PB 94-205804EPA 402-R-94-012

June 1994

A TECHNICAL GUIDE TOGROUND-WATER MODEL SELECTION

AT SITES CONTAMINATED WITHRADIOACTIVE SUBSTANCES

A Cooperative Effort By

Office of Radiation and Indoor AirOffice of Solid Waste and Emergency Response

U.S. Environmental Protection AgencyWashington, D.C. 20460

Office of Environmental RestorationU.S. Department of EnergyWashington, D.C. 20585

Office of Nuclear Material Safety and SafeguardsNuclear Regulatory Commission

Washington, D.C. 20555

i

PREFACE

A joint program is underway between the EPA Offices of Radiation and Indoor Air (ORIA) andSolid Waste and Emergency Response (OSWER), the DOE Office of Environmental Restorationand Waste Management (EM), and the NRC Office of Nuclear Material Safety and Safeguards(NMSS). The purpose of the program is to promote the appropriate and consistent use ofmathematical models in the remediation and restoration process at sites containing, orcontaminated with, radioactive materials. This report is one of a series of reports designed toaccomplish this objective. Other reports completed under this program have identified the modelsin actual use at NPL sites and facilities licensed under RCRA, and at DOE sites and NRC sitesundergoing decontamination and decommissioning (D&D), as well as the role of modeling andmodeling needs in each phase of the remedial investigation. This report specifically addresses theselection of ground-water flow and contaminant transport models and is intended to be used byhydrogeologists and geoscientists responsibile for identifying and selecting ground-water flow andcontaminant transport models for use at sites containing radioactive materials.

ii

ACKNOWLEDGMENTS

This project is coordinated by the Office of Radiation and Indoor Air, U.S. EnvironmentalProtection Agency, Washington, D.C., and jointly funded by the following organizations:

EPA Office of Radiation and Indoor Air (ORIA)EPA Office of Solid Waste and Emergency Response (OSWER)DOE Office of Environmental Restoration and Waste Management (EM)NRC Office of Nuclear Material Safety and Safeguards (NMSS)

The project Steering Committee for this effort includes:

EPA

Beverly Irla, EPA/ORIA Project OfficerRonald Wilhelm, EPA/ORIAKung-Wei Yeh, EPA/ORIALoren Henning, EPA/OSWER

DOE

Paul Beam, DOE/EM

NRC

Harvey Spiro, NRC/NMSS

Consultants and Contractors

John Mauro, S. Cohen & Associates, Inc.David Back, HydroGeoLogic, Inc.*Paul Moskowitz, Brookhaven National LaboratoryRichard Pardi, Brookhaven National LaboratoryJames Rumbaugh, Geraghty & Miller, Inc.

*principal author

We acknowledge the technical support and cooperation provided by these organizations andindividuals. We also thank all reviewers for their valuable observations and comments.

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CONTENTS

Page

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S-1

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-11.1 Background - Purpose and Scope of the Joint EPA/DOE/NRC Program . . . . . . . . . . 1-11.2 Purpose and Scope of this Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-31.3 Principal Sources of Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-41.4 Key Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-41.5 Organization of the Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5

2 Modeling Decisions Facing the Site Remediation Manager . . . . . . . . . . . . . . . . . . . . . . . . 2-12.1 Is Ground Water a Potentially Important Exposure Pathway? . . . . . . . . . . . . . . . . . . . 2-12.2 Reasons for Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-32.3 Planning for Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3

2.3.1 Identifying Modeling Needs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-32.3.2 Sources of Assistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7

2.3.2.1 Branches and Divisions Within Agencies . . . . . . . . . . . . . . . . . . . . 2-72.3.2.2 Electronic Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7

3 Constructing and Refining the Conceptual Model of the Site . . . . . . . . . . . . . . . . . . . . . . 3-13.1 Basic Questions that Will Need to be Answered . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-23.2 Components of the Conceptual Model for the Ground-water Pathways . . . . . . . . . . . 3-2

3.2.1 Contaminant/Waste Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-23.2.2 Environmental Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-33.2.3 Land Use and Demography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-5

4 Code Selection - Recognizing Important Model Capabilities . . . . . . . . . . . . . . . . . . . . . . . 4-14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-14.2 General Considerations - Code Selection During Each Phase in the Remedial Process 4-1

4.2.1 Scoping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-34.2.1.1 Conservative Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-34.2.1.2 Steady-State Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-54.2.1.3 Restricted Dimensionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-54.2.1.4 Uncomplicated Boundary and Uniform Initial Conditions . . . . . . . . 4-74.2.1.5 Simplified Flow and Transport Processes . . . . . . . . . . . . . . . . . . . . 4-84.2.1.6 Uniform Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-8

iv

CONTENTS (Continued)

Page

4.2.2 Site Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-94.2.2.1 Site-Specific Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-104.2.2.2 Steady-State Flow/Transient Transport . . . . . . . . . . . . . . . . . . . . 4-104.2.2.3 Multi-Dimensional . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-114.2.2.4 Constant Boundary and Non-uniform Initial Conditions . . . . . . . . 4-124.2.2.5 Complex Flow and Transport Processes . . . . . . . . . . . . . . . . . . . . 4-134.2.2.6 System Heterogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-14

4.2.3 Remedial Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-144.2.3.1 Remedial Action Specific . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-154.2.3.2 Transient Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-184.2.3.3 Multi-Dimensional . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-184.2.3.4 Transient Boundary and Non-Uniform Initial Conditions . . . . . . . 4-184.2.3.5 Specialized Flow and Transport Processes . . . . . . . . . . . . . . . . . . 4-194.2.3.6 System Heterogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-20

4.3 Specific Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-204.3.1 Site-Related Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-23

4.3.1.1 Source Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-234.3.1.2 Aquifer and Soil/Rock Characteristics . . . . . . . . . . . . . . . . . . . . . 4-274.3.1.3 Transport and Fate Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-364.3.1.4 Multiphase Fluid Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-414.3.1.5 Flow Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-424.3.1.6 Time Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-43

4.3.2 Code-Related Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-434.3.2.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-444.3.2.2 Source Code Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-454.3.2.3 Code Testing and Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-454.3.2.4 Model Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-47

4.4 Modeling Dilemmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-47

5 The Code Selection Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-15.1 Overview of the Code Review and Selection Process . . . . . . . . . . . . . . . . . . . . . . . . . 5-15.2 Evaluation Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-5

5.2.1 Administrative Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-55.2.2 Criteria Based on Phase in the Remedial Process . . . . . . . . . . . . . . . . . . . . 5-75.2.3 Criteria Based on Waste and Site Characteristics . . . . . . . . . . . . . . . . . . . . 5-75.2.4 Criteria Based on Code Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . 5-10

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R-1

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-1

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CONTENTS (Continued)

Page

Appendices

A Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-1B Ground-water Modeling Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-1C Solution Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-1D Code Attribute Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-1E Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E-1

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FIGURES

Number Page

1-1 Exposure Pathways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1

3-1 Example Conceptual Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1

4-1 One-Dimensional Representation of Conceptual Model. . . . . . . . . . . . . . . . . . . . . . . . 4-54-2 Two-Dimensional Cross-Sectional Representation of Unsaturated Zone in

Conceptual Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-64-3 Two-Dimensional Areal Representation of Saturated Zone Conceptual Model. . . . . . 4-64-4 Three-Dimensional Representation of Conceptual Model. . . . . . . . . . . . . . . . . . . . . . 4-64-5 Typical System Boundary Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-74-6 Water Table and Confined Aquifers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-284-7 Perched Water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-314-8 Macropores and Fractures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-324-9 Hydrodynamic Dispersion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-384-10 Matrix Dispersion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-39

5-1 Code Selection Review Process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-35-2 General Classification of Selection Criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-65-3 Physical, Chemical, and Temporal Site-Related Selection Criteria . . . . . . . . . . . . . . . . 5-95-4 Source Code Availability and History of Use Selection Criteria . . . . . . . . . . . . . . . . 5-115-5 Quality Assurance Selection Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-125-6 Hardware Requirements Selection Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-175-7 Mathematical Solution Methodology Acceptance Criteria. . . . . . . . . . . . . . . . . . . . . 5-185-8 Code Output Selection Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-195-9 Code Dimensionality Selection Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-21

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TABLES

Number Page

2-1 Matrix of Reasons for Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4

4-1 General Modeling Approach as a Function of Project Phase . . . . . . . . . . . . . . . . . . . . 4-2

4-2 Questions Pertinent to Model Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-214-3 Site-Related Features of Ground-Water Flow and Transport Codes . . . . . . . . . . . . . 4-244-4 Code-Related Features of Ground-Water Flow and Transport Codes . . . . . . . . . . . . 4-25

5-1 Model Selection Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-4

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SUMMARY

A TECHNICAL GUIDE TO GROUND-WATER MODEL SELECTIONAT SITES CONTAMINATED WITH RADIOACTIVE SUBSTANCES

S.1 INTRODUCTION

A joint program is underway between theEnvironmental Protection Agency (EPA) Offices ofRadiation and Indoor Air (ORIA) and Solid Waste andEmergency Response (OSWER), the Department ofEnergy (DOE) Office of Environmental Restorationand Waste Management (EM), and the NuclearRegulatory Commission (NRC) Office of NuclearMaterial Safety and Safeguards (NMSS). The purposeof the program is to promote the appropriate andconsistent use of mathematical models in theremediation and restoration process at sites containing,or contaminated with, radioactive materials. Thisreport, which is one of a series of reports designed toaccomplish this objective, specifically addresses theselection of ground-water flow and contaminanttransport models. It is intended to be used byhydrogeologists and geoscientists responsible foridentifying and selecting ground-water flow andcontaminant transport models for use at sitescontaining or contaminated with radioactive materials.

