OF RADIONUCLIDES

-------
                                Contents - Appendix A

A. 1    Physical Transport and Retardation Processes	 A-2
A.2    Chemical Transport and Retardation Processes	 A-5
A.3    References  	 A-14
                                         A-i

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            APPENDIX A. FATE AND TRANSPORT OF RADIONUCLIDES

The following discussion is intended to explicate the potential effects that simplifying
assumptions (e.g., K^) may have on the modeling results.

The nature of the ground water environment restricts the number of processes that control the
fate of radionuclides as they are transported from their source to the accessible environment.
These processes fall into two categories: radioactive decay and those processes related to
transport.  Transport-related processes (e.g., sorption, ion exchange, and precipitation) can
facilitate or retard the movement of ground-water contaminants, but radioactive decay always
results in a loss of activity of the original radionuclide.  Radioactive decay, however, can result in
an increase in radioactive or chemically toxic daughter products as the original radionuclide
disintegrates.

Various mechanical and geochemical processes will affect the transport of contaminants by flow
through either a porous matrix or a fracture system in a porous matrix. The mechanical processes
considered are advection, dispersive effects (hydrodynamic dispersion, channeling), and
diffusion.  Among the chemical processes considered in this paper are adsorption on mineral
surfaces, including the kinetics of adsorption, and processes leading to precipitation. Although
vapor transport is not always directly  associated with ground-water flow, the two processes are
closely related; therefore, gaseous transport is also  briefly discussed.  Furthermore, some
radionuclides can occur and migrate in the gaseous phase. Gas phase migration can therefore be
an important mechanism for some radionuclides to migrate from the repository to the accessible
environment. For example, radioactive carbon-14  can be in the form of carbon dioxide gas, and
tritium (radioactive hydrogen) can be in the form of hydrogen gas or tritiated water vapor.

A. 1    Physical Transport and Retardation Processes

In both saturated and partially saturated conditions, ground water can carry material along in
solution or as suspended solids.  The rate at which  the transported material moves is affected by a
variety of factors, the most important  being the velocity  of the flowing water and the partitioning
of the material between liquid (i.e., water) and solid (i.e., rock) phases. The dominant physical
processes  are advection, dispersive effects, and diffusion.

   (a) Advection and hydrodynamic dispersion. The process by which solutes are

                                           A-l

-------
transported by the bulk motion of water is known as advection.  There is a tendency, however,
for the solute to spread out from the path that it would be expected to follow according to the
advective hydraulics of the flow system. This spreading phenomenon is called hydrodynamic
dispersion. It causes dilution of the solute and occurs because of spatial variations in ground-
water flow velocities and mechanical mixing during fluid advection; molecular diffusion, due to
the thermal-kinetic energy of the solute particles, also contributes to the dispersion process.

Dispersion can result from diffusion, channeling, and turbulent flow, but dispersion by itself does
not affect the average rate at which the transported material moves. It can, however, cause some
of the contaminant (in a diluted state) to move faster than the average ground-water flow
velocity. This may be significant for radionuclides with relatively short decay half-lives; if some
of the radionuclide arrives relatively quickly at the accessible environment due to dispersion, it
will have higher radioactivity because of the shorter decay time.

Dispersion is generally responsible for the shape of the tracer-test breakthrough curves.  The low
concentrations of the radionuclides that mark the first arrival at the withdrawal well have been
dispersed ahead of the bulk or average ground-water velocity. The peak of the breakthrough
curve represents the average velocity of the contaminant (advection dominated), and the tail of
the breakthrough curve is formed by radionuclides that have been dispersed along longer flow
paths and at slower velocities than the average rate of ground water.

Dispersion is the primary mechanism responsible for dilution (mixing) processes in ground water
but is generally less significant than in air and in surface water.  In both air and surface water,
dispersive dilution is often a major phenomenon because the flow can be turbulent. Turbulent
flow means that all the flow paths are not essentially parallel to the gross direction of motion.
Flow components that are perpendicular to the bulk fluid motion cause the plume to spread
laterally not longitudinally, thus reducing the concentration in the plume, as the volume of
contaminated air or surface water increases. In ground water, however, the magnitude of dilution
is usually much smaller, partly because turbulent flow rarely exists.  The slow speed of ground
water, coupled with the effects of small channels in the intergranular pore space, tends to keep
the flow smooth and laminar. In an idealized conceptual model, the interconnecting pore spaces
can be thought of as forming flow channels  or tubes; any tendency for the flow to eddy is resisted
by the sides of the  flow channel.  However,  since the interconnecting pore spaces do not make a
continuous flow channel in real materials, there is some lateral mixing due to branching of flow
channels and spatial variation in flow velocity.

                                          A-2

-------
Dispersion (neglecting molecular diffusion) is not significantly affected by laminar eddy currents.
If molecular diffusion is momentarily disregarded, dispersion in porous or fractured media is
caused by five principal phenomena: anisotropic permeability, varying pore sizes, varying path
length, variation in the velocity gradient across pore space, and flow splitting around soil
particles with mixing within the pore space.  These five phenomena all contribute to longitudinal
dispersion; anisotropic permeability and flow splitting around the soil particles can cause lateral
dispersion. In nearly all ground-water systems, longitudinal dispersion effects are much larger
than lateral dispersion effects. Researchers have reported longitudinal dispersivity values
ranging from about 1 to 25 times higher than transverse dispersivity values (GELS5).  In
fractured systems, the longitudinal dispersivity would likely be much greater than the transverse.

   (b) Molecular diffusion. Diffusion in solutions is the process whereby ionic or molecular
constituents move under the influence of their kinetic activity in the direction of their
concentration gradient.  Molecular diffusion is a relatively slow process but also contributes to
the overall dispersion process, primarily through micro-scale mixing within individual pore or
fracture channels which leads to large-scale bulk dilution and spreading in very slow moving
ground water.

The  diffusion of radionuclides from water moving within fractures, or coarse-grained material,
into  the finer-grained rock matrix (i.e., matrix diffusion) can be an important means of slowing
the transport of the dissolved radionuclides, particularly for non-sorbing or low-sorbing soluble
species. The apparent diffusion coefficient for a given radionuclide depends on properties that
are intrinsic to the chemical species (e.g., ion mobility), as well as properties of the rocks (such
as porosity, tortuosity, and sorption ratios).

A radionuclide introduced into a fractured porous medium will migrate through the fracture
openings by means of advection as well as hydrodynamic dispersion. The radionuclide may also
diffuse slowly into the porous matrix. If molecular diffusion is occurring, it will  dominate flow
and transport within the porous matrix because the fluid velocity in the porous matrix is usually
very low.  When introduced into a fractured aquifer, the radionuclide moves rapidly within the
fracture network.  As time passes, the zone of contamination will diffuse farther into the porous
matrix.  Since the porous matrix has a very large capacity to store the contaminant, it plays a
significant role in retarding the advance of the concentration front in the fractures. If the source
of contamination is discontinued and the water-bearing unit is flushed by non-contaminated
water, the contaminant mass in the fractures will be removed relatively quickly, whereas the

                                           A-3

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contaminant in the porous matrix will be removed very slowly via diffusion back into the fracture
openings.

   (c) Gaseous transport. A limited number of radionuclides can form volatile species capable
of being transported in a moving vapor or gas. Among these are tritium, carbon-14, and iodine-
129. On a macroscopic scale, factors that affect transport in flowing ground water also affect
transport in flowing gas (i.e., the velocity of the gas determines the potential for advective
transport). In the absence of flow, diffusion is the only mechanism for transport in the gaseous
state. The processes of partitioning of the volatile species between the gaseous, liquid, and solid
state and isotopic exchange must also be considered when assessing the impact of gaseous
transport.

A.2    Chemical Transport and Retardation Processes

In addition to the physical processes, the transport of radionuclides is affected by a wide range of
chemical processes. Many of these reactions  are poorly understood and are the subject of on-
going research. From a practical view, the important aspect is the removal of solute from
solution irrespective of the process. For this reason, most computer codes simply lump all of the
cumulative effects of the geochemical processes into a single term (i.e., distribution coefficient-
Kd) which describes the degree to which the radionuclide is retarded relative to the ground water.
Thus, the distribution  coefficient relates the radionuclide concentration in solution to
concentrations adsorbed on the rocks.  The following paragraphs summarize the primary
geochemical processes that can play a role in the transport of radionuclides.

   (a) Sorption. An important mechanism in retarding the migration of radionuclides in ground
water is sorption, which is defined to include all solute-rock interactions that cause the
radionuclides to migrate at a slower rate than the ground water itself.  The amount of sorption is
dependent on both the chemistry of the water and of the rocks; because some of the chemical
reactions are relatively slow, it can be a function of time as well.

Sorption coefficients are usually obtained using a standard batch test where rocks or soils are put
in contact with ground water in which small amounts of dissolved radionuclides have been
mixed. A problem with this technique is that more  detailed geochemical data are necessary to
support the validity of applying the sorption measurement to the real-world physical and
chemical conditions and expected travel time of the radionuclides (which may be of the order of

                                           A-4

-------
hundreds to thousands of years).  Such mechanisms as dissolution/ precipitation, complexing,
adsorption/desorption, phase transformations, and solubility should be understood for
radionuclides of interest in the geochemical environment.

The tendency of a radionuclide dissolved in ground water to be sorbed by the aquifer's solid
phase can be expressed in terms of the soil/solution partition coefficient, Kd,  also referred to as a
distribution coefficient.  Kd is the simplest mathematical approach to adsorption and may be
derived from the Freundlich isotherm equation
                      x/m  = KdC1/n                                                 (1)
where x/m is the amount adsorbed (Ci chemical per gram of soil), and C is the concentration of
chemical Ci/ml in the aqueous phase. The value of 1/n depends on the sorbate and sorbent being
studied and is usually close to 1 (LYM82).

Sorption of radionuclides in the saturated zone will be due primarily to the high surface area (per
unit mass) of minerals such as clays.  Lipophilic substances tend to form films at water/solid
interfaces just as they do at the air/water interface. Thus, if the saturated zone contains clays or
other high surface area minerals, the ground water is presented with a large water/solid interface
on which some types of contaminants can form a surface film. Adsorption isotherms in which
sorption can be correlated with the surface area of the adsorbent are called Langmuir isotherms.
Adsorption phenomena of this type are not linear and can reach a saturation limit after which
further adsorption will not occur, even from water with greater concentrations of radionuclides.

Several variations of the adsorption isotherm equation are available for the fitting of empirical
data from experimental sorption studies (KIN86). The means for calculating sorption retardation
of dissolved inorganic radionuclides is similar to the method used for computing retardation of
organic contaminants by soil carbon content and octanol/water partition  coefficients. The
distribution coefficient for a specific radionuclide depends in part on chemical composition of
aqueous solutions. Thus, for a given geologic material, a radionuclide can have a wide range of
distribution coefficients, depending on the total chemical characteristics  of the water.
Limitations of the distribution-coefficient approach to geologic investigations include:

    •   The assumption of a linear sorption isotherm. The terms "sorption isotherm," "Freundlich
       isotherm," or "Langmuir isotherm" are generally used to define the relationships between

                                           A-5

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       sorption and the concentration of the element being sorbed at a constant temperature.

   •   Total reversibility in the sorption/desorption reaction is assumed. However, the
       distribution between the solid phase and the aqueous phase may include precipitation or
       irreversible reactions or both.

   •   Sorption/desorption reactions are generally assumed to be instantaneous. However, in
       some cases the reaction rate may be too slow to justify that assumption.

   •   The aqueous-phase speciation is not well known for many of the radionuclides.

These limitations do not necessarily apply to all of the radionuclides. For example, the solution
chemistry of the alkaline earths (Cs, Ra, and Sr) is well known, and the aqueous-phase species
can be predicted with relatively high certainty provided that the nature of the soil and rocks is
known. When measured sorption values are very high or very low, the range of individual
measurements may be quite large. A very high or very low Kd indicates that one phase, either the
solution or the solid, has very little of the radionuclide present; therefore, very few detectible
radioactive disintegrations occur, giving rise to relative high potential counting errors compared
to those obtained where sorption ratios are close to unity.

   (b) Ion exchange phenomena.  Ion exchange is one of several possible sorption processes. It
is a particularly important process for many common cationic radionuclides and therefore
deserves separate focus.  The primary retardation mechanisms for both organic and inorganic
ionic contaminants in ground-water systems are ion exchange and precipitation.  Ion exchange is
primarily effective on cations (positively charged ions), although in certain hydrogeochemical
environments anions are also retarded by ion exchange.  Ion exchange capacity within a geologic
material is almost exclusively limited to colloidal clay and silica particles (diameters in the range
10~3 to 10~6 mm), because these particles have a large ionic charge relative to their surface areas.
This charge is the result  of (1) cationic substitutions within the crystal lattice and (2) ionic
dissociation at the surface.  To neutralize this charge, an adsorbed layer of cations and anions
forms a zone adjacent to the hydroxylated layer (PAR67).  The net charge of this zone can be
negative or positive, depending on the pH of the immediate environment. At low pH, a
positively charged surface prevails; at neutral to high pH, a negatively charged surface develops
(FRE79).  The tendency for sorption of either cations or anions therefore depends on the pH.
Most natural ground-water systems have a pH in the neutral to positive range. Therefore, most
systems tend to have a stronger tendency for cation exchange than for anion exchange.
                                           A-6

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Neutralized colloidal particles maybe transported in the ground water with organic and inorganic
contaminants on their surfaces. Additionally, humic substances can exist as colloidal particles
and also serve as ion exchangers. Some radionuclide species such as plutonium and other
transuranic elements have been reported to exist as suspended colloids (CLE81). Some
contaminants that might otherwise be sorbed to stationary material in the aquifer could be
transported in the sorbed layers of these mobile colloids. Sorption in this case has facilitated
transport.  The cation exchange capacity (CEC) of soils and other geological materials is usually
expressed as the number of milliequivalents of cations that can be exchanged in a sample with
dry mass of 100 grams.