Previous reports in this series have determined that thetypes of models and the processes that requiremodeling during the remedial process depend on acombination of the following five factors:

1. reasons for modeling,2. contaminant/waste characteristics,3. site environmental characteristics,4. site land use and demography, and5. phase of the remedial process.

This report describes and provides a rationale for themethods for selecting ground-water flow andcontaminant transport models and computer codes thatmeet the modeling needs at sites containing, orcontaminated with, radioactive materials. Theselection process is described in terms of the varioussite characteristics and processes requiring modelingand the availability, reliability, and useability of thecomputer codes that meet the modeling needs.

Though this report is limited to a discussion of themodel selection process, the proper application of the

selected codes is as important, if not more important,than code selection. A code, no matter how well suitedto a particular application, could give erroneous andhighly misleading results if used improperly or withincomplete or erroneous input data. Conversely, evena code with very limited capabilities, or a code used ata site which has not been well characterized, can givevery useful results if used intelligently and with a fullappreciation of the limitations of the code and theinput data.

It was not possible, within the scope of this report, toaddress computer code applications, quality control,and the presentation and interpretation of modelingresults. Future reports to be prepared under thisprogram will address these important topics.

The report is divided into five sections. Following thisintroduction, Section 2 presents an overview of thetypes of ground-water modeling decisions facing thesite remediation manager. This section is designed tohelp the site manager and/or earth scientists todetermine the role of, and need for, modeling insupport of remedial decision making.

Section 3 addresses the construction of a conceptualmodel of a site and how it is used in the initialplanning and scoping phases of a site remediation,especially as it pertains to the selection and use ofground-water flow and contaminant transport codes.

Section 4 describes the various site characteristics andground-water flow and contaminant transportprocesses that may need to be explicitly modeled. Thepurpose of this section is to help the earth scientistsrecognize the conditions under which specific codefeatures and capabilities are needed to supportremedial decision making during each phase in the siteremediation process.

Section 5 describes the computer code review andevaluation process for screening and selecting thecomputer codes that are best suited to meet site-specificmodeling needs.

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S.2 MODELING QUESTIONS FACING THESITE REMEDIATION MANAGER

A review of current regulations and guidelinespertaining to the remediation of sites on the NationalPriorities List (NPL) and in the NRC's SitesDecommissioning Management Program (SDMP)reveals that fate and effects modeling is not explicitlyrequired. However, in order to make informed anddefensible remedial decisions, ground-water flow andcontaminant transport modeling can be useful and isoften necessary.

S.2.1 When is Ground-Water ModelingNeeded?

The first questions that a site remediation managerwill need to answer regarding ground-water modelinginclude: Is ground-water modeling needed, and howwill modeling aid in the remedial decision makingprocess?

The ground-water pathway may be considered apotentially significant exposure pathway if (1) theradionuclide concentrations in the ground waterexceed the levels acceptable to the cognizant regulatoryauthorities or (2) the contamination at the site couldeventually cause the radionuclide concentrations inground water to exceed the applicable criteria. On thisbasis, if the measured concentrations of radionuclidesin ground water downgradient from the site, or inleachate at the site, exceed the applicable criteria, andthe ground water in the vicinity of the site is beingused, or has the potential to be used, as a source ofdrinking water, it is likely that ground-water modelingwill be useful, if not necessary, in support of remedialdecision making at the site.

The "applicable criteria" are ill-defined at this timebecause both NRC and EPA are engaged inrulemaking activities intended to define the criteria.However, in the interim, the drinking-water standardsset forth in 40 CFR 141 should guide remedialdecision making. For example, 40 CFR 141 has beencited as an applicable or relevant and appropriateregulation (ARAR) in establishing the remediationgoals at most of the approximately 50 sitescontaminated with radioactive material that arecurrently on the National Priorities List.

At some sites, information may not be availableregarding the levels of radionuclide contamination inground water or leachate. Alternatively, radionuclide

measurements may have been made, but yieldinconclusive results. Under these conditions, theradionuclide concentrations in leachate and groundwater can be estimated based on knowledge of theradionuclide concentrations in the soil or the waste atthe site and empirically determined partition factors.Partition factors relate a given concentration of acontaminant in the waste or the soil to that in theleachate or ground water.

If the product of the radionuclide concentrations in thewaste or contaminated soil with the appropriatepartition factors results in radionuclide concentrationsin leachate or ground water in excess of the applicablecriteria, it may be concluded that the radionuclideconcentrations in ground water in the vicinity of thesite could exceed the applicable criteria. Though it isnot necessarily always the case, if the measured orderived concentrations of radionuclides in groundwater exceed the applicable criteria, it is likely thatground-water modeling will serve a useful role insupport of remedial decision making at the site.

S.2.2 When is Modeling Not Needed orInappropriate?

It is important to be able to recognize thecircumstances under which modeling would beineffective and should probably not be performed.There are three general scenarios in which modelingwould be of limited value. These are:

1. Presumptive remedies can be readilyidentified,

2. Decision making is based on highlyconservative assumptions, and/or

3. The site is too complex to modelrealistically.

The first case arises in situations where a presumptiveremedy is apparent; that is, where the remedy isobvious based on regulatory requirements or previousexperience, and there is a high level of assurance thatthe site is well understood and the presumptive remedywill be effective. An example would be conditions thatobviously require excavation or removal of thecontaminant source.The second case is based on the assumption thatdecision making can proceed based on conservativeestimates of the behavior and impacts of contaminantsat the site rather than detailed modeling. This strategy

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could be used in the initial scoping, sitecharacterization, or remedial phase of theinvestigation. For example, a conservative approachto the risk assessment would be to assume that thecontaminant concentrations at the receptor(s) areidentical to the higher concentrations detected at thecontaminant source. Thus, the need for modeling todetermine the effects of dilution and attenuation oncontaminant concentrations is removed.

The third case involves sites where modeling would behelpful in supporting remedial decision making, butthe complexity of the site precludes reliable modeling.These complexities could be associated with thecontaminant source, flow and transport processes, orcharacteristics of the wastes and contaminants. Forexample, the contaminant source may be so poorlydefined in terms of areal extent, release history, andcomposition that it cannot be reliably defined and littlewould be gained from flow and transport modeling.

Complex flow and contaminant transport processespresent another difficulty in that user-friendlycomputer codes currently do not exist thataccommodate a number of these processes, whichinclude: turbulent ground-water flow, facilitatedtransport (e.g., due to the formation of colloids), andflow and transport through a fractured unsaturatedzone.

The availability of computer codes is also an issuewhen characteristics of the contaminants are typifiedby complex geochemical reactions, such as phasetransformations and non-linear sorption processes.Currently, ground-water flow and contaminanttransport codes that provide credible mathematicaldescriptions of the more complex geochemicalprocesses have not been developed. If modeling is notpossible because of the overall complexity of the sitecharacteristics, it is common for a greater emphasis tobe placed on empirical rather than predicted data.This may involve establishing long-

term monitoring programs, which, in effect, haveobjectives similar to those of ground-water modeling.

S.2.3 What Role Will Ground-Water ModelingPlay in Support of RemedialDecision Making?

Once it is determined that the ground-water exposurepathway is potentially important, ground-water flowand transport modeling can have a wide range of usesin support of remedial decision making. The followingare the principal reasons for modeling on a remedialproject. These applications can surface during anyphase of the remedial process. However, some of thesereasons are more likely to occur during specific phasesof a remedial project.

1. When it is not feasible to perform fieldmeasurements; i.e.,

! Cannot get access to sampling locations! Budget is limited! Time is limited

2. When there is concern that downgradient locationsmay become contaminated at some time in thefuture; i.e.,

! When transport times from the source of thecontamination to potential receptor locationsare long relative to the period of time thesource of the contaminant has been present.

! When planning to store or dispose of waste ata specific location and impacts can beassessed only through the use of models.

3. When field data alone are not sufficient tocharacterize fully the nature and extent of thecontamination; i.e.,

! When field sampling is limited in space andtime, and

! When field sampling results are ambiguous orsuspect.

4. When there is concern that conditions at a sitemay change, thereby changing the fate andtransport of the contaminants; i.e.,

! seasonal changes in environmental conditions! severe weather (e.g., floods)! accidents (e.g., fires)

5. When there is concern that institutional control atthe site may be lost at some time in the future

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resulting in new exposure scenarios, or a changein the fate and transport of the contaminants; i.e.,

! trespassers! inadvertent intruder (construction/

agriculture)! human intervention (drilling, excavations,

mining)

6. When remedial actions are planned and there is aneed to predict the effectiveness of alternativeremedies.

7. When there is a need to predict the time when theconcentration of specific contaminants at specificlocations will decline to acceptable levels (e.g.,natural flushing).

8. When there is concern that at some time in thepast individuals were exposed to elevated levels ofcontamination and it is desirable to reconstruct thedoses.

9. When there is concern that contaminants may bepresent but below the lower limits of detection.

10. When field measurements reveal the presence ofsome contaminants, and it is desirable todetermine if and when other contaminantsassociated with the source may arrive, and at whatlevels.

11. When field measurements reveal the presence ofcontaminants and it is desirable to identify thesource or sources of the contamination.

12. When there is a need to determine the timing ofthe remedy; i.e., if the remedy is delayed, is therea potential for environmental or public healthimpacts in the future?

13. When there is a need to determine remedial actionpriorities.

14. When demonstrating compliance with regulatoryrequirements.

15. When estimating the benefit in a cost-benefitanalysis of alternative remedies.

16. When performing a quantitative dose or riskassessment pertaining to the protection of

remediation workers, the public, and theenvironment prior to, during, and followingremedial activities.

17. When designing the site characterization program(e.g., placement of monitor wells, determiningdata needs) and identifying exposure pathways ofpotential significance.

18. When there is a need to compute or predict theconcentration distribution in space and time ofdaughter products from the original source ofradionuclides.

19. When there is a need to quantify the degree ofuncertainty in the anticipated behavior of theradionuclides in the environment and theassociated doses and risks.

20. When communicating with the public on thepotential impacts of the site and the benefits of theselected remedy.

S.2.4 What Will the Results of a ModelingExercise Yield?

Once the need for, and role of, modeling is identified,it is appropriate to determine or define the form of theresults or output of the modeling exercise. In general,the results are expressed as a concentration, such aspCi/L in ground water at a specific location. Thederived radionuclide concentrations could also beexpressed as a function of time or as a time-averagedvalue.

Some computer codes have the ability to convert thederived radionuclide concentrations in ground water todoses or risks to individuals exposed to thecontaminated ground water. These results aregenerally expressed in units of mrem/yr or lifetime riskof cancer for the exposed individuals.

Some computer codes can present the results in termsof cumulative population impacts. These results aregenerally expressed in terms of person-rems/yr or totalnumber of cancers induced per year in the exposedpopulation.

The specific regulatory requirements that apply to theremedial program determine which of these "endproducts" are needed. In general, these modelingresults are used to assess impacts or compliance with

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applicable regulations; however, information regardingradionuclide flux and plume arrival times anddistributions is also used to support a broad range ofremedial decisions.

These modeling endpoints must be clearly defined,since the type of endpoint will help to determine thetype of ground-water flow and contaminant transportmodel that will support the endpoint of interest. Forexample, a baseline risk assessment at a sitecontaminated with radioactive material is used indetermining the annual radiation dose to an individualdrinking water obtained from a potentiallycontaminated well. The endpoint in this case is thedose to an individual expressed in units of mrem/yr.In order to estimate this dose, it is necessary toestimate the average concentration of radionuclides inthe well water over the course of a year. The models,input parameters, and assumptions needed to predictthe annual average radionuclide concentration aredifferent than those needed to predict the time varyingconcentration at a given location. The latter usuallyrequires much more input data and models capable ofsimulating dynamic processes.

S.3 CONSTRUCTING A CONCEPTUALMODEL OF A SITE - THE FIRST STEPIN THE MODEL SELECTIONPROCESS

The first step in the model selection process is theconstruction of a conceptual model of the site. Theconceptual model depicts the types of waste andcontaminants, where they are located (e.g., are theycurrently only in the surficial soil or have theymigrated to the underlying aquifer?), and how they arebeing transported offsite (e.g., by runoff, percolationinto the ground, and transport in ground water, orsuspension or volatilization into the air and transportby the prevailing meteorological conditions). Theconceptual model also attempts to help visualize thedirection and path followed by the contaminants, thecontrolling factors that affect the contaminantmigration through the subsurface (i.e., hydrogeology,system boundary conditions), the actual or potentiallocations of the receptors, and the ways in whichreceptors may be exposed, such as direct contact withthe source, ingestion of contaminated food or water, orinhalation of airborne contaminants. As informationregarding a site accumulates, the conceptual model iscontinually revised and refined.

A mathematical model translates the conceptual modelinto a series of equations which simulate the fate andeffects of the contaminants as depicted in theconceptual model at a level of accuracy that cansupport remedial decision making. A computer codeis simply a tool that is used to solve the equationswhich constitute the mathematical model of the siteand display the results in a manner convenient tosupport remedial decision making. Accordingly, codeselection must begin with the construction of aconceptual model of the site.

The components that make up the initial conceptualmodel of the site include:

1. the waste/contaminant characteristics, 2. the site characteristics, including

hydrogeology, land use, and demography, and3. the exposure scenarios and pathways.

S.3.1 Waste/Contaminant Characteristics

To the extent feasible, the site conceptual model shouldaddress the following characteristics of thewaste/contaminants:

! Types and chemical composition of theradionuclides

! Waste form and containment

! Source geometry (e.g., volume, area, depth,homogeneity)

Within the context of ground-water modeling, thesecharacteristics are pertinent to modeling the sourceterm, i.e., the rate at which radionuclides aremobilized from the source and enter the unsaturatedand saturated zones of a site.

S.3.2 Site Characteristics

The conceptual model of the site should begin toaddress the complexity of the environmental andhydrogeological setting. A complex setting, such ascomplex lithology, a thick unsaturated zone, and/orstreams or other bodies of water on site, generallyindicates that the direction and velocity of ground-water flow and radionuclide transport at the site cannotbe reliably simulated using simple models.

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However, even at complex sites, complex models maynot be needed. For example, if a conservativeapproach is taken, where transport through theunsaturated zone is assumed to be instantaneous, thenthe complex processes associated with flow andtransport through the unsaturated zone would not needto be modeled. Such an approach would beappropriate at sites where the remedy is likely to beremoval of the contaminated surface and near-surfacematerial.

The site conceptual model will also need to identify thelocations where ground water is currently being used,or may be used in the future, as a private or municipalwater supply. At sites with multiple user locations, anunderstanding of ground-water flow in two or threedimensions is needed in order to predict realisticallythe likelihood that the contaminated plume will becaptured by the wells located at different directions,distances, and depths relative to the sources ofcontamination.

Simple ground-water flow and transport modelstypically are limited to estimating the radionuclideconcentration in the plume centerline down-gradientfrom the source. Accordingly, if it is assumed that thereceptors are located at the plume centerline, a simplemodel may be appropriate. Such an assumption isoften appropriate even if a receptor is not currentlypresent at the centerline location because the resultsare generally conservative. In addition, riskassessments often postulate that a receptor could belocated directly down-gradient of the source at sometime in the future.

The need for complex models increases if there are anumber of water supplies in the vicinity of the source.Under these circumstances, it may be necessary tocalculate the cumulative population doses and risks,which require modeling the radionuclideconcentrations at a number of specific receptorlocations. Accordingly, off-centerline modeling whichincludes dispersion may be needed.

S.3.3 Exposure Scenarios and Pathways

The conceptual model of the site will also need todefine the exposure scenarios and pathways at the site.An exposure scenario pertains to the assumed initialconditions or initiating events responsible for the

transport of the radionuclides and exposure of thenearby population. Depending on the regulatoryrequirements and the phase in the remedial process,the exposure scenarios that will need to be modeledcan include any one or combination of the following:

! The no action alternative - Under thisscenario, the radiation doses and risks tomembers of the public, now and in the future,are derived assuming no action is taken toremedy the site or protect the public fromgaining access to the site.

! Trespassers - This scenario postulates that anindividual trespasses on the site.

! Inadvertent intruder - This scenariopostulates that an individual establishesresidence at the site.

! Routine emissions - This scenario simplyassesses offsite doses and risks associatedwith the normally anticipated releases fromthe site. (This concept is similar to the "NoAction Alternatives," but is used within thecontext of NRC licensed facilities.)

! Accidents - This scenario assesses doses andrisks associated with postulated accidentalreleases from the site.

! Alternative remedies - This set of scenariosassesses the doses and risks to workers andthe public associated with the implementationof specific remedies and the reduction inpublic doses and risks followingimplementation of the remedy.

The number of scenarios that may be postulated isvirtually unlimited. Accordingly, it is necessary todetermine which scenarios reasonably bound what mayin fact occur at the site. The types of scenarios selectedfor consideration influence modeling needs becausethey define the receptor locations and exposurepathways that need to be modeled.

For each scenario, an individual or group ofindividuals may be exposed by a wide variety ofpathways. The principal pathways include:

! External exposure to deposited radionuclides

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! External exposures to airborne, suspended,and resuspended radionuclides

! Inhalation exposures to airborne, suspended,and resuspended radionuclides

! Ingestion of radionuclides in food items anddrinking water

! Ingestion of contaminated soil and sediment

! External exposures from immersion incontaminated water

S.4 CODE SELECTION - RECOGNIZINGIMPORTANT MODEL CAPABILITIES

The greatest difficulty facing the investigator duringthe code selection process is not determining whichcodes have specific capabilities, but rather whichcapabilities are actually required to support remedial

decision making during each remedial phase at aspecific site. This section is designed to help theremedial manager recognize the conditions underwhich specific model features and capabilities areneeded to support remedial decision making.

S.4.1 Code Selection During the Different Phasesof a Remedial Program

Successful ground-water modeling requires theselection of a computer code that is not only consistentwith the site characteristics but also with the modelingobjectives, which are strongly dependent on the phaseof the remedial process; i.e., scoping versus sitecharacterization versus the selection andimplementation of a remedy. Table S-1 presents anoverview of how the overall approach to modeling asite differs as a function of the phase of the remedialprocess.

The most common code selection mistakes areselecting codes that are more sophisticated than areappropriate for the available data or the level of theresult desired, and the application of a lesssophisticated code that does not account for the flowand transport processes that dominate the system.