   (c) Speciation. The solubility of the waste elements can influence their transport by limiting
the maximum concentration of the elements dissolved in the aqueous phase. Speciation, defined
as the formation of various complexes and oxidation states in the aqueous phase, in turn affects
the solubility and mobility.  Speciation and solubility of individual waste elements depend on the
chemical properties of the waste element, on the state of the local water (composition, pH,
oxidation state, and temperature), and, if nonequilibrium processes are important, on factors such
as precipitation and dissolution kinetics, oxidation-reduction kinetics, the identity of the solids
present, water-flow conditions, and colloid formation.

Elements dissolved in water can exist as various chemical species such as different oxidation
states or complexes with other ions in water (STU81). Solubility generally increases as the
variety and concentration of complexes of an element increase; thus, the solubility is influenced
by the tendency of a given element to form complexes and the concentrations of species with
which it can complex. Sorptive behavior depends on the size and charge of the sorbing species;
both of these quantities vary among the complexes of a given element. Thus, speciation can
influence sorption.  Plutonium, for example, can exist at several different oxidation states in
either a cationic or anionic form.  It can also be complexed with various other ionic species such
as carbonate. Each of the various species may have different solubility and mobility
characteristics.

Aqueous species of most elements can be experimentally detected in solution by a number of
techniques; spectroscopy is most commonly used.  However, concentrations of aqueous species
are normally calculated from a knowledge of the overall composition of the solution (total
concentrations of the elements in solution) and the formation constants of possible aqueous
species using equilibrium thermodynamic methods. Equilibrium thermodynamic methods work

                                           A-7

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well (given the proper data) for the various complexes of a particular oxidation state, but may
yield inaccurate results for the distribution of the element among possible oxidation states
(LIN84).

   (d) Precipitation (phase separation from ground water). After a radionuclide has entered
the ground water, changes in the temperature, pH, and other chemical constituents may bring
about precipitation (i.e., phase separation) of the intruding radionuclide. The solubility of most
radionuclides varies directly with the temperature, and the groundwater's level of acidity can also
affect the solubility (SPO81). If an element can also exist in various oxidation states, variables
that control oxidation-reduction behavior also influence solubility. Unlike complex formation,
which is essentially always an equilibrium process, precipitation processes are often not in
equilibrium or in metastable equilibrium (STU81). If dissolution and precipitation kinetics are
relatively rapid, over the time frame of interest, equilibrium behavior can be assumed.  If kinetics
are very slow, a metastable equilibrium may exist where the aqueous phase is in metastable
equilibrium with some solid other than the most stable (least soluble) one.  In some intermediate
cases, the dissolution or precipitation rates maybe comparable to  the time scale of interest; for
these cases, kinetic data are required to describe aqueous concentrations accurately.

Coprecipitation refers to a group of processes whereby more than one compound precipitates at
one time (SPO81). Three examples are mixed-solid  formation, adsorption during precipitation,
and inclusion during precipitation.

   (e) Natural colloid formation. A number of actinides, plutonium in particular, can form
natural colloids under  conditions  of near neutral solutions of low ionic strength (AVO84).
These colloids are optically clear in solution, show a characteristic adsorption spectrum, and do
not settle out of solution. Colloidal plutonium shows x-ray diffraction patterns similar to
crystalline plutonium dioxide; higher order lines are missing, indicating small crystalline size (20
to 30 angstroms).  There is also some indication that americium may form colloids under similar
conditions (OLO84).

A possible mode of radionuclide transport involves the movement of radioactive particles
suspended in the ground water.  Colloidal particles (up to 0.5 micrometers in diameter) remain
suspended for long periods and hence may migrate with the ground water.  As the solid waste
form is leached, particles containing radionuclides may form by the sorption of dissolved
radionuclides on nonradioactive particles.

                                           A-8

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To estimate the amount of radionuclides that can be transported by colloidal suspension, it is first
necessary to determine whether colloidal-sized particles exist in the ground water.  Then, the
sorption ratios for waste elements on these particles must be measured or estimated from the
composition of the particles. In addition, the conditions under which colloids can form from the
waste elements or from the waste and their stability after formation must be determined. Finally,
the conditions necessary for the filtration or sorption of the particles by the rock matrix itself
must be defined.

Matter in the colloidal state has a relatively large surface area; thus the most important properties
of colloids  are those that depend on surface interactions, such as adsorption. Drever (DRE82)
discusses the nature and geochemistry of colloids, with emphasis on the charge surrounding
colloids and its effect on suspension stability.

Olofsson et. al. (OLO81) classify radiocolloids (colloids containing radionuclides)  as true
colloids or  pseudocolloids depending on their formation process.  True colloids are formed by
condensation of molecules or ions as a result of hydrolytic or precipitation processes. Colloids
consist mostly of hydroxides or polymers formed by hydrolysis, and they have a very rapid
formation rate. Pseudocolloids, on the other hand, are formed as a result of adsorption on
impurities in the solution and tend to be much larger than true colloids.  Pseudocolloids can be of
two types, reversible and irreversible.  The formation rate of pseudocolloids is basically
determined by the sorption rate on colloidal impurities (OLO82).

Radiocolloids are believed to be a significant factor for the transport of radionuclides in some
environments and might facilitate their transport away from the source area (AVO82).
Radiocolloids may arise from a variety of sources.  The corrosion of metal containers can lead to
the formation of absorbent colloids. Degradation of engineered backfills may also  lead to
colloidal formation.  If the waste form is leached by ground water, naturally occurring colloids
derived from smectites, vermiculites, illites, kaolinite,  and chlorite present in groundwater may
also adsorb radionuclides. Champ et. al. (CHA82)  have demonstrated experimentally the
existence of rapid transport of plutonium colloids using core samples and ground water.

Transport of particulates in geologic media will depend on aqueous flow rate, on pore and
fracture size in the rock, on ions carried in the water, and on the nature of the particulate matter.
Several mechanisms may remove colloidal particulates from ground water such as mechanical
filtration by the rock matrix, sorption on the surface of the rock pores (van der Waals forces), and

                                           A-9

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neutralization of the repulsive charges on the colloids, thus allowing them to coagulate. In
addition, colloids will be subject to gravitational settling for particles larger than about 0.1
micrometer (TRA87).

   (f)  Radiolysis. Radiation can affect the solubility of waste elements by altering the
composition of the water or by influencing the crystallinity of the solids that form (AUS69). The
primary effect of gamma radiation will be a reduction in water pH and a trend toward more
oxidizing conditions as long as air is present; secondary effects will be the production of nitrate
(or nitrite) anions if nitrogen is present.  Gamma-emitting radionuclides tend to be relatively
short-lived and will be most important early in the life of a repository and, if ground water travel
rates are slow, will have the greatest effect on the water near the waste.

Alpha radiation can affect water compositions in ways that are similar to the effects of gamma
radiation. The primary effects of alpha radiation are a decrease in pH and a trend toward more
oxidizing conditions in the water.  Solids composed of alpha-emitters tend to show self-
irradiation damage to their crystal structure; the solubilities of solids like the actinide  oxides and
hydroxides are affected in that amorphous solids, which are generally more soluble than
crystalline solids, are more likely to be the natural precipitation products (NIT85).  Some alpha-
emitters are relatively long-lived and maybe of concern for hundreds or thousands  of years.
Neutron radiation can have effects on other elements through neutron capture reactions.
However, these effects are generally only significant near the source of strong neutron-emitters
and would not be expected to affect ground-water chemistry or the migration of radionuclides
downgradient, away from the waste source. Beta radiation is relatively weak and similarly would
not be expected to have significant effects on ground-water chemistry or radionuclide migration
away from  the immediate vicinity of the source.

   (g) Biofixation.  A mechanism that appears to affect the transport of radionuclides under
some conditions is microbial fixation (WES84).  Radionuclides may be immobilized and/or
mobilized by organisms in the repository environment. Immobilization may occur if
radionuclides are incorporated into the cell structure of microorganisms or plants that are
relatively stationary.  On the other hand, radionuclides may be mobilized by forming biocolloids
with bacteria, spores, and viruses.

   (h) Natural organic matter interactions. Organic matter, in some instances, plays a
significant role in the transport of radionuclides (LEV79). Wastes in the repository will contain a

                                          A-10

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significant quantity of organic matter. The most important transport-related interactions between
organic matter and radionuclides are:

   •   Mobilization - Decomposition of organic material raises the partial pressure of carbon
       dioxide (CO2) in ground water and soil and adds organic CO2 and organic acids which
       leach and mobilize certain radionuclides (e.g., uranium).

   •   Transportation - Uranium can then be transported as bicarbonate anion or as soluble
       organic complex in ground water.

   •   Concentration - The humic acid can precipitate in ground water when pH becomes more
       acidic or where increased salt content is encountered. The humic acids can exchange or
       chelate uranium. Concentration factors greater than 10,000 times that of the ground water
       have been observed on the organic material.

   (i)  Anion exclusion. The negative charge present on many mineral surfaces can repel the
approach of anions. The exclusion may limit the diffusion of anions into the matrix, thereby
allowing the anions to move at the higher velocity of the water moving in the center of the
fractures or intergranular pore space, away from the surface film.  The same phenomenon can
restrict the entry of anions into the smaller pores.  This process is significant to the transport of
radionuclides because negatively charged radiocolloids could potentially move faster than the
average rate of the ground water. Under some geochemical conditions (i.e., very low pH),
mineral surfaces may assume a more positive charge and thus repel cations rather than anions
and cause the cations to move faster than the average ground- water rate.

   (j)  Organic complexation. Natural and anthropogenic organic colloids occurring in the
subsurface can act as a sorbent for radionuclides in adsorption-desorption and cation exchange
processes. This association of radionuclides with organic matter is a relationship that has been
well documented in both the field and laboratory.  Due to the large surface area per unit mass and
anionic surface functional groups associated with  some organic colloidal material, radionuclides
have a significant potential to be adsorbed. If the  radionuclide is adsorbed onto mobil colloidal
matter, the radionuclide may be transported as a colloid.

The chemical and/or physical reaction which influences the radionuclide complexation with
organic colloids will vary considerably with a number of experimental variables. Complexation
increases at higher pH's and high humic substance concentrations and decreases at high ionic
strengths.

                                          A-ll

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The chemical and/or physical reaction which influences the radionuclide complexation with
organic colloids is a reversible process. Parameters that influence reversibility include:
pH, ionic strength, and radionuclide and organic compound concentrations.  Complexation
reversibility may be an important factor when ground water from various flow regions mix
together in common hydrogeological units.  When complexation reactions are reversed, the fate
and transport mechanisms associated with the complexation may change accordingly.
                                         A-12

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A. 3    References

AUS69      Ausloos, P., 1969. Fundamental Processes in Radiation Chemistry. Interscience
             Publishers, New York, pp. 651-685.

AVO84      Avogadro, A., and G. DeMarsily, 1984. "The Role of Colloids in Nuclear Waste
             Disposal," in Scientific Symposia Proceedings. Boston. Massachusetts. November
             1983. G.L.  McVay (ed.), Vol. 25, North-Holland, Elsevier Science Publishing
             Co., Inc., New York, pp. 405-505.

AVO82      Avogadro, A., and F. Lanza, 1982.  "Relationship Between Glass Leaching
             Mechanism and Geochemical Transport of Radionuclides," in Scientific Basis
             Proceedings. Berlin. Germany. June 7-10. 1982. W. Lutze (ed.), Vol. 5, North-
             Holland, Elsevier Science Publishing Co., Inc., New York, pp. 103-112.

CHA82      Champ, D.R, W.F. Merritt, and J.L. Young, 1982.  "Potential for the Rapid
             Transport of Plutonium in Groundwater as Demonstrated by Core Column
             Studies," in Scientific Basis for Nuclear Waste Management V. Materials
             Research Society Symposia Proceedings. Berlin. Germany. June 7-10. 1982. W.
             Lutze (ed.), Vol. 5, North-Holland, Elsevier Science Publishing Co., Inc., New
             York, pp. 745-754.

DRE82      Drever, J.L, 1982. "Colloid Properties." The Geochemistry of Natural Waters.
             Prentice Hall, New Jersey, pp. 78-79.

FRE79       Freeze, R.A. and J. Cherry, 1979.  Groundwater. Prentice-Hall, Englewood Cliffs,
             N.J.

GEL85       Gelhar, L.W., A. Montoglou, C. Welty, and K.R. Rehfeldt, 1985. A review of
             field-scale physical solute transport processes in saturated and unsaturated porous
             media. Palo Alto, CA: Electric Power Research Institute. EPRIEA-190. As
             cited in EPA88b.

KIN86 Kinniburgh, D.G.,  1986. General purpose adsorption isotherms, Environ. Sci. Technol.
       20:895-904.

LEV79       Leventhal, J.S., 1979.  Organic Matter and Sandstone-type Uranium Deposits:  A
             Primer, Open File Report 79-1310.