Table S-1. General Modeling Approach as a Function of Project Phase

Attributes Scoping Characterization Remediation

Accuracy Conservative Approximations

Site-Specific Approximations

Remedial Action Specific

Temporal Representation ofFlow and Transport Processes

Steady-State Flow and Transport Assumptions

Steady-State Flow/TransientTransport Assumptions

Transient Flow and Transport Assumptions

Dimensionality One Dimensional 1,2-Dimensional/Quasi-3-dimensional

Fully 3-Dimensional/Quasi-3-dimensional

Boundary and InitialConditions

UncomplicatedBoundary and UniformInitial Conditions

Non-Transient Boundaryand Nonuniform InitialConditions

Transient Boundary and Nonuniform InitialConditions

Assumptions Regarding Flowand Transport Processes

Simplified Flow andTransport Processes

Complex Flow andTransport Processes

Specialized Flow and Transport Processes

Lithology Homogeneous/Isotropic Heterogeneous/Anisotropic Heterogeneous/Anisotropic

Methodology Analytical Semi-Analytical/Numerical Numerical

Data Requirements Limited Moderate Extensive

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For example, a typical question that often arises is:should three-dimensional codes be used as opposed totwo- or one-dimensional codes? Inclusion of the thirddimension requires substantially more data than one-and two- dimensional codes. Similar questions need tobe considered which involve the underlyingassumptions in the selection of an approach and thephysical processes which are to be addressed. If themodeler is not practical, sophisticated codes are usedtoo early in the problem analysis. In other instances,the complexity of the modeling is commensurate withthe qualifications of the modeler.

An inexperienced modeler may take an unacceptablysimplistic approach. One should begin with thesimplest code appropriate to the problem and progresstoward the more sophisticated codes until the modelingobjectives are achieved.

The remedial process is generally structured in a waythat is consistent with this philosophy; i.e., as theinvestigation proceeds, additional data becomeavailable to support more sophisticated ground-watermodeling.

The data available in the early phases of the remedialprocess may limit the modeling to one or twodimensions. In certain cases, this may be sufficient tosupport remedial decision making. If the modelingobjectives cannot be met in this manner, additionaldata will be needed to support the use of more complexmodels.

It is generally in the later phases of the investigationthat sufficient data have been obtained to meet moreambitious objectives through complex three-dimensional modeling.

The necessary degree of sophistication of the modelingeffort can be evaluated in terms of both site-relatedissues and objectives, as well as the qualities inherentin the computational methods available for solvingground-water flow and transport equations.

Modeling objectives at each stage of the remedialinvestigation must be very specific and well definedearly in the project. All too often, modeling isperformed without developing a clear rationale to meetthe objectives, and only after the modeling iscompleted are the weaknesses in the approachdiscovered.

The modeling objectives must consider the availabledata and the remedial decisions that the model resultsare intended to support. The selected modelingapproach should not be driven by the data availability,but the modeling objectives should be defined in termsof what can be accomplished with the available data.If the modeling objectives demand more sophisticatedmodels and input data, the necessary data should beobtained.

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

S.4.2 The Effects of Waste/Contaminant and SiteCharacteristics on Code Selection

After the conceptual model is formulated and themodeling objectives are clearly defined, theinvestigator should have a relatively good idea of thelevel of sophistication that the anticipated modelingwill require. It now becomes necessary to select one ormore computer code(s) that have the attributesnecessary to mathematically describe the conceptualmodel at the desired level of detail. This step in thecode selection process requires detailed analysis of theconceptual model to determine the degree to whichspecific waste/contaminant and site characteristicsneed to be explicitly modeled.

The code selection process consists primarily ofdetermining which waste/contaminant and site charac-teristics and flow and transport processes need to beexplicitly modeled in order to achieve the modelingobjectives. Once these are determined, the codeselection process becomes simply a matter of identi-fying the codes that meet the defined modeling needs.

Table S-2 lists code attributes related to variouswaste/contaminant and site characteristics. This tableillustrates the site-related criteria generally consideredin the identification of candidate computer codes.

The general components of the conceptual model thatneed to be considered when selecting an appropriatecomputer code are the following:

! Source Characteristics

! Aquifer and Soil/Rock Characteristics

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Table S-2. Site-Related Features of Ground-Water Flow and Transport Codes

Section 4.3.1.1 Source CharacteristicsPoint SourceLine SourceAreally Distributed Source Multiple SourcesSpecified ConcentrationSpecified Source RateTime-Dependent Release

Section 4.3.1.2 Aquifer and Soil/Rock CharacteristicsConfined AquifersConfining Unit(s)Water-Table AquifersConvertible AquifersMultiple AquifersHomogeneousHeterogeneousIsotropicAnisotropicFracturesMacroporesLayered Soils

Section 4.3.1.3 Fate and Transport ProcessesDispersionAdvectionMatrix DiffusionDensity-Dependent Flow and TransportRetardationNon-linear SorptionChemical Reactions/SpeciationSingle Species First Order DecayMulti-Species Transport with Chained Decay Reactions

Section 4.3.1.4 Multiphase Fluid ConditionsTwo-Phase Water/NAPLTwo-Phase Water/AirThree-Phase Water/NAPL/Air

Section 4.3.1.5 Flow ConditionsFully SaturatedConvertible AquifersVariably Saturated/Non-HystereticVariably Saturated/Hysteretic

Section 4.3.1.6 Time DependenceSteady-StateTransient

! Fate and Transport Processes ! Multiphase Fluid Conditions

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Each of these topics is presented as a major heading inTable S-2. These broad subjects are further brokendown into their individual components both in TableS-2 and in the discussion that follows.

Source Characteristics

Computer codes can accommodate the spatialdistribution of the contaminant source in a number ofways. The most common are:

• Point source, such as a waste drum or tank,

• Line source, such as a trench, and

• Area source, such as ponds, lagoons, orlandfills.

The determination of how the spatial distribution ofthe source term should be modeled (i.e., point, line, orarea) is dependent on a number of factors, the mostimportant of which is the scale at which the site will beinvestigated and modeled. If the region of interest isvery large, as compared to the contaminant sourcearea, even sizable lagoons or landfills could beconsidered point sources.

The modeling objectives are also important indetermining the way in which the source term shouldbe modeled. For example, if simple scopingcalculations are being performed, treating the source asa point will yield generally conservativeapproximations of contaminant concentrations becauseof limited dispersion. However, if more realisticestimates of concentrations and plume geometry arerequired, it will be generally necessary to simulate thesource term characteristics more accurately, especiallyif the receptor is close to a relatively large source.

In addition to the geometry of the source, codeselection is determined by whether the source is to bemodeled as a continuous or time-varying release.Computer codes can simulate the introduction ofcontaminants to the ground water as an instantaneouspulse or as a continuous release over time. Acontinuous release may either be constant or vary withtime.

The need to model the source as a constant or time-varying release primarily depends on the half-life ofthe radionuclide relative to the time period of interestand whether average impacts or time-varying impacts

of a release are of interest. In general, the simplestcalculations, which assume a continuous release, aresufficient when determining the average annual dosesto ground-water users at sites with relatively long-livedradionuclides.

Aquifer and Soil/Rock Characteristics

The most common site characteristics with regard toaquifers that influence code selection include thefollowing:

! Confined aquifers

! Water-table (unconfined) aquifers

! Convertible aquifers

! Multiple aquifers/aquitards

! Heterogeneous aquifers

! Anisotropic aquifers

! Fractures/Macropores

! Layered soils/rocks

Recognizing when and if these processes need to beexplicitly modeled is critical to the code selectionprocess. There are no simple answers to thesequestions. However, the following general guidancemay be helpful in making these determinations.

Confined versus Unconfined Aquifers

In most circumstances, the concern at a contaminatedsite is contamination of unconfined aquifers sincesources of ground water generally becomecontaminated by leachate migrating fromcontaminated surface soil through an unsaturated zoneof varying thicknesses to an aquifer. However,confined aquifers could be of concern at sites wherecontaminants were disposed in injection wells andlayered sites with "leaky aquitards."

Multiple Aquifers/Aquitards

Computer codes have been developed that have theability to simulate either single or multiple

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hydrogeologic layers. Generally, a single-layer code isused if the bulk of the contamination is confined tothat layer or if the difference in the flow and transportparameters between the various layers is not significantenough to warrant the incorporation of various layers.It generally does not make much sense to modeldiscrete layers if estimated parameter values,separating different layers, fall within probable errorranges for the parameters of interest. Furthermore,unless the discrete hydrogeologic units are continuousover the majority of the flow path, it is often possibleand preferable to model the system as one layer usingaverage flow and transport properties.

Layered Soil/Rocks in the Unsaturated Zone

Rarely would soils and rocks within the unsaturatedzone not exhibit some form of natural layering. Thefirst consideration as to how this natural layeringshould be treated in the modeling analysis is related towhether the various soil layers have significantlydifferent flow and transport properties. If theseproperties do not vary significantly from layer to layer,there would be little need for the code to havemultiple-layer capability. On the other hand, if thelayers have distinctive properties that could affect flowand transport, a decision needs to be made about howbest to achieve the modeling objectives; i.e., shouldeach layer be discretely treated or should all of thelayers be combined into a single layer.

Macropores/Fractures

Modeling flow through the unsaturated zone is basedon the assumption that the soil is a continuousunsaturated solid matrix that holds water within thepores. Actual soil, however, has a number of cracks,root holes, animal burrows, etc., where the physicalproperties differ enormously from the surrounding soilmatrix. Under appropriate conditions, these flowchannels have the capacity to carry water at velocitiesand concentrations that greatly exceed those in thesurrounding matrix. Accordingly, it is critical todetermine whether ground-water flow and contaminanttransport at a site is dominated by macropores andfractures because this factor could determine whethera contaminant can reach the saturated zone almostimmediately versus a transit time on the order ofhundreds to thousands of years. This issue isespecially important for radionuclides whereradioactive decay in transit in the unsaturated zone

could virtually eliminate the concern over ground-water contamination.

Anisotropic/Isotropic

In a porous medium made of spheres of the samediameter packed uniformly, the geometry of the voidsis the same in all directions. Thus, the intrinsicpermeability of the unit is the same in all directions,and the unit is said to be isotropic. On the other hand,if the geometry of the voids is not uniform, and thephysical properties of the medium are dependent ondirection, the medium is said to be anisotropic.

In most sedimentary environments, clays and silts aredeposited as horizontal layers. This preferentialorientation of the mineral particles allows thehorizontal velocity of the contaminants to greatlyexceed those in the vertical direction. If anisotropy isnot taken into account for the modeling analysis, thecontaminants will be predicted to be more dispersed inthe vertical direction than would probably be occurringin the real world. The result could be an under-prediction of the concentration of the contaminant inthe centerline and an over-prediction of thecontaminant concentration off-center in the verticaldirection.

Homogeneous/Heterogeneous

A homogeneous unit is one that has the sameproperties at all locations. For example, for asandstone, this would mean that the grain-sizedistribution, porosity, degree of cementation, andthickness vary only within small limits. As a result,the velocity and the volume of ground water would beabout the same at all locations. In heterogeneousformations, hydraulic properties change spatially.

For example, if it is expected that the aquifer thicknesswill vary significantly (e.g., greater than ten percent),a computer code capable of simulating variablethicknesses is needed. If a code does not properlysimulate the aquifer thicknesses, the contaminantvelocities will be too large in areas where thesimulated aquifer is thinner than the true aquiferthickness and too small in those regions that have toogreat a simulated thickness.

The ability to simulate aquifer heterogeneities may alsobe important during the remedial design phase of theinvestigation. If engineered barriers of low

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permeability are evaluated as potential remedialoptions, it would be necessary to determine theiroverall effectiveness. In this scenario, it would notonly be important to select a computer code that hasthe capability to simulate highly variable ground-watervelocities but also to ensure that the sharp changes inground-water velocities do not cause instabilities in themathematical solutions.

Fate and Transport Processes

The transport of radionuclides will be affected byvarious geochemical and mechanical processes.Among the geochemical processes are adsorption onmineral surfaces and processes leading to precipi-tation. These processes are important primarilybecause they reduce the velocity of the radionuclidesrelative to the ground water (i.e., retardation), whichincreases the transit time to receptor locations andresults in additional radioactive decay in transit.

The following summarizes the primary processes thataffect the mobility and concentrations of radionuclidesbeing transported by ground water, including:

! Advection! Dispersion! Matrix Diffusion! Retardation! Radioactive Decay

Advection

The process by which solutes are transported by thebulk movement of water is known as advection. Theamount of solute that is being transported is a functionof its concentration in the ground water and the flowrate of the ground water.

Computer codes that consider only advection are idealfor designing remedial systems (e.g., pump and treat)because the model output is in the form of solutepathlines (i.e., particle tracks) which delineate theactual paths that a contaminant would follow.Therefore, capture zones created by pumping wells arebased solely on hydraulic gradients and are not subjectto typical problems that occur when solvingcontaminant transport equations that includedispersion and diffusion.

Advective codes are also excellent in the remedialdesign stage for determining the number and

placement of extraction or injection wells and inevaluating the effect that low permeability barriers mayhave on the flow system. They also tend to yield moreaccurate travel-time determinations of unretardedcontaminants because the solution techniques areinherently more stable, and numerical oscillations,which artificially advance the contaminant front, areminimized. Another important advantage of advectivecodes is that the output (i.e., particle tracks) are a veryeffective means of ensuring that ground-watergradients, both vertical and horizontal, are consistentwith the conceptual model.

Notwithstanding these advantages, advective codeshave some drawbacks. The most significant of theseare their inability to address adsorption and matrixdiffusion. As discussed below, these processes candetermine the length of time that a pump and treatsystem must operate before clean-up goals will be met.Without the ability to evaluate the effects thatadsorption and diffusion may have on solute transport,it would be very difficult to estimate remediation times.

A second potential problem with advection-basedcodes is that dispersion will tend to spreadcontaminants over a much wider area than would bepredicted if only advective processes are considered,thereby underestimating the extent of contamination.However, because dilution due to dispersion is under-accounted for, unrealistically high peak concentrationsare generally obtained, which may be appropriate ifconservative estimates are desired. An additionaldisadvantage is that pure advection-based problemsresult in hyperbolic instead of parabolic equationswhich cannot be solved numerically due to severe gridand time-step constraints.

Hydrodynamic Dispersion

In addition to advective transport, the transport ofcontaminants in porous media is also influenced bydispersion and diffusion, which tend to spread thesolute out from the path that it would be expected tofollow if transported only by advection. Thisspreading of the contamination over an ever-increasingarea, called hydrodynamic dispersion, has twocomponents: mechanical dispersion and diffusion.Hydrodynamic dispersion causes dilution of the soluteand occurs because of spatial variations in ground-water flow velocities and mechanical mixing duringfluid advection. Molecular diffusion, the othercomponent of hydrodynamic dispersion, is due to the

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thermal-kinetic energy of solute particles and alsocontributes to the dispersion process. Diffusion insolutions is the process whereby ionic or molecularconstituents move in the direction of theirconcentration gradient. Thus, if hydrodynamicdispersion is factored into the solute transportprocesses, ground-water contamination will cover amuch larger region than in the case of pure advection,with a corresponding reduction in the maximumconcentrations of the contaminant.

Matrix Diffusion

The diffusion of radionuclides from water movingwithin fractures, or coarse-grained material, into therock matrix or finer grained clays can be an importantmeans of slowing the transport of the dissolvedradionuclides, particularly for non-sorbing or low-sorbing soluble species.

Matrix diffusion is frequently insignificant and is oftenneglected in many of the contaminant-transport codes.However, a number of potential problems arise whenmatrix diffusion is ignored and contaminant velocitiesare based solely on advective-dispersive principles.For example, ground-water pump and treatremediation systems work on the premise that acapture zone is created by the pumping well and all ofthe contaminants within the capture zone willeventually flow to the well. The rate at which thecontaminants flow to the well may, however, be verydependent on the degree to which the contaminantshave diffused into the fine grained matrix (e.g., clays).This is because the rate at which they will diffuse backout of the fine grained materials may be stronglycontrolled by concentration gradients, rather than thehydraulic gradient created by the pumping well.Therefore, matrix diffusion can significantly retard themovement of contaminants, and, if the computer codedoes not explicitly account for this process, the overalleffectiveness of the remediation system (i.e., clean-uptimes) could be grossly underestimated. Matrixdiffusion processes can also lead to erroneous modelpredictions in the determination of radionuclide traveltimes, peak concentrations, and flushing volumes.

In general, matrix diffusion can be a potentiallyimportant process in silty/sandy soil which containslayers of clay or fractured rock. Through the processof matrix diffusion, the clay and rock can serve asreservoirs of contaminants that slowly leak back intothe ground water over a long period of time.

Retardation

In addition to the physical processes, the transport ofradionuclides is affected by chemical processes. Themost important include:

! Sorption -- the sorption of chemical specieson mineral surfaces, such as ion exchange,chemisorption, van der Waals attraction, etc.,or ion exchange within the crystal structure.

! Ion exchange phenomena -- that type ofsorption restricted to interactions betweenionic contaminants and geologic materialswith charged surfaces which can retard themigration of radionuclides.

A wide range of complex geochemical reactions canaffect the transport of radionuclides, many of whichare poorly understood and are primarily researchtopics. From a practical view, the important aspect isthe removal of solute from solution, irrespective of theprocess. For this reason, most computer codes simplylump all of the cumulative effects of the geochemicalprocesses into a single term (i.e., distributioncoefficient) which describes the degree to which theradionuclide is retarded relative to the ground water.Thus, the distribution coefficient relates theradionuclide concentration in solution toconcentrations adsorbed to the soil. Because thedistribution coefficient is strongly affected by site-specific conditions, it is frequently obtained from batchor column studies in which aliquots of the solute, invarying concentrations, are well mixed withrepresentative solids from the site, and the amount ofsolute removed from the water to the solid isdetermined.

From the perspective of model selection, virtually allcomputer codes explicitly address retardation throughthe use of retardation factors, which are derived fromthe distribution coefficient. The primary concern isthat the retardation factors are appropriate for the siteand conditions under consideration. Spacial andtemporal changes in pH and the presence of chelatingagents could invalidate the retardation factors selectedfor use at a site.

Radioactive Decay

Radionuclides decay to either radioactively stable orunstable decay products. For some radionuclides,

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several decay products may be produced before theparent species decays to a stable element. Theseradioactive decay products may present a potentiallygreater adverse health risk than the parent.Accounting for the chain-decay process is particularlyimportant for predicting the potential impacts ofnaturally occurring radionuclides, such as uranium andthorium, and transuranics. In considering this processover the transport path of radionuclides, one transportequation must be written for each original species andeach decay product to yield the concentration of eachradionuclide (original species and decay products) atpoints of interest along the flow path in order toestimate total radiological exposures. However, not allcomputer codes that simulate radioactive decay allowfor ingrowth of the decay products, which may notcause a problem if the half-lives of the parent anddaughters are very long (i.e., it takes a long time forthe daughter products to grow in) or if the decayproducts are of little interest.

Multiphase Fluid Conditions

The movement of contaminants that are immiscible inwater (i.e., non-aqueous phase liquids - NAPL)through the unsaturated zone and below the water tableresults in systems that have multiple phases (i.e., air,water, NAPL). This coexistence of multiple phasescan be an important facet in many contaminant-transport analyses. However, only the water and thevapor phase are generally of concern when evaluatingthe transport of radionuclides. A limited number ofradionuclides can form volatile species that are capableof being transported in a moving vapor or gas. Amongthese are tritium, carbon-14, radon-220/222, andiodine-129. Accordingly, if these radionuclides arepresent, vapor phase transport may need to beexplicitly considered.