LIN84 Lindberg, R.D., and D.D. Runnells,  1984.  "Ground Water Redox Reactions: An Analysis
       of Equilibrium State Applied to Eh Measurements and Geochemical Modeling," Science.
       Vol. 225, pp. 925-927.
                                        A-13

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NIT85 Nitsche, H., andN.M. Edelstein, 1985. Determination of Solubilities and Complexation
       of Waste Radionuclides Pertinent to Geologic Disposal at the Nevada Tuff Site, LBL-
       18900, Lawrence Berkeley Laboratory, Berkeley, Calif.

OLO81      Olofsson, U., B. Allard, K. Andersson, and B. Torstenfelt, 1981.  Formation and
             Properties of Radiocolloids in Aqueous Solution—A Literature Survey. National
             Council for Radioactive Waste Report Prav 4.25, Department of Nuclear
             Chemistry, Chalmers University of Technology, Goteborg, Sweden.

OLO82      Olofsson, U., B. Allard, B. Torstenfelt, and K. Andersson, 1982.  "Properties and
             Mobilities of Actinide Colloids in Geologic Systems," in Scientific Basis for
             Nuclear Waste Management V. Materials Research Society Symposia
             Proceedings. Berlin. Germany. June 7-10. 1982. W. Lutze (ed.), Vol. 5, North-
             Holland, Elsevier Science Publishing Co., Inc., New York, pp. 755-764.

OLO84      Olofsson, U., M. Bengtsson, and B. Allard, 1984. "Generation and Transport
             Properties of Colloidal Tri- and Tetravalent Actinide Species in Geologic
             Environments," in Scientific Basis for Nuclear Waste Management VII. Materials
             Research Society Symposia Proceedings. Boston. Massachusetts. November 1983.
             G.L. McVay (ed.), Vol. 26, North-Holland, Elsevier Science Publishing Co., Inc.,
             New York, pp. 859-866.

PAR67      Parks, G.A., 1967.  Aqueous surface chemistry of oxides and complex oxide
             minerals. Equilibrium concepts in natural water systems. Washington, D.C:
             American Chemical Society, pp. 121-160.  As quoted in Freeze and Cherry
             (1979).

SPO81       Sposito, G., 1981. The Thermodynamics of Soil Solutions. Oxford Clarendon
             Press, New York, pp. 66-69, 95.

STU81       Stumm, W., and J.J. Morgan, 1981. Aquatic Chemistry. A Wiley-Interscience
             Publication, John Wiley & Sons, New York, pp. 8-9, 68-73, 94-95, 230-237, 248-
             263, 274-275, 323-325, 332-333, 348-351,  366-367, 418-421.

TRA87      Travis. B.J. andH.E. Nuttall, 1987. Two-Dimensional Numerical Simulation of
             Geochemical Transport in Yucca Mountain. LA-10532-MS, Los Alamos National
             Laboratory, Los Alamos, N. Mex.

WES84      West, J.M., and I.G. McKinley, 1984.  "The Geomicrobiology of Nuclear Waste
             Disposal," in Scientific Basis for Nuclear Waste Management VII. Materials
             Research Society Symposia Proceedings. Boston. Massachusetts. November 1983.
             G.L. McVay (ed.), Vol. 26, North-Holland, Elsevier Science Publishing Co., New
             York, pp. 487-494.
                                         A-14

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        APPENDIX B




SCOPING ANALYSIS PROCEDURES

-------
                                 Contents - Appendix B

                                                                                   Page

B. 1    Release Analysis - Ground Water 	B-l

B.2    Fate Analysis - Ground Water	B-5
   B.2.1      Estimations of Ground-water Concentration	B-5

B.3 Quantitative Fate Estimation 	B-6

B.4    Analytical Methods for Aquifer Flow and Transport  	B-l9
   B.4.1      Point Concentration Model  	B-21
   B.4.2      Flux Models	B-26
   B.4.3      Source Released from a Vertical Plane (x = 0)  	B-28
   B.4.4      Horizontal Area Source	B-28
   B.4.5      Generalization of Instantaneous Models 	B-29

B.5    Simplified Analytical Methods for Minimum Dilutions	B-30
   B.5.1      Dilution at Downgradient Wells in Confined Aquifers for an
       Instantaneous Point Source at the Surface	B-30
   B.5.2      Ground Water-Surface Water Interface-Instantaneous Source  	B-33
   B.5.3      Quantity of Released Radioactivity Crossing a Vertical Plane  	B-33
   B.5.4      Direct Ground-Water Usage  	B-34

B.6    References 	B-43

Figure B. 1     Idealized ground-water system for point concentration model, point
       source (COD83)	B-23

Figure B.2     Idealized ground-water system for point concentration model, horizontal
       line source (COD83)  	B-23

Figure B.3     Vertically averaged ground-water dispersion model (COD83)	B-25

Figure B.4     Concentration in downgradient wells for Example B.3	B-27

Figure B.5     Ground-water surface-water  interface, flux model 	B-27

Figure B.6     Flux of pollutant into river for Example B.4	B-29

Figure B.7     Mixing factor for confined aquifers	B-33
                                          B-i

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                 APPENDIX B - SCOPING ANALYSIS PROCEDURES

Prior to scoping calculations, the appropriate release mechanisms for the movement of
radionuclides to the ground water need to be determined. If it is relatively certain that one or
more transport mechanisms (e.g., unsaturated zone) is unimportant, than it may be neglected.
The physical and chemical processes that may affect the fate and transport of radionuclides at the
site (e.g., fracture flow, vapor transport) also need to be determined. A previous report issued as
part of this interagency agreement outlines how to determine what site related characteristics may
be important (EPA94).

Having made these determinations, it must then be decided how accurate the results need to be
and what level analysis is appropriate to obtain the desired results.  If the physical and chemical
processes at the site are complex and will not be satisfactrily predicted with simplistic data
analysis, then it may be necessary to consult with experts in the field regarding how to proceed.
It is not practical to perform complex analyses without the use of computer programs and
considerable expert help.

The calculational methods presented in this appendix have been divided into two parts:  the
release analysis and the fate analysis.  The equations in the release analysis section are used to
estimate contaminant release concentrations and volumetric release rates. The fate analysis deals
with the processes influencing radionuclide transport and how to estimate radionuclide
concentration in ground water.

B.I  Release Analysis - Ground Water

(1)    Estimating contaminant release concentration. The release concentration of a
       radionuclide depends upon characteristics of both the waste and the site.  For lagoons or
       impoundments, the concentration of the radionuclide in the lagoon or impoundment is
       considered to be the concentration of the leachate. For solid-waste disposal sites, the
       equilibrium solubility of the solid waste is generally used as the initial concentration, with
       the  assumption that the waste will have equilibrated with the percolating rainwater. This
       may not be the case, however, for all radionuclides.  Therefore, it may be necessary to
       estimate radionuclide concentrations as a function of the equilibrium partitioning between
       the  solid and solution, i.e., the distribution coefficient, Kd. The following formulae
       provide a means to estimate leachate concentration under equilibrium partitioning
       conditions.
                                           B-l

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                      wat~ A'Q'T+pK.
       Cwat    =      concentration in the leachate (Ci/m3-H20)
              MCi    =      amount of nuclide in source (Ci)
              A      =      area of the source (m2)
              T      =      thickness of the source (m)
              Kd     =      distribution coefficient (crrrVgr)
              p      =      bulk density (gr/cm2)
              0      =      volumetric water content


       where

                       0=0   * R                                                  re T\
                            sat   sat                                                \D~*-)

              QSat    =      total porosity
              RSat    =      saturation ratio


       Under saturated conditions Rsat = 1. Under unsaturated conditions, the saturation ratio is a
       function of the infiltration rate, the saturated hydraulic conductivity, and the texture of the
       soil.  The saturation ratio can be estimated using the following equation (CLA78):
                                    D   _ /   -i   v 2b+3
                                    J\  , — l 	 )
                                     sat  ^  if    '
                                             sat
       where
              /      =      infiltration rate (m/yr)
              Ksat    =      saturated hydraulic conductivity (m/yr), and
              b      =      soil-specific exponential parameter (dimensionless)

       Representative values ofKsat, Qsat and b for various soil textures are listed in Table C.2-
       C.4 (Appendix C).

(2)    Estimating volumetric release rate. The volume of leachate is calculated in two ways, one
       for solid wastes and one for liquid wastes. For solid wastes, percolating water (from
       direct precipitation and/or stormwater runoff onto the site) is frequently the primary
       source  of liquid. In some cases the waste may be buried below the water table so that

                                            B-2

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   direct contact with groundwater is the principal leaching mechanism.  The release rate to
   groundwater for radionuclides leaching from percolating precipitation through a buried
   source, can thus be calculated using the following equation:
                L  =
                 c
                                                                             (B-3)
   where
         Lc     =      contaminant release rate (Ci/day)
         /      =      infiltration rate (M/day)
         A      =      area of contributing source (M2)


   The release rate to ground water for leaching of wastes that are disposed of below the
   water table can be calculated using the following equation:
L. =  KiA  •
                  c
                                                                             (B-4)
   where
         K = hydraulic conductivity (M/day)
         i = hydraulic gradient (M/M)


   For liquid wastes (i.e., lagoons or surface impoundments), precipitation has a minimal
   effect, since the liquid wastes will percolate to ground water under the influence of
   gravity.  In this case, the rate of percolation depends on the permeability of the liner or the
   underlying or surrounding soil at the disposal site.  The volumetric release rate for liquid
   wastes can be estimated using the following equation (BOW79):

                   Q  =  Ks i  A                                              (B-5)

   where
         Q     =      volumetric flow rate (mVsec)
         Ks     =      Darcys coefficient; for unlined lagoons use native soil hydraulic
                       conductivity (m/sec)
         A     =      area of lagoon (m2).
i =
   The hydraulic gradient, i, is determined as follows:

                   Hydraulic head
                                                             (B-6)
      liner  thickness  or underlying soil

   The hydraulic head is the sum of the pressure and gravitational heads. In this case, it is


                                      B-3

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approximately equal to the depth from the top of the free liquid in the lagoon to the base
of the liner or soil layer from which the parameter Ks in Equation B-5 is obtained; the
liner thickness in Equation B-6 refers to the thickness of a liner when present, or for an
unlined system, the depth of the soil to the water table.  When the depth to the water table
is large relative to the depth of free liquid in the lagoon, the hydraulic gradient will be
approximately equal to 1 .0. Alternatively, for systems with a thin liner and an
appreciable depth of free liquid, the hydraulic gradient can be much greater.

The Q, in Equation B-5, is then used to estimate activity release with the following
equation:
                  L  = M  2                                                (B-7)
                   c     c
where
       Lc     =      contaminant release rate (Ci/day)
       Mc     =      contaminant concentration in lagoon fluid (Ci/m3)
       Q     =      volume release rate (mVday).

Equations B-5 and B-7 model the release rate from a lagoon regardless of whether the
flow is saturated or unsaturated.  For unlined active lagoons, the flow is typically
saturated all the way to the water table. For clay-lined lagoons, the flow is saturated
through the liner and unsaturated between the liner and the water table. Equations

B-5 and B-7 are appropriate when lagoon releases are analyzed but should not be used for
spills or other conditions where there is no ponding of the radionuclides on the surface for
a long period of time.  Under these conditions, the assumption of saturated flow (through
the liner or soil) may be violated.

Equations B-4 and B-6 apply to liquids that are mostly water.  The hydraulic conductivity
is defined in terms of the fluid properties density and viscosity. For liquids with a density
or viscosity that differs from water, Ks can be corrected for this viscosity and density by
calculating the term IQ, using the following:
         K  =
          c
                                                                            (B-8)
where
       Kc     =      corrected Kg term = hydraulic conductivity of liquid contaminant
                     (m/sec)

                                    B-4

-------
              Kw     =      hydraulic conductivity for water (m/sec)
              p      =      density of liquids; c = non-aqueous; w = water (mg/liter)
              \i      =      dynamic viscosity of liquids; c = non-aqueous; w = water;
                            (mg/m/sec).

       and then substituting Kc for Ks in Equation B-5. For waste sites that are lined with
       flexible membrane liners (FML), the release rate depends on the characteristics of the
       contaminant as well as the liner (STE78).  Liners that have been in place for long periods
       of time or otherwise subjected to significant chemical, radiological, physical, or
       geological degradation processes may have significantly greater permeation properties
       than in their original undergraded state.

B.2    Fate Analysis - Ground Water

The nature of the ground-water environment restricts the number of processes that control the
fate of radionuclides as they are transported from their source to the receptor area. These
processes fall into two categories:  radioactive decay and transport processes.  Transport-related
processes (i.e., sorption, ion exchange, and precipitation of solids) can facilitate or retard the
movement of ground-water contaminants, but radioactive decay always results in a loss of
activity (disintegrations or decays per second) of the original radionuclide. However, radioactive
decay can result in an increase in radioactive or chemically toxic daughter products as the parent
radionuclide disintegrates.

B.2.1 Estimations of Ground-water Concentration

There are several different approaches to estimating the concentration of a radionuclide at the
receptor if radioactive decay is the only process affecting concentrations (i.e., no dilution).  One
approach is based on the  proportionality of volume and concentration of the waste versus those
of ground water.

If limited ground-water monitoring data at the release point are available and sufficient
environmental fate data are available to calculate an overall dilution rate (see Section B.3),  the
concentration at the receptor well can be calculated.

The concentration of a decaying substance at the selected point downgradient from the release
point is given by the following equation:

                                           B-5

-------
                    C    =C   -e     <                                             '
                     well   wat e

       where
              Cwe//   =     concentration at downgradient distance x (Ci/m3)
              Cwat   =     leachate concentration (Ci/m3-H20)
              e     =     2.71828
              x     =     distance downgradient from point of introduction (m)
              Vc    =     contaminant velocity (m/yr)
              A     =     the radioactive decay constant which is equal to Hr\2 /half-life of the
                           isotope (yr"1 for A).