S.5 THE CODE SELECTION PROCESS

Given that an investigator understands the variouswaste/contaminant and site characteristics that need tobe modeled in order to meet specific modelingobjectives, there will often be several suitable computercodes that could potentially be chosen from a largenumber of published codes presented in the scientificliterature. Ideally, each candidate code should beevaluated in detail to identify the one most appropriatefor the particular site and modeling objectives.However, the resources to complete a detailed study areseldom available, and usually only one to two codes are

selected based upon a cursory review of codecapabilities and the experience of the modeler.

Regardless of whether a detailed or more cursoryreview is performed, it is important for the reviewer/investigator to be cognizant of the following factorsand how they will affect code selection:

1. Code Capabilities consistent with: User needs Modeling objectives Site characteristics Contaminant characteristics Quality and quantity of data

2. Code Testing Documentation Verification Validation

3. History of Use Acceptance

The first aspect of the review concentrates on theappropriateness of the particular code to meet themodeling needs of the project. The reviewer must alsodetermine whether the data requirements of the codeare consistent with the quantity and quality of dataavailable from the site. Next, the review mustdetermine whether the code has been properly testedfor its intended use. Finally, the code should havesome history of use on similar projects, be generallyaccepted within the modeling community, and readilyavailable to the public.

Evaluating a code in each of the three categories canbe a significant undertaking, especially with respect tocode testing. Theoretically, the reviewer should obtaina copy of the computer code, learn to use the code,select a set of verification problems with knownanswers, and compare the results of the model to thebenchmark problems. This task is complicated, largelybecause no standard set of benchmark problems existsand the mathematical formulation for each processdescribed within the code has to be verified throughthe benchmarking process. It is recommended,primarily for this reason, that the codes selectedalready be widely tested and accepted. Modelvalidation, which involves checking the modelpredictions against independent field investigationsdesigned specifically to test the accuracy of the model,would almost never be practical during the codeevaluation and selection process.

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The model evaluation process involves the followingsteps:

1. Contact the author of the code and obtain thefollowing:

- Documentation and other model-related publications

- List of users- Information related to code testing

2. Read all publications related to the model,including documentation, technical papers, andtesting reports.

3. Contact code users to find out their opinions.

4. Complete the written evaluation using the criteriashown in Table S-3.

Much of the information needed for a thoroughevaluation can be obtained from the author ordistributor of the code. In fact, inability to obtain thenecessary publications can be an indication that thecode is either not well documented or that the code isproprietary. In either case, inaccessibility of thedocumentation and related publications should begrounds for evaluating the code as unacceptable.

Most of the items in Table S-3 should be described inthe code documentation, although excessive use ofmodeling jargon may make some items difficult tofind. For this reason, some assistance from anexperienced modeler may be required to complete theevaluation. Conversations with users can also helpdecipher cryptic aspects of the documentation.

The evaluation process must rely on user opinions andpublished information to take the place of hands-onexperience and testing. User opinions are especiallyvaluable in determining whether the code functions asdocumented or has significant errors (bugs). In someinstances, users have performed extensive testing andbenchmarking or are familiar with published papersdocumenting the use of the code. In essence, theevaluation process substitutes second-hand experiencefor first-hand knowledge (user opinions) to shorten thetime it takes to perform the review.

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Table S-3. Model Selection Criteria

CRITERIA

Section 5.2.1 Administrative DataAuthor(s)Development Objective (research, general use, education)Organization(s) Distributing the CodeOrganization(s) Supporting the CodeDate of First ReleaseCurrent Version NumberReferences (e.g., documentation)Hardware RequirementsAccessibility of Source CodeCostInstalled User BaseComputer language (e.g., FORTRAN)

Section 5.2.2 Remedial ProcessScopingCharacterizationRemediation

Section 5.2.3 Site-Related CriteriaBoundary/Source Characteristics

Source CharacteristicsMultiple sourcesGeometry

linepointarea

Release typeconstantvariable

Aquifer System Characteristicsconfined aquifersunconfined aquifers (water-table)aquitardsmultiple aquifersconvertible

Soil/Rock Characteristicsheterogeneity in propertiesanisotropy in propertiesfracturedmacroporeslayered soils

Transport and Fate Processesdispersionadvectiondiffusiondensity dependentpartitioning between phases

solid-gassolid-liquid

Table S-3. (Continued)

CRITERIA

S-17

equilibrium isotherm:linear (simple retardation)LangmuirFreundlichnonequilibrium isotherm

radioactive decay and chain decayspeciation

Multiphase Fluid Conditionstwo-phase water/NAPLtwo-phase water/airthree-phase water/NAPL/air

Flow Conditionsfully saturatedvariably saturated

Temporal Discretization (steady-state or transient)

Section 5.2.4 Code-Related CriteriaSource Code AvailabilityHistory of UseCode UsabilityQuality Assurance

code documentationcode testing

Hardware RequirementsSolution MethodologyCode OutputCode Dimensionality

1-1

SECTION 1

INTRODUCTION

1.1 BACKGROUND - PURPOSE AND SCOPE OFTHE JOINT EPA/DOE/NRC PROGRAM

The overall joint EPA/DOE/NRC program isconcerned with the selection and use of mathematicalmodels that simulate the environmental behavior andimpacts of radionuclides via all potential pathways ofexposure, including the air, surface water, groundwater, and terrestrial pathways. Figure 1-1 presents anoverview of the various exposure pathways.

Though the joint program is concerned with allpathways, it has been determined that, due to themagnitude of the undertaking, it would be appropriateto divide the program into smaller, more manageablephases, corresponding to each of the principalpathways of exposure. It was also determined that inthe first phase of the project greatest attention wouldbe given to the ground-water pathways.

Ground-water pathways were selected forconsideration first for several reasons. At a largenumber of sites currently regulated by the EPA and theNRC or owned by the DOE, the principal concern isthe existence of, or potential for, contamination of theaquifers underlying the various sites. In addition,relative to the air, surface water, and terrestrialpathways, ground-water contamination is moredifficult to sample and monitor, thereby necessitatinggreater dependence on models to predict the locationsand levels of contamination in the environment.

The types of models used to simulate the behavior ofradionuclides in ground water must be more complexthan surface water and atmospheric pathway transportmodels in order to address the more complex settingsand the highly diverse types of settings associated withdifferent sites. As a result, the methods used to

Figure 1-1. Exposure Pathways

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model ground water have not been standardized to thesame extent as has surface water and air dispersionmodeling, and, therefore, there is considerably lessregulatory guidance regarding appropriate methods forperforming ground-water modeling.

In addition to pathways of exposure, the scope of Phase1 of the joint program also considered the range ofcategories of sites that should be considered. The fullrange of sites in the United States that containradioactive materials can be divided into the followingcategories:

! Federal facilities under the authority of 18 federalagencies, predominantly consisting of DOE andDepartment of Defense (DOD) sites and facilities,and sites listed on the National Priorities List(NPL),

! NRC and NRC Agreement State licensedfacilities,

! State licensed facilities,

! Facilities and sites under the authority of thestates but not governed by specific regulations.These include sites containing elevated levels ofnaturally occurring radionuclides (NORM).

All of these sites are of interest to the program.However, a number of categories of facilities and siteswere excluded from consideration in the joint programbecause they are being licensed specifically to receiveradioactive material for storage and disposal; i.e.,licensed low-level and high-level waste storage anddisposal sites. These sites are being managed withina highly structured regulatory context to receiveradioactive materials, and, though models are used tosupport the siting and design of such facilities, they arenot remedial sites.

It was also necessary to limit the range of thecategories of sites of interest to the program in order tokeep the number of categories of sites to a manageablesize. It was determined that this phase of the projectwill be limited to (1) sites currently listed on the NPLthat contain radioactive materials and (2) sitescurrently or formerly licensed by the NRC that are partof the Site Decommissioning Management Program(SDMP). The SDMP has been established by theNRC to decommission 46 facilities

that require special attention by the NRC staff.

Ground-water modeling needed to support remedialdecision making at NPL sites containing radioactivematerials is in many ways similar to the ground-watermodeling needs of the SDMP.

These categories of sites were selected forconsideration because decisions are currently beingmade regarding their decontamination andremediation, which, in many cases, require the use ofmodels to support decision making and demonstratecompliance with remediation goals. Though theproject is designed to address the modeling needs ofthese categories of sites, the information gathered onthis project should have applicability to the full rangeof categories of sites concerned with the disposition ofradioactive contamination.

In conclusion, in order to meet its mission ofpromoting the appropriate and consistent use ofmathematical models in the remediation andrestoration process at sites containing, or contaminatedwith, radioactive materials, this first phase of the jointprogram is designed to achieve the following fourobjectives:

1) Describe the roles of modeling and themodeling needs at each phase in the remedialprocess (MAU93);

2) Identify models in actual use at NPL sites andfacilities licensed under RCRA, at DOE sites,and at NRC sites undergoing decontaminationand decommissioning (D&D) (PAR92);

3) Produce detailed critical reviews of selectedmodels in widespread use; and

4) Produce draft guidance for hydrogeologists andgeoscientists tasked with the responsibility ofselecting and reviewing ground-water flow andtransport models used in the remediation,decommissioning, and restoration process.

This report fulfills the fourth objective of Phase 1 ofthe joint program. Specifically, this report describes aprocess for reviewing and selecting ground-water flowand transport models that will aid remedial decisionmaking during each phase of the remedial process,from the initial scoping phase, to the detailedcharacterization of the site, to the selection andimplementation of remedial alternatives.