In the absence of ground-water monitoring data, mathematical models are often used to estimate
concentrations of contaminants in ground water at receptor wells or discharge points. Two
general classes of models can be used for this purpose:  numerical and analytical.  Numerical
models use various numerical analysis methods to solve the partial differential equations of flow
and transport.  Analytical models generally consist of algebraic equations which approximate the
true solution of the differential equations. Both approaches have advantages, disadvantages, and
limitations. For the purpose of scoping calculations, only analytical models will be considered
(Section B.4).

B.3    Quantitative Fate Estimation

Radioactive releases may travel in the unsaturated zone before entering the  zone of saturation.
However, the release can also be  directly into the zone of saturation.  The predominant direction
of the unsaturated zone flow is downward until the flow reaches the zone of saturation.  Within
the zone of saturation, the flow is predominantly lateral. Ground-water velocity can be
determined for both the vadose (unsaturated) and saturated zones and is examined in the next
section.

(1)    Equations for ground-water flow  and radioactivity transport.  The movement of
       radionuclides in ground water can be described by two equations: one for the movement
       of the carrier fluid (water) and one for the mass transport of the dissolved constituents
       (radionuclides). In using  these equations, the movement of the water in the region under
       consideration must be known before the transport equation can be solved.
                                           B-6

-------
(a)     Unsaturated flow. The most significant nongaseous contaminant movement in
       soils is a function of liquid movement.  Vapor phase movement can be significant
       for certain volatile contaminants (e.g., tritium and carbon-14).  Soluble solid
       radionuclides dissolved in rainwater, surface run-off onto the site, or water
       applied through human activity will percolate into the soil.  After rainwater
       infiltrates the surface of the ground, it generally travels vertically downward
       through the unsaturated zone (vadose zone) under the influence of gravity and
       capillary forces until it reaches the water table.

       The movement of water through partially saturated soil is described by Richards
       equation, which can be written for an incompressible soil medium as

        —  = V(Kkr  (Q))_yh + Vz                                     (B-10)
       where
              0     =      volumetric water content
              h     =      pressure head (length)
              z     =      elevation above datum (length)

              K     =      saturated hydraulic conductivity tensor (length/time)

              kr     =      relative permeability
              t      =      time (time)
              V     =      divergence operator.

       Solving Equation B-10 to predict rates of water flow and changes in water content
       in a soil, is best accomplished by using a numerical computer model. A variety of
       such models exist for simulating one, two, and three dimensional unsaturated flow
       problems.

       While computer modeling is often an integral part of exposure assessment
       analysis, utilization of complex computer models can require a very skilled and
       experienced modeler. Another consideration is that the prediction accuracy of
       models is often compromised since key parameters (e.g., soil hydraulic
       characteristics, heterogeneity), are imperfectly known, and values may have to be
       estimated from literature references in the absence of actual site-specific

                                    B-7

-------
measurements.

For these reasons, reliance on relatively simple approaches for determining travel
times through the unsaturated (vadose) zone may be justified.  The interstitial pore
water velocity for transport through the unsaturated zone can be calculated from
the average percolation or recharge rate as follows (ENF82):

            VPW =   -f                                                (B-ll)

where
       Vpw    =     interstitial ground-water (pore water) velocity (length per
                    unit time)
       /      =     average infiltration or recharge rate which is the volumetric
                    flow rate per unit area per unit time
       0      =     average volumetric water content of the unsaturated zone
                    (decimal fraction, representing volume of water per volume
                    of soil).
In general, the flow rate q varies with time, for instance, in response to
atmospheric conditions (rainfall) or man-induced hydraulic loadings.  The soil
water content 0 will vary with time and also with depth.  However, for the
purposes of estimating travel times, the use of time-averaged flow rates and water
contents may be justified.  Under steady-state flow conditions, the volumetric
water content, 0, of the soil will approach a constant and spatially uniform value,
that the soil can support the imposed flow rate, I; i.e., the hydraulic conductivity
of the soil under the unsaturated conditions will be equal to the flow rate, I:
           I =  K_k

where
(B-12)
       Ks     =      vertical hydraulic conductivity of soil under saturated
                     conductivity (length/time)

The relative hydraulic conductivity, kr, is generally obtained from an equation that
describes the dependence of hydraulic conductivity or soil water content. One
commonly used expression is the Brooks-Corey relation:
                    2b+ 3
                                                                    (B-13)
                             B-S

-------
where
       Qs     =      volumetric water content of soil under saturated conditions
                     (porosity) (volume/volume)
       b      =      pore size index (dimensionless)

Equations B-12 and B-13 can be combined to yield the following equation for the
average soil water content (CLA78):
      e =  e
Representative values of 0, b, and the term l/(2b+3) are listed in Tables C-l -  C-
4 (Appendix C).

The saturated volumetric water content, Qs, saturated hydraulic conductivity, Ks,
and the exponential coefficient, b, are all related to soil properties and are usually
different in different soil types. The most reliable values for these parameters are
empirical values (if available) measured at the site. Where empirical values are
unavailable, the values in Tables  C-l and C-2 provide guides for the rough
estimation of Qs and the  term l/(2b+3). Representative values of Ks from two
different sources are presented in Tables C-3 and C-4. These tables demonstrate
the variability in estimates for these values.

Theoretically, the value  of 0 cannot exceed Qs, which is the saturated soil moisture
content.  Note also that the percolation rate, /, cannot exceed the saturated
hydraulic conductivity, K^ for the site  soil. Whenever / > Ks (and therefore 0 as
calculated by Equation B-14 >  Qs) for the duration of the study period, it must be
assumed that saturated conditions exist and that saturated flow prevails.
Equations B-17 and B-18 in the next subsection provide a means of estimating
saturated flow velocities. Records of estimated percolation rates, /, for the site
locality during the time period in question (or annual average recharge rate
estimates) are often available from local hydrology, climate, or soil authorities,
including regional U.S. Geological Survey (USGS) and U.S. Soil Conservation
Service offices. The following equation can be used to estimate the term /
(ENF82):
   I =  HL + Pr -  ET -  Qr                                       (B-15)

                             B-9

-------
where
       /      =      average infiltration or recharge rate
       HL    =      hydraulic loading from manmade sources (length per unit
                     time), which is the flow rate divided by the contaminant
                     source area.
       Pr     =      precipitation (length per unit time)
       ET    =      evapotranspiration (length per unit time)
       Qr     =      runoff (length per unit time).

This estimation procedure can be used to evaluate infiltration rates, 7, at sites
where the information sources listed above cannot provide them directly.  This
estimation procedure requires data for precipitation, evapotranspiration, and
runoff rates.  In addition to the above sources,  the National Weather Service,
Forest Service offices, National Oceanic and Atmospheric Administration
(NOAA) gauging stations, or other first order weather stations (e.g., at local
airports) are possible sources for these three  types of data. The average
precipitation rate per unit time, Pr, for the study period can be obtained from
various local weather authorities such as those listed.

A value of ET for substitution into Equation B-15 can be estimated by using
measured Class A pan evaporation rates (a measure of local evaporation rates
under standardized conditions, available from  the nearest NOAA gauging station)
in the equation:
   ET =  EVAP x  cefc  x  cveg                                       (B-16)

where:

       EVAP =      region-specific or site-specific measured evaporation rates
                     (length per unit time)
       Cet    =      correction factor for converting measured pan evaporation
                     rates to evapotranspiration rates from turf grass (unitless)
       Cveg    =      correction factor for converting evapotranspiration from
                     turf grass to evapotranspiration from other vegetative cover
                     types (unitless).

Values for Cet are taken from Table C-7, which requires climatological and pan
descriptive information.
                             B-10

-------
       The term Cveg is used mainly for agricultural crops (Table C-8) and varies with the
       thickness, depth, and characteristics of vegetative cover. Typical values are 0.87
       for shorter broadleaf plants (alfalfa) to 0.6 for taller broadleaf plants (potatoes,
       sugar beets) and 0.6 for taller grains and grasses. Where crop-specific data are
       unavailable, a conservative default value for this term is the smallest reasonable
       value, or 0.6. ET rates can vary significantly,  of course, if vegetative cover varies.

       A value of Qr, or the average runoff over the study period, for input into Equation
       B-15, however, can generally be obtained from local USGS gauging stations. For
       relatively level sites, a reasonable conservative default value is Qr = 0, where site-
       specific data are unavailable or cannot be estimated.
       The above method for predicting the average velocity of water migrating through
       the unsaturated zone will in many cases yield reasonable approximations;
       however, heterogeneities, such as root holes and macropores, can result in faster
       velocities than predicted. The analyst is not expected to correct for this, yet it is
       important to be aware of the limitations of the method.

(b)    Saturated flow. Darcy's law may be used to describe the volumetric flow of
       water through a porous medium under saturated conditions. The volumetric flow
       (or discharge) is proportional to the product of the driving force, the soil's ability
       to transmit water, and the cross-sectional area perpendicular to the flow direction.
       The driving force is the difference in the energy (hydraulic head) between two
       points in the aquifer divided by the distance between the two points. This driving
       force is called the hydraulic gradient. The ability of soil or rock to transmit water
       is represented by an empirically determined coefficient of hydraulic conductivity.
       The hydraulic conductivity is determined by the properties of the liquid (water or
       contaminant) and the permeability of the porous medium. Typical examples of
       hydraulic conductivity for different porous materials are presented in Table C-6.
       The soil has an intrinsic of permeability, which is determined by the size,
       orientation, and connectedness of the pore spaces.

       Estimating radionuclide transport velocity is based on estimating the velocity of
       water.  For those contaminants that flow with the water, contaminant velocity
       equals water velocity (vertical and/or horizontal).  For those that flow at rates that
       differ from water, the estimated water velocity must be multiplied by a factor to
                                    B-ll

-------
approximate the contaminant velocity.

Ground-water flux per unit cross-sectional area in the saturated zone is calculated
using Darcy's law, which is as follows (BOU78):
           v =  Ks i                                                (B-17)

where
       V     =      Darcy flux of water, also termed the specific discharge
                     (length/time)
       Ks     =      hydraulic conductivity of soil or aquifer material
                     (length/time)
       i       =      hydraulic gradient (length/length).
Although Fhas the units of velocity (length per time), it is a specific discharge
rate or flux (volume of water flowing per unit cross-sectional area of geologic
material per unit time).  However, V, is the Darcy flux, rather than the
macroscopic velocity of the water.  The actual ground-water velocity is calculated
from the Darcy flux, by  dividing it by soil porosity, or, for precise modeling, by
effective porosity. (This approach takes into account the fact that the entire cross-
section of the pore is not flowing because of boundary layer effects, dead end
pores, and unconnected  pores.)  For clay soils, the effective porosity also corrects
for the effect of electro-osmotic counterfiow and the development of
electrokinetic streaming potentials (BOU78). The equation for calculating
ground-water velocity from Darcy velocity using effective porosity is as follows
(BOU78):

          VPW  = v/ne                                               (B-18)

where
       Vpw    =      ground-water (pore water) velocity (length/time)
       V     =      Darcy velocity (superficial velocity, specific discharge
                     (length/time)
       ne     =      effective porosity (dimensionless fraction).

The above terms should be determined for the site being studied. If this is not
possible  for all parameters, then literature values can be used when site-specific
data are not available (Tables C-9 and C-10).

The hydraulic  gradient (the change in the hydraulic head or elevation of the water

                             B-12

-------
              table over a measured distance) should also be taken from field data obtained
              during the site investigation.  Water levels in existing nearby wells screened at
              appropriate intervals can indicate hydraulic gradient.

              Effective porosity, ne, can be approximated by the difference between the moisture
              content at saturation and the "wilting point" (-15 bar)3.  The equation is as follows
              (RAW86):
                    ^e  =  nsat  ~  ^(-15)                                           (B-19)

              where
                     ne     =      effective porosity (fraction, dimensionless)
                     nsat    =      water content when the pores are fully saturated (fraction,
                                   dimensionless)
                     n(_15)   =      wilting point moisture content (fraction, dimensionless).

This estimation procedure addresses the fraction of the pore spaces that contributes to flow, but
does not address the effect of electro-osmotic counterfiow and the development of electrokinetic
streaming potentials.  For clays, this can be a significant difference.  Literature values listed in
Table C-10 should be used for clay solids (these values incorporate the effects of the clay's ionic
double layer (RAW82); either technique Equation B-19 or the tables, can be used for sand or
loam soil.

The above method for predicting the average velocity of groundwater is the most widely accepted
approximation; however, it is only an approximation, and further refinement can be made to this
approach to improve its accuracy. Corrections for the path length difference between the straight
line distance versus the tortuous path that groundwater flows through can improve the precision
(FRE79). However, this correction factor is difficult to estimate.

Example B.I. For saturated ground-water flow, calculate the pore or seepage velocity in an
"average" sandstone under a gradient of 0.01 cm/cm. Use arithmetic mean values in tables
(Appendix C).

Equation B-18 applies.  The arithmetic mean hydraulic conductivity, K, is 3.31 x 10"4 cm/s from
       The wilting point is determined by drawing a suction of -15 bar to draw water out of the soil in a manner similar
       to the section of a plant root; the bar is a measure of pressure (dynes/cm2).

                                           B-13

-------
Table C-6.  The arithmetic mean effective porosity, ne, is 0.21 from Table C-10.  Therefore,
        Vpw =  V/ne =  ~Ki/ne =  3.31 x 10"4 cm/ s x 0.01/0.21

                     =  1.58 x lO'5 cm/s.

                                  [End of Example B.I]

       (c)    Mass transport.  Cationic radionuclides that are migrating as a dilute solute may
             be subject to retardation effects. Concentrated plumes are not as susceptible to
             this phenomenon.  Algorithms describing retardation are based on the assumption
             that adsorption of radionuclides is primary due to sorption on mineral surfaces.
             The mass transport equation uses the retardation coefficient to estimate the rate of
             movement of the radionuclide. The most general form of the mass transport
             equation is for transport in saturated-unsaturated media.  If local equilibrium of
             mass transfer and first-order chemical reactions are assumed, sorption can be
             represented as a linear relationship, and the general mass transport equation can be
             written as:
          -V- (9  D-Vc) +  V-(Vc)  +  [(e^F)  +  XQeRFl  c =  °,
-------
       ne     =     the effective porosity,
       pb     =     the bulk density (g/cm3),
       Kd    =     the distribution coefficient (mL/g).

By assuming n = ne, Rp can be more conservatively estimated as

       R   -  1  +  P"K
       KF  ~  L  + — Kd
                                                                                (B-22)
             An equivalent retardation factor may be defined for fracture flow where the
             exposed area of the fracture is used rather than the porosity (FRE79).

             Example B.2.  Calculate the retardation factor, Rp, for strontium in an "average"
             fine sandstone with a bulk density, pb, of 2.8 g/cm3 and a distribution coefficient
             of 20 mL/g.

             The arithmetic mean values of n, ne are found from Tables C-l 1 and C-12 to be
             0.34 and 0.21, respectively. The retardation coefficient, Rd, calculated from
             Equation B-21 is therefore

                         RF=  ^!!+^x20  = 268.3.
                          F    0.21     0.21

             Equation B-22 gives

                           R   =  l +  _L_§_ x 20  =  267.7.
                            F         0.21

                                                             [End of Example B.2]

             The approximate rate of movement of the radionuclide is  VpJRp (Vpw is equal to
             the pore velocity which is defined in Equation B-18), which maybe used to
             estimate travel time.

(2)     Chain decay of radionuclides. Radionuclides decay to stable products or to other
       radioactive species called daughters. In some species, several daughter products maybe
       produced before the parent species decays to a stable element. For some radionuclides,
       the daughter(s) may present a potentially greater adverse health risk than the parent.

                                         B-15

-------
       Accounting for the chain-decay process is particularly important for predicting potential
       impacts of actinide and transuranic migration. In considering this process over the
       transport path of radionuclides, one transport equation must be written for each original
       species and each daughter product to yield the concentration of each radionuclide
       (original species and daughter products) at points of interest along the flow path in order
       to estimate total radiological exposures. In a constant one-dimensional velocity field, the
       general equations can be written as (BUR80):

        dc,         dc,        d2 c,
                   dc         d2
        dc .         dc .        d2c.
               V   — -  =  D  - -  -  R^.X.c.
      . — -        — -        - -      ^...     r •  -,
     Fl  dt      pw  dx      x dx2         1  *      '
       where
              RFi     =     the retardation factor for species i
              Vpw     =     the pore velocity = V/ne
              Ct      =     the concentration of species i
              Dx     =     the dispersion coefficient
              A;      =     the decay coefficient for species i.

       Equation B-23 describes the material balances of the ith member of a decay chain and all
       preceding chain members.

(3)     Net Dilution.  Dilution (mixing) processes in ground water are generally less significant
       than dilution processes in air and in surface water. In both air and surface water,
       dispersive dilution is often a major phenomenon because the flow can be turbulent.
       Turbulent flow means that all the flow paths are not essentially parallel to the gross
       direction of motion. Flow components that are perpendicular to the bulk fluid motion
       cause the plume to spread laterally not longitudinally, thus reducing the concentration in
       the plume, while the volume of contaminated air or surface water increases.

       However, in ground water, the magnitude of dilution is usually much smaller, partly
       because turbulent flow rarely exists.  The slow speed of ground water, coupled with the

                                           B-16

-------
effects of small channels in the intergranular pore space, tends to keep the flow smooth
and laminar.  In an idealized conceptual model, the interconnecting pore spaces can be
thought of as forming flow channels or tubes; any tendency for the flow to eddy is
resisted by the sides of the flow channel. However, since the interconnecting pore spaces
do not make a continuous flow channel, in real soil there is some lateral mixing due to
branching of flow channels and spatial variation in flow velocity.  Dispersion (neglecting
molecular diffusion) is not significantly affected by laminar eddy currents. If molecular
diffusion is momentarily disregarded, dispersion in porous or fractured media is caused
by six principal phenomena: (1) varying permeability, (2) varying pore sizes, (3) varying
path length, (4) variation in the velocity gradient across pore space, (5) anisotropic
permeability and (6) flow splitting around soil particles with mixing within the pore
space. These six phenomena contribute to longitudinal dispersion; the first and last two
phenomena can cause lateral dispersion. In nearly all ground-water systems, longitudinal
dispersion effects are much larger than lateral dispersion effects. Researchers have
reported longitudinal dispersivity values ranging from about 1 to 25 times higher than
transverse dispersivity values (GEL85).

Molecular diffusion is a relatively slow process but also contributes to the overall
dispersion process in two ways: micro-scale mixing within an individual pore or fracture
channels that lead to large-scale bulk dilution and spreading in a slow-moving ground-
water system. For short-term releases (i.e., spills), longitudinal mixing and resulting
dilution of plume concentrations can be significant.  In this case, the plume can
effectively mix with the uncontaminated water in front of and behind the slug of
contamination, whereas continuous-release sources can result in plumes of sufficient
length that the middle section cannot effectively mix with clean water in front or behind
it.

A very simplistic approximation of the net dilution may be made by using a form of
Darcys law in conjunction with Equation B-9.  The results of Equation B-9 were used in
Section B.3 to estimate the concentration of a radionuclide reaching a receptor if
radioactive decay were the only means by which the  concentration was diminished. That
is, there were no dilution effects along the radionuclides' travel path to the receptor. In  an
actual system, leachate concentrations would be diluted by mixing with the ambient water
along the travel path.  As a first approximation, the degree of mixing may be estimated  by
the following:
                                    B-17

-------
                      Vol=KiTeWQT                                            (B-24)

       where
              Vol   =     aquifer volumetric flow rate (mVy)
              K     =     hydraulic conductivity of the aquifer (m/y)
              i      =     hydraulic gradient (m/m)
              W    =     width of the Source Area (m)
              Te     =     effective mixing thickness (m)
              0r    =     total porosity of aquifer (dimensionless)

The effective mixing thickness (Te) of the aquifer may be estimated from the following formula:

                         Te=<->«                                              (B-25)
       where
       /=     infiltration rate (m/y)
       V=    specific aquifer (m/y) discharge (B-17)
       Q. =     distance from the contaminant source to the receptor.

Equation B-25 represents the vertical distance traveled by the contaminant over length H,
assuming the vertical velocity is /, and the horizontal velocity is the aquifer flow rate.

The maximum value for the effective mixing thickness would be the thickness of the aquifer.
The concentration of a radionuclide in a downgradient receptor may subsequently be adjusted for
dilution using the Cwell concentration obtained from formula B-10, in conjunction with Equation
B-26.
                                _x_
                 M    = C   • e ~c • I • A                                       (B-26>
                 1 well   wat

       where
              Cwat    = leachate concentration (Ci/m3)
              /      = infiltration rate (m/yr)
              A      = source area
                                              M
                                      D
                                        wel1   Vol

       where
              Dwell =  concentration of radionuclide in downgradient well corrected for dilution

                                          B-18

-------
                    (Ci/m3)
             Mwell = Mass of radionuclide corrected only for radioactive decay (Ci)

B.4    Analytical Methods for Aquifer Flow and Transport

An excellent discussion of simple mathematical methods to compute radionuclide travel times
and dilution rates is included as Chapter 4 in NUREG/CR-3332 (COD83).  The relevant portions
of that discussion, as well as the example problems, figures, and tables, have been excerpted to
form the basis of Sections B.4 and B.5.

Analytical ground-water transport models can be used for certain types of analyses where
available data do not warrant a more complicated numerical analysis.  Such models are useful for
scoping the transport problem and may frequently be adequate for regulatory needs if model and
corresponding input data are chosen conservatively.

In this section and Section B.5, a series of simple analytical models used at the U.S. Nuclear
Regulatory Commission (NRC) is presented.  Many of these models have been computerized and
are available from the NRC (COD 82). In their simplest forms, however, most can be used with
the aid of only a calculator.

The models are developed for the limiting case of unidirectional saturated advective transport of
a single dissolved substance with three-dimensional dispersion in an isotropic homogeneous
aquifer as discussed in Section B.2.1. Equation B-27 is the governing differential equation of
solute transport for that set of conditions.
  8c     Vpw 8c    Dx  d2c     D   92C     Dz
 -^-  + —^ -=- =  — 	 +  — 	  +  —-
  dt      R   8X    R   x2     R     2     R
       where
       c      =     the concentration in the liquid phase (Ci/cm3)
       Dx, Dy, D=   the dispersion coefficients in the x, y, and z directions respectively (cm2/s)
       A      =     the decay coefficient, (1/s)
       Vpw    =     the x component ground-water pore velocity (cm/s)
       Rp     =     the retardation factor (dimensionless).

       The dispersion coefficient can be approximated from Equation B-28. For unidirectional

                                          B-19

-------
       flow, V2 = V3 = 0, V] = V, and 0 can be approximated for saturated flow by the effective
       porosity, ne.  Also, since Vpw = V/ne,


                       Dx =  aLVpw                                             (B-27a)


                       Dy =  aTVpw                                             (B-27b)


                       DZ =  ^TVpw,                                             (B-27c)


       where oc£ and ccr are the longitudinal and transverse dispersivities respectively.
9D..  = arV5..  +  (aL -  og  l^/V,                               (B-28)
            ..

       where
              8!y     =     1 for i =j, by = 0 for i * j (Kronecker delta function)
              0     =     the volumetric water content
              ccr     =     the transverse dispersivity (cm)
              oc£     =     the longitudinal dispersivity (cm)
              V     =     the magnitude of the flux (cm/s)
              VpVj  =     the components of the flux (cm/s).


B.4.1  Point Concentration Model


The first model presented can be used for calculating the concentration in the aquifer at some
point downgradient of a release (e.g., water supply well).


Equation B-27 is solved in terms of Green's functions:

          c± = —^—X(x,t)  Y(y,t)  Z(z,t],                                (B_29)
                neRF

where Ci is the concentration at any point in space for an instantaneous one-curie release, ne is the
effective porosity of the medium, andX,  Y, Z are the Green's functions in the x, y, z coordinate
directions, respectively. Equation B-29 has been developed for a variety of boundary and source
configurations:
                                          B-20

-------
(1)    For the case of a point source at (0, 0, zs) in an aquifer of infinite lateral (x, y) extent and

       depth b, as illustrated in Figure B.I,
                  ec. =
                                                                                  (B-30)
       where
                       exp
(B-31)
                              exp
(B-32)
                                       d   )
                                             cos m n —- cosmn — r.     (B-33)
                                                      b          b\
(2)    For the vertically averaged concentration in case 1 above (equivalent to a vertical line

       source of length b),
                          neRF
                                                                                  (B-34)
where
                                                                                  (B-35)
(3)    For a horizontal line source of length w centered at (0, 0, zs), as illustrated in Figure B.2,
                          neRF
                                                                                  (B-36)
       where
                                          B-21

-------
Y  -
 2    2w
                                   (w/2-y)
                                                                   (B-37)
      and erf is the error function. Tables of the error function are available in standard
      mathematical texts (ABR70).
                                              QRNL-OWG 82-14406
       POINT SOURCE AT
       x = 0, Y = 
-------
             ]	IQRIZQNTAL LINE SOURCE
                   CENTERED AT
                  x = 0, y = 0, z = z.
                    TO?'Or Aouirrn  OR
                  BOTTOM Of AQUIFER
Figure B.2.   Idealized ground-water system for point concentration model, horizontal line
           source (Codell and Duguid, 1983).
                                   B-23

-------
(4)
For the vertically averaged concentration in case 3 above (equivalent to an area source of
width w and depth b),
                         neRF
                                                                                 (B-38)
(5)     For a point source at (0, 0, zs) in an aquifer of infinite lateral extent and depth,
                                                                                 (B-39)
(7)
                     exp
                           -u-
                                      exp
           (B-40)
       where
(6)    For a horizontal line source of width w centered at (0, 0, zs) in an aquifer of infinite lateral
       extent and depth,
                          neRF
                                                                                 (B-41)
For a horizontal area source of length / and width w centered at (0, 0, 0) in an aquifer of
constant depth b, as illustrated in Figure B.3, the solution to Equation B-29 becomes:

                         " "2Z2'                                         (B-42)
                   Cl "   neRF
       where
          erf
                            -  erf-
exp (-Xt) .
                                                                                  (B-43)
                                          B-24

-------
                                                        97-14403
                                             SOURCE AREA
                                                         x
                         BOTTOM BOUNDARY
Figure B.3 Vertically averaged ground-water dispersion model (Codell and Duguid, 1983).

    Example B.3. Concentration in an aquifer of limited thickness.

    One curie of a radioactive pollutant leaks quickly into a water table aquifer through a
    highly permeable ground cover over a square surface area 50 m on each side. The
    pollutant has a half-life of 30 y. A well tracer test indicates that the ground water is
    moving in the  direction of two wells at a speed, Vpw, of 1.5 m/d and that the longitudinal
    and transverse dispersivities, oc£ and ccr, are 20 to 10 m, respectively.