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1.2 PURPOSE AND SCOPE OF THIS REPORT

Remedial contractors, with the concurrence of the sitemanagers, generally select and apply ground-waterflow and transport models. However, unlessspecifically trained in ground-water flow and transportmodeling, it is difficult for the site manager toparticipate actively in these decisions. Ground-waterflow and transport modeling requires highlyspecialized training and experience, and, as a result,the site manager must usually depend heavily on theexpertise and judgement of staff hydrogeologists aswell as outside contractors and consultants. Thisreport provides background information that shouldhelp hydrogeologists and geoscientists assist the sitemanager in making more informed decisions regardingthe selection and use of ground-water flow andtransport models and computer codes throughout theremedial process.

Previous reports in this series (MOS92, PAR92) havedetermined that the types of models and the processesthat require modeling during the remedial processdepend on a combination of the following five factors:

1. reasons for modeling,2. contaminant waste characteristics,3. site environmental characteristics,4. site land use and demography, and5. phase of the remedial process.

The principal reasons for modeling that, in part,influence model selection include: (1) developmentand refinement of the site conceptual model fromwhich hypotheses may be tested, (2) the performanceof risk assessments and the evaluation of compliancewith applicable health and safety regulations, (3) thedesign of environmental measurements programs,primarily to determine the optimal location forboreholes, and (4) the identification, selection, anddesign of remedial alternatives. Each of these reasonsfor modeling influences modeling needs and modelselection differently.

A review of the physical, chemical, and radiologicalproperties of the waste at a number of remedial sitesreveals that the waste characteristics can be diverse.At sites currently undergoing or scheduled forremediation, over 30 different types of radionuclideshave been identified, each with its own radiologicaland chemical properties. The waste is found in avariety of chemical forms and physical settings,including contaminated soil, in ponds, in storage pilesand landfills, buried in trenches, and in tanks and

drums. Each of these physical and chemical settingsinfluences the areal distribution of the contaminantsand rate at which they may leach into the underlyingaquifer, which, in turn, influences model selection.

In a similar manner, the environmental characteristicsof remedial sites are highly diverse (PAR92). The sitescontaining radioactive materials that are currentlyundergoing remediation include both humid and drysites, sites with and without an extensive unsaturatedzone, and sites with simple and complexhydrogeological characteristics. These differentenvironmental settings determine the processes thatneed to be modeled, which, in turn, influence theselection of models and computer codes.

The land use and demographic patterns at a site,especially the location and extent of ground-water use,affect the types and complexity of the models requiredto assess the potential impacts of the site on publichealth. At many of the sites contaminated withradioactive materials, the principal concern is the useof the ground water by current or future residentslocated close to, and downgradient from, the source ofcontamination. At other sites, the concern is the use ofprivate and municipal wells located at some distanceand in a variety of directions from the source. Each ofthese usage patterns influences the selection of ground-water flow and transport models and computer codes.

Superimposed on these waste and site-related issuesare the different modeling needs associated with thevarious phases of the remedial process. The phase ofthe remedial process from scoping and planning, tosite characterization, to remediation, creates widelydifferent opportunities for modeling, which, togetherwith the other factors, influences model and codeselection.

This report describes the methods for selecting ground-water flow and transport models and computer codesthat meet the modeling needs at sites contaminatedwith radioactive materials. The selection process isdescribed in terms of the various site characteristicsand processes requiring modeling and the availability,reliability, and costs of the computer codes that meetthe modeling needs.

Though this report is limited to a discussion of themodel selection process, it is recognized that theproper application of the selected models is asimportant, if not more important, than model selection.A model, no matter how well suited to a particularapplication, could give erroneous and highly

1-4

misleading results if used improperly or withincomplete or erroneous input data. Conversely, evena model with very limited capabilities, or a model usedat a site which has not been well characterized, cangive very useful results if used intelligently and with afull appreciation of the limitations of the model andthe input data. It is not possible within the scope ofthis project to address model applications, qualitycontrol, and the presentation and interpretation ofmodeling results. Future reports prepared under thisprogram will address these important topics.

1.3 PRINCIPAL SOURCES OF INFORMATION

In accomplishing its objectives, this report makes useof the information contained in the previous reportsprepared on this program, including:

! "Environmental Pathway Models - Ground WaterModeling in Support of Remedial DecisionMaking at Sites Contaminated with RadioactiveMaterial," EPA 402-R-93-009, March 1993.

! "Environmental Characteristics of EPA, NRC,and DOE Sites Contaminated with RadioactiveSubstances," EPA 402-R-93-001, March 1993.

! "Computer Models Used to Support CleanupDecision Making at Hazardous and RadioactiveWaste Sites," EPA 402-R-93-005, March 1993.

In addition, extensive use was made of:

! "Superfund Exposure Assessment Manual,"EPA/540/1-88/001, April 1988.

! "Leachate Plume Management," EPA/540/2-85/004, November 1985.

! IMES, "Integrated Model Evaluation System,"Prototype, Version 1, September 1991.Developed by Versar, Inc. for the ExposureAssessment Group, Office of Health andEnvironmental Assessment, Office of Researchand Development, Environmental ProtectionAgency.

Finally, this report relies heavily on the experiencegained by the project team during the review of threeexisting codes: RESRAD, VAM2D, and MT3D. Aspart of this project, these three computer codes werereviewed as if they were being considered for use on a

remedial project. The review of these codes, includingthe process used to review these codes, has beendocumented in a separate report (EPA 402-R-93-005)in this series. The procedures used to perform thesereviews contributed to the generic guidance presentedin this report.

1.4 KEY TERMS

A glossary of terms used in this report is presented inAppendix A. In addition, an index directs the readerto the pages in the report where key terms are definedand discussed. Described below are three keyterms/concepts that are fundamental to understandingthe report.

Conceptual Model. The conceptual model of a site isa flow diagram, sketch, and/or description of a site andits setting. The conceptual model describes thesubsurface physical system including the nature,properties, and variability of the aquifer system (e.g.,aquifers, confining units), and also depicts the types ofcontaminants/wastes at a site, where they are located,and how they are being transported offsite by runoff,percolation into the ground and transport offsite inground water, or suspension or volatization into the airand transport by the prevailing meteorologicalconditions. The conceptual model also attempts tohelp visualize the direction and path followed by thecontaminants, the actual or potential locations of thereceptors, and the ways in which receptors may beexposed, such as direct contact with the source,ingestion of contaminated food or water, or inhalationof airborne contaminants. As information regarding asite accumulates, the conceptual model is continuallyrevised and refined.

Mathematical Model. A mathematical modeltranslates the conceptual model into a series ofequations which, at a minimum, describe the geometryand dimensionality of the system, initial and boundaryconditions, time dependence, and the nature of therelevant physical and chemical processes. Themathematical model essentially transforms theconceptual model to the level of mathematical accuracyneeded to support remedial decision making.

Computer Code. A computer code is simply a tool thatis used to solve the equations which constitute themathematical model of the site and display the resultsin a manner convenient to support remedial decisionmaking.

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1.5 ORGANIZATION OF THE REPORT

This report is divided into five sections. Followingthis introduction, Section 2 presents an overview of thetypes of ground-water modeling decisions facing thesite remediation manager. The section is designed tohelp the site manager determine the role of, and needfor, modeling in support of remedial decision making.

Section 3 addresses the construction of a conceptualmodel of a site and how it is used in the initialplanning and scoping phases of a site remediation,especially as it pertains to the selection and use ofground-water flow and contaminant transport models.

Section 4 describes the various site characteristics andground-water flow and contaminant transportprocesses that may need to be explicitly modeled. Thepurpose of this section is to help the site managerrecognize the conditions under which specific modelfeatures and capabilities are needed to supportremedial decision making during each phase in the siteremediation process.

Section 5 summarizes the computer code attributes thatshould be considered for screening and selecting thepotential computer codes that are best suited to meetsite-specific modeling needs.

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SECTION 2

MODELING DECISIONS FACING THE SITEREMEDIATION MANAGER

A review of current regulations and guidelines pertaining to the remediation of sites on the National Priorities List andin the Nuclear Regulatory Commission's Sites Decommissioning Management Program (SDMP) reveals that fate andeffects modeling is not explicitly required. However, in order to make informed and defensible remedial decisions,ground-water flow and transport modeling can be useful. This section presents a methodology for determining whenground water may be a significant pathway of exposure and discusses the roles ground-water modeling may play insupport of remedial decision making. The section concludes with a discussion of the various resources available to theremediation manager to help in identifying and fulfilling modeling needs.

2.1 IS GROUND WATER A POTENTIALLYIMPORTANT EXPOSURE PATHWAY?

The ground-water pathway may be considered apotentially significant exposure pathway if: (1) theradionuclide concentrations in the ground waterexceed the levels acceptable to the cognizant regulatoryauthorities; or (2) the contamination at the site couldeventually cause the radionuclide concentrations inground water to exceed the applicable criteria. On thisbasis, if the measured concentrations of radionuclidesin ground water downgradient from the site, or inleachate at the site, exceed the applicable criteria, andthe ground water in the vicinity of the site is beingused, or has the potential to be used as a source ofdrinking water, it is likely that ground-water modelingwill be useful, if not necessary, in support of remedialdecision making at the site.

Until additional regulatory guidance is available, thedrinking water standards set forth in 40 CFR 141should guide remedial decision making. Section 1412of the Safe Drinking Water Act (SDWA), as amendedin 1986, requires EPA to publish MaximumContaminant Level Goals (MCLGs) and promulgateNational Primary Drinking Water Regulations forcontaminants in drinking water which may cause anyadverse effects on the health of persons and which areknown or anticipated to occur in public water systems.On July 9, 1976, the EPA published "Interim PrimaryDrinking Water Regulations, Promulgation ofRegulations on Radionuclides" (41 FR 28402).