    The saturated thickness of the water table aquifer, b, is 50 m and has an effective
    porosity, ne, of 0.2. The pollutant has been determined to have a retardation factor, RF, of
    20 in the aquifer.

    Calculate the concentration of the pollutant in wells whose downgradient coordinates
    with respect to the center of the source area are

           (a)  x = 200m, y = 0m
                                        B-25

-------
              (b) x = 400m, y = 50m

       The wells are open to the entire depth of the aquifer.

       Case 7 in the preceding section applies to this example, since the source is a horizontal
       area type and the wells are screened over the total depth, which would vertically average
       the concentration (Figure B.4).

       Equation B-42 is therefore evaluated with Green's function:

              X2 determined by Eq. B-43,
              Y2 determined by Eq. B-37, and
              Z2 determined by Eq. B-35.

       The dispersion coefficients are calculated by Equations B-27a and B-27b.

              Dx = ccLVpw = 20 x 1.5 = 30m2
              Dy = ccTVpw= 10 x 1.5= 15m2

       Figure B.4 shows the concentration as a function of time calculated for the two wells.
                                                                     [End of Example B.3]

B.4.2  Flux Models

The flux model is used to calculate the discharge rate of a radionuclide entering a surface water
body that has intercepted the aquifer containing the transported material as depicted in Figure
B.5.  It is assumed that all material entering the aquifer eventually enters the surface water except
for that which has been lost through radioactive decay. The assumptions that apply to the point
concentration model also apply to this model.  The model provides only the rate of input to the
surface water at an average distance x downgradient from the surface.  Actually, the contaminant
would enter the surface water as a diffuse patch, but the model described here gives no
information about the spatial distribution of this patch.
                                          B-26

-------
                                              ORM.-DWS BZC-207SI
      TO
       O
                                  10

                              TIME OOQO
      Figure B.4 Concentration in downgradient wells for Example B.3.
                                                QRNL-DWG
                     APPROXIMATE O.ISTANCE

                            TO RIVER
                                X
SOURCE AT x = 0
        Figure B.5.  Ground-water/surface-water interface, flux model.
                                B-27

-------
In the unidirectional flow field assumed, the flux F (Ci/s) of material crossing an area dA = dy dz
perpendicular to the x axis is described by the equation
               dF    („      „  Bc\
                    =   VDWC ~ Dx -5-   ne '                                     (B-44)
                      i   pw      x :j_, i   e                                      v    /
where c is the concentration in the dissolved phase. The total flux across the plane would be
                       /           -,  \
                  t>  <• I  Tr
F =  n
—  dydz .
                                                                              (B-45)
B.4.3  Source Released from a Vertical Plane (x = 0)

If Q is the concentration from an instantaneous release of 1 Ci at x = 0 and time t = 0, as
described by Equation B-29, then the resulting flux at distance x downgradient would be
           x+ V
                pw R
                        exp
                      x- V
                           pw R
                                               - At
                                                                              (B-46)
BAA  Horizontal Area Source
For conditions expressed by Equation B-43, the corresponding flux would be
  Fi "
                        pw
                       R
                                  ?1)  - erf(z2)]
                     D
                  -  -2 [exp(-zO - exp(-z^)]
                     R
                                           •exp(-Xt)  ,
                                                                         (B-47)
where
  z  =
         x -
   ^t+±
    D       O
    X\,_,      ^
                                      x
                                        -5~t-±
                           and
                                         B-28

-------
       Example B.4. For the same conditions in the previous example, calculate the flux of the
       pollutant into a river intercepting the ground-water flow, which is a distance x of 2000 m
       downgradient from the center of the source.

       Equation B-47 applies in this case. Figure B.6 shows the flux into the river as a function
       of time.
                                                               [End of Example B.4]
                     24


                     20


                      16
                  ^*
                  _>
                  o
                  .5  12
                  x
                  ZJ
                            I
                                    J_^J'
I
                            4    a   12    16   tO   2<   28   32   36   40
                                         tliul (1000 -a}
                   Figure B.6. Flux of pollutant into river for Example B.4.
B.4.5  Generalization of Instantaneous Models
Equations B-5 and B-27 are formulated only in terms of instantaneous releases. They can be
generalized for arbitrary releases by use of the convolution integral:
               6  = htf(T)Q.(t-T)dT
               (B-48)
where 0 is the solution at time t for the arbitrary release, 0;(t -1) is the solution at time
(t - t) for an instantaneous release at (t - t) = 0, and^t) is the source release rate at T in curies/s.
                                           B-29

-------
Certain analytical solutions can be found to Equation B-48 for simple source release rate
functions. For example, Wilson and Miller (WIL78) develop the solution to Equation B-48 for a
continuous release in terms of the "well function." Most useful solutions to Equation B-48 use
numerical integration, generally involving a digital computer.

Several special precautions must  be taken, however, to preserve computational accuracy, because
the terms within the integral of Equation B-48 can be very nearly zero over part of the integration
range.  Computer programs for solving the equations in this section are described by Codell et.
al. (COD82). Program listings in BASIC and FORTRAN are given in this reference.  An
alternative method for simulating a continuous source function is to present the continuous
source as a series of instantaneous ones.  The analytical solutions are then linearly summed.
Complicated areal source terms can also be solved in an analogous fashion by representing the
source area by a series of point sources and linearly summing the solutions.

B.5    Simplified Analytical Methods for Minimum Dilutions

Simplified forms of the equations of Section B.4 have been developed for calculating the
minimum dilutions (i.e., maximum concentration) of volume Vr of a substance instantaneously
released from a point source into  an aquifer.

B.5.1  Dilution at Downgradient Wells in Confined Aquifers for an Instantaneous Point Source
       at the Surface

At some distance downgradient from a release at the surface of a confined aquifer, the
concentration can be considered to be mixed in the vertical direction.  Close to the point of
release, or in an unconfined aquifer, the vertical dispersion will not be influenced by the vertical
boundaries of the aquifer.  Between these regions, there is a region where the concentration
cannot be considered mixed, but  the boundaries (top and bottom) affect the dispersion. The
degree of vertical mixing can be characterized in a confined aquifer of constant thickness and
uniform transport properties by the factor
                             — '                                              (B-49)
where
                     the vertical (transverse) dispersivity (ft)
                     the thickness of the aquifer (ft)
                                          B-30

-------
       x      =      the distance downgradient of the release (ft).


The factor (J) can be used to characterize the aquifer in three approximate regions:


       (a)     If (J) < 3.3, the release may be considered to be within 10% of being
              vertically mixed in the aquifer;

       (b)     If (J) > 12, the release maybe considered to be within 10% of the
              aquifer;

       (c)     If 3.3 < (J) < 12, the release is neither completely mixed nor
              unaffected by the boundaries.


       Different methods apply to each of the three regions.


Vertically Mixed Region ((J) < 3.3). For an instantaneous release at x = 0, the minimum dilution
corrected for decay directly downgradient of a source would be
           DL =  RF4nnexb±_exp(xt) ,                                 (B-50)
where
       DL            =     minimum dilution = c0/c
       Rf            =     retardation factor
       ne            =     effective porosity
       VT            =     volume of liquid source term (cm3)
       aL,aT         =     dispersivities (cm) in the indicated direction
       x             =     distance downgradient (cm)
       b             =     aquifer thickness (cm)
       t             =     travel time (y)
       A             =     decay constant = In 2/t1/2(l/y).


The travel time, t, can be approximated as
                             V
                              pw
where V  is the pore velocity defined by Equation B-18.
                                          B-31

-------
Unmixed Region ((J) > 12). For an instantaneous release at x = 0 on the surface of the aquifer,
the minimum dilution of the surface of the aquifer directly downgradient from the source would
be determined from Equation B-52,
                                      exp (Xt)  ,                                (B-52)
where CCL, CCT are dispersivities in the indicated direction and the other terms are as previously
defined.

Intermediate Region (3.3 < (J) < 12). For an instantaneous release at x = 0 on the surface of an
aquifer, the minimum dilution on the surface of the aquifer directly downgradient from the
source would be
                   £ 4nrz  x£>A/a a  exp (Xt)
                                      	                                  (B-53)
where
and the other terms are as previously defined.
The function F((J>) is conveniently plotted in Figure B.7. It can be easily seen that for small
values of (J), F approaches the value of 1 .0, which yields the vertically mixed case.  For large
values of (J), the slope of F is 1/2, and the unmixed case prevails.  This method may be used for
any value of (J) that can be read on Figure B.5.
                                          B-32

-------
                      Figure B.7. Mixing factor for confined aquifers.
B.5.2  Ground-Water/Surface Water Interface-Instantaneous Source
For an instantaneous release to the ground-water at x = 0, the minimum dilution in an
intercepting river, corrected for decay, can be determined from:
              DL =
                     2RQnuTx
              exp(Xt) ,
(B-55)
where
       fi
       V,
        pw
flow rate of river (cmVs)
the longitudinal dispersivity of the aquifer (cm)
the volume of release (e.g., tank volume) (cm3)
pore velocity of ground water (cm/s).
Relatively simple equations can be used for estimating average concentration in ground water or
in surface water supplies contaminated by ground water (Equations B.56 and B.57).


B.5.3  Quantity of Released Radioactivity Crossing a Vertical Plane


In the case of ground-water flow to an intercepting river, the total quantity M (curies) of the
dissolved substance entering the river would be
                                          B-33

-------
                      M =  /; Fdt  '                                             (B-56)

where F is the flux defined for either an instantaneous point or vertical plane source by Equation
B-45 or a horizontal area source by Equation B-47. Equation B-56 can be integrated graphically
or numerically and in some cases may have an analytical solution.

If dispersion is relatively small (e.g., ccx « C), the following approximation may be used:
                  M=  MQe~xt curies,                                        (B-57)


where M0 is the quantity of radioactivity released instantaneously from the source (curies), t is the
travel time (y), and A is the decay coefficient (1/y).

If the substance is being released from the source at a rate proportional to the quantity remaining
(e.g., an exponentially decaying source term),

                  M= M°         e"Xt '                                        (B'58)
where A' is the release rate from the source (1/y), andM0 is the initial quantity of material in the
source term (curies).

B.5.4  Direct Ground- Water Usage

The U.S. Nuclear Regulatory Commission developed a model for calculating the quantity of a
radionuclide ingested by a population using the contaminated ground water (NRC78). Ground-
water usage was considered to be spatially continuous instead of being from discrete well points.

The total amount of the released radionuclide ingested by the population is
              I  =    °°  °°   °° cQ dxdydtf
                     JD j-~ j-~    g
       where

                                          B-34

-------
       I
       c
       Q*
the ultimate number of curies ingested from the release
the ground-water concentration (Ci/L)
the ground-water withdrawal rate for drinking water purposes
(m3/d/m2).
If all usage is restricted to a downgradient distance C and beyond from the release point, Equation
B-59 may be integrated in closed form to give
   I   =
MQQg ^
2neRFb °"P
«%,
2Dx
/ \
RFP (X+y)
( D* J
1/2
                                                                                 (B-60)
where
                      Y   =
                                pw'
M0 is the total quantity of the radionuclide discharged to the point source, and the other terms are
as previously defined.

If usage of the ground water is restricted between two downgradient distances, ^ and £2, the
curies ingested would be defined as:
       where IftJ and/(1>^) are evaluations of Equation B-60 for fj and H2 respectively.

       Example B.5.  The use of several of the simpler analytical models in Section B.4 will be
       demonstrated by way of a hypothetical example:

       Leakage into the ground water rapidly empties a 1000-ft3 tank containing 4000 |j,Ci/mL of
       3H, 2000 jiCi/mL of 90Sr, and 3000 jiCi/mL of 137Cs at a radioactive waste site.  The site is
       50 ft above the mean  level and 3000 ft upgradient from a river that has representative low
       flow of 5000 ft3/s and is the sink for all surficial ground water in the area. Two shallow
       wells are located 400  and 2500 ft directly downgradient from the site of the spill. Ground
       water exists in a homogeneous alluvial sand layer 100 ft thick under water table
                                          B-35

-------
conditions. Dispersivities for the sand have been determined in the near field from
single-well tracer tests to be 0.5 ft for CCT and 1.0 ft for OCL. The bulk density pb of the sand
is 2.6 g/cm3. Its total porosity n and effective porosity ne are 0.4 and 0.25, respectively.
The permeability K is 0.02 cm/s. Distribution coefficients Kd for the sand have been
determined to be 0, 2.0, and 20.0 mL/g for dilute solutions of 3H, 90Sr and 137Cs,
respectively. Using this information, calculate the following:

       (a)    the maximum concentrations of the radioactive components in the river,

       (b)    the maximum concentrations of the components in the near well,

       (c)    the maximum concentrations of the components in the far well, and

       (d)    the total quantity of each radionuclide escaping to the river.

Solution

(a)     If it is assumed that the source is released over a short period, Equation B-55 for
       instantaneous releases may be used to calculate the maximum river concentrations
       of 3H, 90Sr, and 137Cs. First determine the pore velocity Vpw from Equation B-18
       and the effective porosity ne:
                                            K—
                       v   -     -  -   -
                                        =   - 0.0167  ;
                                  ne          ne

        The gradient
                    _AH   =   - 50 ft
                    Ax       3000 ft

        therefore,

         - 2 x 10"2  cm/sx - 0.0167      86,000s/d   _   ->nof.,,
v    —   	  x  	   —   J./D  ft/a
 pw                  0.25                30.48  cm/ft

        The retardation factors for 3H, 90Sr and 137Cs can be determined from
        Equation B-22:
                                   B-36

-------
3U    D      1  j.  ^ ' U

 H    ^  "  X    ^4
*>Sr  R   =   i + 111 x 2.0  -  14 ,
      F
                 0.4
137Cs £P  =   1 +   l  x 20   =   131 .
      F          0.4
The travel times for the three components are calculated by Equation B-47:
           .   **_,   .   3000 ft x 1 x _^_   _

               Vp       3.78 ft/d     365 d
 oc      *.      3000  ft x 14      y        _-  .
 Sr     t  =   	 x  —i—   =   30.4 y,
                3.78 ft  d     365 d
-Cs    t  -   3000  ft x 131  x  _^_  _  284_

                3.78  ft/d      365  d
The half-lives of 3H, 90Sr, and 137Cs are 12.3 y, 29 y, and 30.1 y, respectively. The

decay-corrected minimum dilutions in the river are found by applying Equation B-

55:
                        5000  ft3
3H
        2  x  1.0 x _^^_^^_  x^nx l.O ft x 3000 ft

DL  =  	£	

            3.78 ft/d x  1000 ft3  x      d
                                           86,400s
                  f   In 2    .  .„ ]
             x exp - x 2.17y
                P                y
         =  2.51 x 107 ,



                        B-37

-------
                             5000  ft3
      9°Sr
            DL
                    2  x  14  x  ^^_^^_ xJnx 1.0 ft x 3000 ft
                       3.78 ft/d x 1000 ft3
                                                86,400s
                         I In 2   on  /,  I
                   x exp  - x 30. 4y
                                     y
                =  6.42  x 10
                              5000  ft3
      137Cs
       2 x 131 x _^^_^^_  x^nx l.Oftx 3000ft

DL  =	

           3.78  ft/d x 1000 ft3       d
                                                86,400s
                   x exp I   ln2  x 284. 8y|
                       P                 Y
                =  2.05 x 1012 .
      The peak concentrations in the river are determined by dividing the tank

      concentrations by the dilution factors:
   c(3H)   =   4000 uCi/mL /2.51 xlO7  =  1 . 59 xlQ'4 yCi / mL ,




  c(90Sr)  =  2000uCi/mL/6.42 xlO8  =  3 . 12 xlQ'5 yd / mL ,




 c(137Cs)  =  3000uCi/mL/2.05 xlO12  =  1 . 46 xlQ'9 yCi / mL .
(b)    Minimum dilution in well (400 ft downgradient).
                             B-38

-------
First determine whether or not the thickness of the aquifer would affect the results
by calculating the factor (J) from Equation B-50:

               *            (100  ^)2      =  50.
                         0.5 ft* 400 ft

Therefore, in this region the release will be relatively unaffected by the thickness
of the aquifer, and Equation B-53 applies.

The travel times are estimated using the retardation factors and pore velocity
calculated above:
      3H         =   400 ft  x  1  x  _^_   _  Q_
                      3.78  ft/d     365  d
       oc      *.      4°0 ft  x  14       y         ......
        Sr     t  =   	  x  —i—   =  4.06y,
                       3.78 ft  d     365 d
       -Cs    t  -   400 ft  x  131  x _^_  __
                        3.78  ft/d      365  d
                           B-39

-------
Applying equation B.52:
3H            0.25  x l x (4nx400 ft)3/2Jl ft* 0.5 ft* 0.5 ft
        L
                               2 xiooo ft3
             x exp [   ln2   x 0 . 2 9 y I
                                 Y
          =  22.6 ,
           =   0.25 x 14 x (4nx400 ft)372/I f t x 0 . 5 f t x 0 . 5 ft

        L                       2 xlOOO ft3

9°Sr                ( in 2
              x exp  	 x 4.06y



           =   343.6 ,
          =   0.25  x 131 x  (4nx400  ft)32l f t x Q . 5 f t x Q . 5 ft
                                2 xlOOO ft3
                  I   In 2    ,.  )
             x exp         x 38y
                  I  30.ly       )

          =  6999.9 .
                                 B-40

-------
The peak well concentrations are therefore 177 |j,Ci/mL for 3H, 5.8 |j,Ci/mL for 90Sr, and 0.43
       for 137Cs.

      (c)    Well 2500 ft downgradient. Calculate (J) for this region from Equation B-49:
                                 (100  ft)2
                             0.5 ft x  2000  ft
                                                      .O.
            Therefore, this well is in the intermediate region, and Equation B-53 applies. The
            factor F ((J>) can be read from Figure B.6 to be 1.6. Travel times for each
            component calculated from Equation B-46 are
                             =   2500 ft x  1  x _^_   __
                                  3.78 ft/d     365 d
                  »              2500 ft x  14
                    Sr     t  -                  x __   __  25
                                   3.78  ft/d      365 d
                    ?Cs       =   2500 ft x  131 x  _^_  __  237.4y.
                                   3.78 ft/d      365  d
            Applying Equation B-53:
            3H          =   1 x 4nx Q.25^/0.5 ft x l.Q ft x 2500 ft x 100 ft
                     x                      1000ft3xl.6
                                 (  ln2    i  on  1
                           x exp  	 x 1. 81 y
                               Pll2-3y        yj
                        =  271.8 ,
                                      B-41

-------
9°
               =   14 x 4nx 0.25^/0.5 ft x l.Q ft x 2500 f t x 100 ft
            L                        1000ft3xl.6
        Sr               / in 2          ^
                         I 29y
               =   8874  ,
       137,
         Cs
    131 x 4nx 0.25^0.5 ft x l.Q ft x 2500 f t x 100
                      1000 ft3 x 1.6

    x exp  	 x 237.4 y

=   1.07 x 107  .
       The peak well concentrations are therefore 14.7 |iCi/mL for 3H, 0.32 |j,Ci/mL for
       90Sr, and 2.8 x 10'4 nCi/mL for 137Cs.

 (d)    Quantity M of each radionuclide eventually reaching river.

       Equation B-57 applies to this case because CCL «C (i.e., 1 ft vs 1000 ft). Travel
       times are estimated in part (a) above. The quantity of each radionuclide initially
       in the tank is the concentration multiplied by the volume. Therefore,
       3H      M  =  4000  uCi/mL x 1000 ft3 x 28,300 mi/ ft3
                                xexp
                                       12.3 y
                   =   1.002  x 105 Ci ,
                                 B-42

-------
90c
 sr   M  =  2000 ]iCi/mL x 1000 ft3 x 28,300 mL/ff
                     xexp —ix30.4y| x 10"6Ci/uCi
                         I   29 y        I
          =  27,370 Ci ,
  Cs M  =  3000 uCi/mL x 1000 ft3 x 28,300 mL/ft3


                   xexpf ~ ln 2  x 284. 7y| xlO~6Ci/iaCi
                        ^ 30.1 y        )

        =  120.7 Ci .
                     B-43

-------
B.6    References

ABR70      Abramowitz, M., and I. Stegun, eds., November 1970. Handbook of
             Mathematical Functions, Applied Mathematics Series 55, Nat. Bur. Standards.

BOU78      Bouwer, H. 1978. Groundwater Hydrology. New York: McGraw-Hill Pub. Co.

BOW79      Bowers, J.F., et al. 1979. Industrial source complex (ISC) dispersion model
             user's guide, volumes I and II. Washington, B.C.:  U.S. Environmental Protection
             Agency. EPA 450/4-79-030.  As reviewed in: Bonazountas, M., Fiksel, J., et al.
             1982. Environmental mathematical pollutant fate modeling handbook/catalog.
             Draft. Washington, B.C.: U.S. Environmental Protection Agency, Office of
             Policy and Resource Management.  Contract No. 68-01-5146. As cited in
             EPA88b.

BUR80      Burkholder, H.C., and E.L.J. Rosinger, June  1980. "A Model for the Transport of
             Radionuclides and Their Decay Products Through Geologic Media," Nucl.
             Tecnol. 49. 150-58.

CLA78      Clapp, R.B., and G.M. Hornberger. 1978.  "Empercial Equations for Some Soil
             Hydraulic Properties." Water Resour. Res. 14(4): 601-604.

COD82      Codell, R.B., K.T. Key,  G. Whelan, 1982.  A collection of mathematical models
             for dispersion in surface water and ground water. Washington, B.C.: U.S.
             Nuclear Regulatory Commission. NUREG/CR-0868. As cited in EPA88b.

COD83      Codell, R.B., and J. Duguid, 1983. Radiological Assessment; A Textbook on
             Environmental Dose Analysis, NUREG/CR-3332, U.S. Nuclear Regulatory
             Commission.

ENF82      Enfield, C.G., R.F. Carsel, S.Z. Cohen, T. Phan, D.M. Walters, 1982.
             Approximating pollutant transport to ground water. Ground Water 20(6):  711-
             722. As cited in EPA88b.

FRE79       Freeze, R.A. and J. Cherry,  1979. Groundwater. Prentice-Hall, Englewood Cliffs,
             N.J.

GEL85      Gelhar, L.W., A. Montoglou, C. Welty, and K.R. Rehfeldt, 1985. A review of
             field-scale physical solute transport processes in saturated and unsaturated porous
             media. Palo Alto, CA: Electric Power Research Institute.  EPRIEA-190.  As
             cited in EPA88b.
RAW82
Rawls, W.J., D.L. Brakensiek, K.E. Saxton, 1982.  Estimation of soil water
                                        B-44

-------
             properties. Trans. Am. Soc. Agri. Eng. 25(5):1316-1320 and 1328. As cited in
             EPA88b.

RAW86      Rawls, W.J., 1986. Computer printouts from the soils data base, dated August 28,
             1986. From WJ Rawls, Beltsville, MD: Beltsville Agricultural Research Center.
             As cited in EPA88b.

STE78       Steingiser, S., S.P. Nemphos, M. Salame, 1978. Barrier polymers. In:  Kirk-
             Othmer encyclopedia of chemical technology, 3rd ed. New York:  John Wiley
             and Sons. As cited in EPA88b.

WIL78       Wilson, J.L. and P.J. Miller, April 1978. "Two Dimensional Plume in Uniform
             Ground-Water Flow." J. Hydraulics Division, ASCE 104 (HY4), 503-14.
                                        B-45

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       APPENDIX C




DEFAULT PARAMETER VALUES

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                                 Contents - Appendix C

Tables

C-l.    Representative Values for Saturated Moisture Contents and Field Capacities of Various
       Soil Types  	C-l

C-2.    Representative Values of Hydraulic Parameters 	C-2

C-3.    Representative Values of Saturated Hydraulic Conductivity	C-3

C-4.    Saturated Hydraulic Conductivity Ranges for Selected Rock and Soil Types	C-4

C-5.    Distribution Coefficient (Kd) of Selected Radionuclides Sorbed by Clays and Cation
       Exchange Capacity for Selected Clay Minerals	C-5

C-6.    Typical Values of Hydraulic Conductivity of Porous Materials  	C-6

C-7.    Suggested Value for Cet Relating Evaporation from a U.S. Class A Pan to
       Evapotranspiration from 8 to 15-cm Tall, Well-Watered Grass Turf	C-7

C-8.    Crop Coefficients for Estimating Evapotranspiration	C-8

C-9.    Typical Values of Porosity of Aquifer Materials	C-9

C-10.  Typical Values of Effective  Porosity (or Specific Yield) of Aquifer Materials  	C-10

C-11.  Dispersivity Values aL and ccr Obtained Directly through Measurements of Tracer
       Breakthrough Curves in Groundwater Solute Transport	C-l 1
                                           C-i

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Table C-l. Representative Values for Saturated Moisture Contents and Field
     Capacities of Various Soil Types
Number of soils
Sand
Loamy sand
Sandy loam
Loam
Silt loam
Sandy clay loam
Clay loam
Silty clay loam
Sandy clay
Silty clay
Clay
762
338
666
383
1,206
498
366
689
45
127
291
Saturated moisture content
(9s)a
Mean ± 1 standard deviation
0.437
0.437
0.453
0.463
0.501
0.398
0.464
0.471
0.430
0.479
0.475
0.347 - 0.500
0.368-0.506
0.351-0.555
0.375-0.551
0.420 - 0.582
0.332 - 0.464
0.409-0.519
0.418-0.524
0.370 - 0.490
0.425 - 0.533
0.427 - 0.523
a From total soil porosity measurements compiled by Rawls et al. (1982) from numerous
sources.
Source: Rawls, W.J.,
Trans. Am. Soc. Asri.
D.L. Brakensiek, K.E.
. Eng. 25(5): 13 16-1320
Saxton, 1982.
and 1328. As
Estimation of soil water props
cited in EPA88b.
                                  C-l

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                 Table C-2.  Representative Values of Hydraulic Parameters
Soil texture
Sand
Loamy sand
Sandy loam
Silt loam
Loam
Sandy clay loam
Silt clay loam
Clay loam
Sandy clay
Silt clay
Clay
No. of
soils3
13
30
204
384
125
80
147
262
19
441
140
bb
4.05(1.78)d
4.38(1.47)
4.90(1.75)
5.30(1.87)
5.39(1.87)
7.12(2.43)
7.75 (2.77)
8.52 (3.44)
10.40(1.64)
10.40 (4.45)
11.40(3.70)
1
2b+3
0.090
0.085
0.080
0.074
0.073
0.058
0.054
0.050
0.042
0.042
0.039
e;
0.395 (0.056)
0.410 (0.068)
0.435 (0.086)
0.485 (0.059)
0.451 (0.078)
0.420 (0.059)
0.477 (0.057)
0.476 (0.053)
0.426 (0.057)
0.492 (0.064)
0.482 (0.050)
a Number of individual soil samples included in data compiled by Clapp and Hornberger
  (1978).
b Empirical parameter relating soil matrix potential and moisture content; shown to be strongly
  dependent on soil texture.
c Volumetric soil moisture content (volume of water per volume of soil).
d Standard deviation in parentheses.

Source: Adapted from: Clapp, R.B., and G.M. Hornberger.  1978.  "Empercial Equations for
Some Soil Hydraulic Properties."  Water Resour. Res. 14(4): 601-604.
                                          C-2

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            Table C-3. Representative Values of Saturated Hydraulic Conductivity
Soil texture
Sand
Loamy sand
Sandy loam
Loam
Silt loam
Sandy clay loam
Silt clay loam
Clay loam
Sandy clay
Silt clay
Clay
Number of soils"
762
338
666
383
1,206
498
366
689
45
127
291
Hydraulic i
(Ks; cm
5.8x
1.7 x
7.2 x
3.7 x
1.9 x
1.2 x
4.2 x
6.4 x
3.3 x
2.5 x
1.7 x
cone
/sec"
io-3
io-3
io-4
io-4
io-4
io-4
io-5
io-5
io-5
io-5
io-5
a Number of individual soil samples included in data compiled by Rawls et al. (1982).
b Predicted values based on compiled soil properties.

Source: Adapted from: Rawls, W.J., 1986.  Computer printouts from the soils data base, dated
August 28, 1986. From WJ Rawls, Beltsville, MD:  Beltsville Agricultural Research Center. As
cited in EPA88b.
                                          C-3

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    Table C-4. Saturated Hydraulic Conductivity Ranges for Selected Rock and Soil Types
Saturated hydraulic
conductivity (cm/sec)
Soils
Unweathered marine clay
Glacial till
Silt, loess
Silty sand
Clean sand
Gravel
Rocks
Unfractured metamorphic and igneous rock
Shale
Sandstone
Limestone and dolomite
Fractured igneous and metamorphic rock
Permeable basalt
Karst limestone
Source: Adapted from: Freeze, R.A. and J. Cherry, 1979.

5 x ID'11
io-7
1Q-io
io-7
io-5
io-4
io-1

io-8
5 x IQ-12
io-8
5 x 1Q-8
ID'6
io-5
io-4
Groundwater.

-
- io-4
- io-3
- io-1
- 1
- IO2

- io-2
- io-7
- 5 x 1Q-4
- 5 x 1Q-4
- io-2
- 1
- 1
Prentice-Hall,
Englewood Cliffs, N.J.
                                          C-4

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                 Table C-5. Distribution Coefficient (Kd) of Selected Radionuclides Sorbed by Clays and Cation
                           Exchange Capacity for Selected Clay Minerals
Material
Illite
Kaolinite
Montmorillonite
Vermiculite
Average
Cesium
98
68
50
100
Percent Activity Sorbed(a)
Cobalt
86
61
62
99
Strontium-85
27
66
67
97
Zirconium-
Niobium-85
94
94
35

Cesium
180,000
2,200
1,000
12,000
Average K^
Cobalt
6,400
3,100
1,700
4,700
Strontium-85
370
4,000
2,100
1,800
Zirconium-
Niobium- 8 5
47,500
56,000
540

(a)  Average percent and average K^ of radionuclides sorbed by clays in distilled water at pH 6 over a period of 7 days (vermiculite, 8
   days).
(b)
   Reported in millequivalents per lOOg of soil [Source:  GRI68].
Source: Derived from:
Webster, G.B. et al., 1976. "Radionuclide Migration from Low-Level Wastes: A Generic Overview," in M.W. Carter et al. (editors),
Management of Low-Level Radioactive Waste. Pergamon Press, New York, NY, pp. 1041-1072.

Grim, 1968.

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           Table C-6. Typical Values of Hydraulic Conductivity of Porous Materials
Material
Number of
analyses
Igneous rocks
 Weathered granite            7
 Weathered gabbro            4
 Basalt                      93

Sedimentary materials
 Sandstone (fine)             20
 Siltstone                     8
 Sand (fine)                 159
 Sand (medium)             255
 Sand (coarse)               158
 Gravel                      40
 Silt                         39
 Clay                       19

Metamorphic rocks
 Schist                      17
Arithmetic
Range
(cm/s)
                           (3.3-52X10'4
                          (0.5-3.8) X10-4
                        (0.2-4250) X1Q-8
                        (0.5-2270) X1Q-6
                         (0.1-142) X10-8
                         (0.2-189)X1Q-4
                         (0.9-567) X10-4
                        (0.3-6610)X1Q-4
                         (0.3-31.2) X10-1
                       (0.09-7090) X10-7
                          (0.1-47)X1Q-8
                      (0.002-1130) X 10
                                      1-6
mean
(cm/s)
                     1.65X10'3
                     1.89X10-4
                     9.45 X1Q-6
                    3.31 X1Q-4
                    1.9X10-7
                    2.88 X1Q-3
                    1.42X10-2
                    5.20X10'2
                    4.03 X ID'1
                    2.83 X ID'5
                    9X10'8
                     1.9X10"
Source: McWhorter, D.B., and D.K. Sunada, 1977. Ground-Water Hydrology and
         Hydraulics, Water Resources Publications, Fort Collins, Colo.
                                           C-6

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             Table C-7. Suggested Value for Cet Relating Evaporation from a U.S. Class A Pan to Evapotranspiration
                       from 8 to 15-cm Tall, Well-Watered Grass Turf
                                                                                                 Pan surrounded by a
short green crop
Wind

Light
< 170 km/day

Moderate
170-425 km/day

Strong
425-700 km/day

Very strong
>700 km/day
Pan surrounded bv a dry surface ground
Upwind
fetch of
crop
(m from pan)
0.75
10
100
1000
0
10
100
1000
0
10
100
1000
0
10
100
1000
Average regional
relative humiditv. %*
20-40
0
0.65
0.7
0.7
0.5
0.6
0.65
0.7
0.45
0.55
0.6
0.65
0.4
0.45
0.5
0.55
* Mean of maximum and minimum relative
Source: Jenson,
Civil Engineers.
M.E., ed., 1973.
As presented by
40-70
0.7
0.75
0.8
0.85
0.6
0.7
0.75
0.8
0.5
0.6
0.65
0.7
0.45
0.55
0.6
0.6
>70
0.8
0.85
0.85
0.85
0.65
0.75
0.8
0.8
0.6
0.65
0.7
0.75
0.5
0.6
0.65
0.65
Upwind
fetch of dry Average regional
fallow relative humiditv. %*
(m from pan) 20-40
0.85
10
100
1000
0
10
100
1000
0
10
100
1000
0
10
100
1000

0.6
0.55
0.5
0.65
0.55
0.5
0.45
0.6
0.5
0.45
0.4
0.5
0.45
0.4
0.3
40-70 >70
0 0.55 (
0.7
0.65
0.6
0.75
0.65
0.6
0.55
0.65
0.55
0.5
0.45
0.6
0.5
0.45
0.4
0.8
0.75
0.7
0.8
0.7
0.65
0.6
0.7
0.65
0.6
0.55
0.65
0.55
0.5
0.45
humidities.
Consumptive use of water and irrigation water requirements. New York
Enfield et al. 1982. Approximating pollutant transport to ground water.
, NY: American Soci
Ground Water 20(6):
                                                                                                                 0.65
722. As cited in EPA88b.

Enfield, C.G., R.F. Carsel, S.Z. Cohen, T. Phan, D.M. Walters, 1982. Approximating pollutant transport to ground water. Ground
Water 20(6): 711-722. As cited in EPA88b.

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               Table C-8. Crop Coefficients for Estimating Evapotranspiration
Crop
Alfalfa
Potatoes
Small grains
Sugar beets
Period
April 1 - October 10
May 10 - September 15
April 1 - July 20
April 10 - October 15
Coefficient
(Cveg)
0.87
0.65
0.6
0.6
Source: Jenson, M.E., ed., 1973.  Consumptive use of water and irrigation water requirements.
New York, NY: American Society of Civil Engineers. As presented by Enfield et al. 1982.
Approximating pollutant transport to ground water. Ground Water 20(6): 711-722. As cited in
EPA88b.

Enfield, C.G., R.F. Carsel, S.Z. Cohen, T. Phan, D.M. Walters, 1982.  Approximating pollutant
transport to ground water. Ground Water 20(6): 711-722. As cited in EPA88b.

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                 Table C-9. Typical Values of Porosity of Aquifer Materials
Aquifer material
Number of
analyses
Range
Igneous Rocks
 Weathered granite
 Weathered gabbro
 Basalt
 4
94
0.34-0.57
0.42-0.45
0.03-0.35
Arithmetic
  mean

   0.45
   0.43
   0.43
   0.17
Sedimentary Materials
 Sandstone                     65
 Siltstone                       7
 Sand (fine)                   245
 Sand (coarse)                  26
 Gravel (fine)            0.2380.38
 Gravel (coarse)                15
 Silt                          281
 Clay                         74
 Limestone                     74
                      0.14-0.49
                      0.21-0.41
                      0.25-0.53
                      0.31-0.46

                      0.24-0.36
                      0.34-0.51
                      0.34-0.57
                      0.07-0.56
                         0.34
                         0.35
                         0.43
                         0.39
                      0.34
                         0.28
                         0.45
                         0.42
                         0.30
Metamorphic Rocks
 Schist
18
0.04-0.49
   0.38
Source: McWhorter, D.B., and D.K. Sunada, 1977. Ground-Water Hydrology and
         Hydraulics, Water Resources Publications, Fort Collins, Colo. Reprinted with
         permission.
                                           C-9

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   Table C-10. Typical Values of Effective Porosity (or Specific Yield) of Aquifer Materials
Aquifer material
Sedimentary Materials
Sandstone (fine)
Sandstone (medium)
Siltstone
Sand (fine)
Sand (medium)
Sand (coarse)
Gravel (fine) 33
Gravel (medium)
Gravel (coarse)
Silt
Clay
Limestone
Wind-Laid Materials
Loess
Eolian Sand
Tuff
Metamorphic Rock
Schist
Number of
analyses

47
10
13
287
297
143
0.13-0.40
13
9
299
27
32

5
14
90

11
Range

0.02-040
0.12-0.41
0.01-0.33
0.01-0.46
0.16-0.46
0.18-0.43
0.28
0.17-0.44
0.13-0.25
0.01-0.39
0.01-0.18
~0-0.36

0.14-0.22
0.32-0.47
0.02-0.47

0.22-0.33
                                                                            Arithmetic
                                                                                  mean
                                                                                     0.21
                                                                                     0.27
                                                                                     0.12
                                                                                     0.33
                                                                                     0.32
                                                                                     0.30

                                                                                     0.24
                                                                                     0.21
                                                                                     0.20
                                                                                     0.06
                                                                                     0.14
                                                                                     0.18
                                                                                     0.38
                                                                                     0.21
Source: McWhorter, D.B., and D.K. Sunada, 1977. Ground-Water Hydrology and
         Hydraulics, Water Resources Publications, Fort Collins, Colo. Reprinted with
         permission.
                                                                                     0.26
                                          C-10

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Table C-l 1.  Dispersivity Values oc£ and ccr Obtained Directly through Measurements of Tracer Breakthrough Curves in
      Groundwater Solute Transport
Setting
Chalk River, Ontario
alluvial aquifer
Chalk River, strata of
high velocity
Alluvial aquifer
Alluvial, strata of
high velocity
Lyons, France
alluvial aquifer
Lyons (full aquifer)
Lyons (full aquifer)

Lyons (full aquifer)

Lyons (full aquifer)

Lyons (full aquifer)

Alsace, France
alluvial sediments
Carlsbad, N. Mex.
fractured dolomite
Savannah River, S.C.
fractured schistgneiss
a£ ccr Axa Ub
(m) (m) (m) (m/d)
0.034

0.034-0.1

0.5
0.1

0.1-0.5

5
12.0 31.1-14 7.2

8 0.015-1 9.6

5 0.145-14.5 13

7 0.009-1 9

12 4

38.1 38.1 0.15

134.1 538 0.4

Method
Single-well tracer
test
Single-well

Two -well
Two -well

Single-well

Single-well
Single-well test
with resistivity
Single-well test
with resistivity
Single-well test
with resistivity
Single-well test
with resistivity
Environmental tracer

Two-well tracer

Two-well


-------
                                              Table C-11 (Continued)
Setting
Barstow, Calif.
alluvial sediments
Dorset, England
chalk (fractured)
(intact)
Berkeley, Calif.
sand/gravel
Mississippi limestone
NTS, carbonate
aquifer
Pensacola, Fla.
limestone
«£
(m)
15.2


3.1
1.0
2-3

11.6
15

10

ccr Axa
(m) (m)
6.4


8
8
8




312

Ub
(m/d)





311-1382




0.6

                                                                                               Method

                                                                                               Two-well
                                                                                               Two-well
                                                                                               Two-well
                                                                                               Multiwell trace test

                                                                                               Single-well
                                                                                               Two-well tracer

                                                                                               Two-well
aAx = distance between wells in two-well test.
bU = groundwater seepage velocity.
Source:  Evenson, D.E., and M.D. Dettinger, 1980. Dispersive Processes in Models of Regional Radionuclide Migration,
        University of California, Lawrence Livermore Laboratory, Livermore.

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