The interim rule establishes maximum contaminantlevels (MCL) for radionuclides in community water.The MCLs limit the concentration of radionuclides atthe tap to:

! 5 pCi/L for Ra-226 plus Ra-228.

! 15 pCi/L for gross alpha, including Ra-226 butexcluding radon and uranium.

! that concentration of manmade beta/gammaemitting radionuclides that could cause4 mrem/yr to the whole body or any organ.

The regulation applies to community public watersystems regularly serving at least 25 personsyear-round or having at least 15 connections usedyear-round.

In response to a need to finalize the rule, expand theregulations to include uranium and radon, and reviseand refine the rule, the EPA published an AdvancedNotice of Proposed Rulemaking (ANPR) on September30, 1986 (51 FR 34836), and on July 18, 1991 the EPAissued an NPR entitled "National Primary DrinkingWater Regulations; Radionuclides" (56 FR 33050). 40CFR 191 is being finalized.

As in the interim rule, the proposed rule applies to allcommunity, and all non-transient, non-communitypublic water systems regularly serving at least 25persons year-round or having at least 15 connectionsused year-round. The proposed standards establish thefollowing requirements:

The Maximum Contaminant Level Goal (MCLG)for all radionuclides is zero since radionuclides areknown carcinogens. MCLGs are non-enforceablehealth goals that are set at levels at which no knownor anticipated adverse effects on the health ofpersons occur and which allow an adequate marginof safety.

The MCLs are as follows:

2-2

Radionuclide MCL

Ra-226 20 pCi/LRa-228 20 pCi/LRn-222 300 pCi/LUranium 20 µg/L (30 pCi/L)

Beta and photon emitters(excluding Ra-228) 4 mrem/yr EDE

Adjusted gross alphaemitters (excluding Ra-226, U, and Rn 222) 15 pCi/L

MCLs are enforceable standards set as close to theMCLGs as is feasible, including economic factors.The proposed rule also establishes specificrequirements regarding the use of control andtreatment technologies and monitoring and reportingrequirements.

The drinking water standards are fundamental health-based standards that apply to public sources ofdrinking water. In addition, the drinking waterstandards have also had extensive use as applicable orrelevant and appropriate regulations (ARARs) for NPLsites. As an ARAR, if the observed concentrations ofradionuclides in drinking water supplies covered by therule exceed the MCLs, the rule applies directly andremedial actions are required. If the potential existsfor ground-water contamination to exceed the MCLs,the rule is considered relevant and appropriate.

For NPL sites, the Hazard Ranking System (HRS)scoring package provides information that will help indetermining if ground-water modeling is needed at asite. Specifically, Section 7.1.1 of the HRS requiresthe sampling and analysis of ground water todetermine if ground-water contamination is present.If radionuclide concentrations in ground water inexcess of background are found and exceed the LevelI benchmarks delineated in Sections 2.5.2 and 7.3.2 ofthe HRS (these benchmarks are keyed to the MCLs),ground-water contamination is a concern at the site,and ground-water modeling will likely be needed tosupport the baseline risk assessment and remedialdecision making.

At some sites, information may not be availableregarding the levels of radionuclide contamination inground water or leachate. Alternatively, radionuclidemeasurements may have been made, but yieldinconclusive results. Under these conditions, anestimate needs to be made of the radionuclideconcentrations in the soil or the waste at the site,

which can then be used to determine if the potentialexists for exceeding the applicable criteria.

For NPL sites, the information needed to make thisdetermination is likely to be available in the HRSscoring package addressing Hazardous Waste Quantityand Likelihood of Release. The preferred method forscoring Hazardous Waste Quantity (Section 7.2.5.1 ofthe HRS) requires information on the concentration ofindividual radionuclides at the site and the volume andarea of the contamination.

Given the radionuclide concentrations in soil or waste,the radionuclide concentration in leachate can beestimated using partition factors. A partition factorestablishes the equilibrium relationship between theaverage radionuclide concentration in soil or waste andthat in leachate. If the product of the radionuclideconcentrations with the appropriate partition factorsresults in radionuclide concentrations in leachatesignificantly in excess of the applicable criteria, it maybe concluded that the radionuclide concentrations inground water in the vicinity of the site could exceedthe criteria, thereby requiring ground-water modelingto assess the potential impacts on nearby userlocations.

Once the leachate comes into contact with theunderlying soil, a new equilibrium begins to beestablished between the leachate and the soil. Theequilibrium ratio of the radionuclide concentration inthe soil to that in the water in intimate contact with thesoil is referred to as the distribution coefficient (Kd).Once site-specific Kds are determined or appropriategeneric Kds are identified, the radionuclideconcentration in the soil divided by the Kd for eachradionuclide yields a crude estimate of theconcentration of the radionuclide in the soil pore waterpercolating through the soil.

Though partition factors are highly site specific,generic values have been used in the past for screeningcalculations which are designed to provide reasonableupper bound radionuclide concentrations in leachateand ground water. Examples of generic partitionfactors are provided in NRC86. Tabulations of Kdvalues that have had widespread application areprovided in BAE83 and SHE90.

If either the measured or derived values for theradionuclide concentrations in ground water exceedthe applicable criteria, resources need to be put intoplace to perform ground-water modeling.

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2.2 REASONS FOR MODELING

Once it is determined that the ground-water exposurepathway is potentially important, ground-water flowand transport modeling can have a wide range of usesin support of remedial decision making. Table 2-1presents the principal reasons for modeling on aremedial project. These uses can surface during anyphase of the remedial process. However, some of thesereasons are more likely to occur during specific phasesof a remedial project.

In Table 2-1, scoping and planning occur early in theproject, wherein regional, sub-regional, and site-specific data are reviewed and analyzed in order todefine the additional data and analyses needed tosupport remedial decision making. In the sitecharacterization phase, the plans developed during thescoping phase are implemented. These data are usedto characterize more fully the nature and extent of thecontamination at the site, to define the environmentaland demographic characteristics of the site, and tosupport assessments of the actual or potential impactsof the site. The results of the site characterizationphase are analyzed to determine compliance withapplicable regulations and to begin to define strategiesfor the remediation of the site. In the site remediationphase, alternative remedies are identified, evaluated,selected, and implemented.

During scoping and planning, modeling can be used toidentify the potentially significant radionuclides andpathways of exposure, which, in turn, can be used tosupport the design of comprehensive and cost-effectivewaste characterization, environmental measurements,and site characterization programs. During sitecharacterization, modeling is used primarily in supportof dose and risk assessment of the site and to evaluatethe adequacy of the site characterization program.During the remediation phase, modeling is usedprimarily to support the selection and implementationof alternative remedies and, along with environmentalmeasurements programs, is used to determine thedegree to which the remedy has achieved the remedialgoals.

Table 2-1 attempts to identify those opportunities formodeling that are more likely to surface during thedifferent phases of the remedial process. In general,the remedial phase often dictates the types of remedialdecisions that need to be made and the amount of site-specific information and time available to make thesedecisions. These, in turn, determine the role of

modeling. For example, during scoping, it may not befeasible to gain access to sampling locations, and theonly way to predict the potential impacts of a source ofcontaminants is by modeling. During sitecharacterization, sampling locations are generallyaccessible; however, the contaminant may have not yetreached a receptor location. Accordingly, modeling isused to predict future impacts. During remedyselection, modeling is used to simulate theperformance of a remedy in order to evaluate its cost-effectiveness and refine its design.

2.3 PLANNING FOR MODELING

2.3.1 Identifying Modeling Needs

Given the phase in the remedial process and thereasons for modeling, the types of models and theinput data required to run the models are determinedby the characteristics of the waste, the sitehydrogeological setting and characteristics, and thecurrent and projected ground-water use in the vicinityof the site. Accordingly, the role of and need formodeling, and the types of models and associated inputdata, are determined by a combination of five factors:

! phase of the remedial process,! reasons for modeling,! waste characteristics,! hydrogeological characteristics, and! local land use and demography.

In order to make informed decisions regarding theselection and application of ground-water flow andtransport models and the interpretation of the results,the remediation manager will require site-specificinformation on each of these five factors. The first twofactors are related and are largely determined by theregulatory structure within which remedial decisionsare being made. The last three factors are of a moretechnical nature and usually require highly specializedexpertise to relate the waste, hydrogeologic, anddemographic characteristics of a site to the modelssuited to these characteristics and the reasons formodeling.

1. M Denotes an important role.F Denotes a less important role. 2-4

Table 2-1. Matrix of Reasons for Modeling

Opportunities for Modeling Scoping1Site

Characterization1 Remediation1

1. When it is not feasible to perform fieldmeasurements, i.e.,! Cannot get access to sampling locations! Budget is limited! Time is limited

M F F

2. When there is concern that downgradient locationsmay become contaminated at some time in the future.

M M M

3. When field data alone are not sufficient tocharacterize fully the nature and extent of thecontamination; i.e.,! when field sampling is limited in space and time

and needs to be supplemented with models! when field sampling results are ambiguous or

suspect

M M M

4. When there is concern that conditions at a site maychange, thereby changing the fate and transport ofthe contaminants; i.e.,! seasonal changes in environmental conditions! severe weather (floods, tornadoes)! accidents (fire)

F M M

5. When there is concern that institutional control at thesite may be lost at some time in the future resultingin unusual exposure scenarios or a change in the fateand transport of the contaminants; i.e.,! trespassers! inadvertent intruder! (construction/agriculture)! drilling, mineral exploration, mining! human intervention (drilling, excavations,

mining)

F M M

6. When remedial actions are planned and there is aneed to predict the effectiveness of alternativeremedies.

F F M

7. When there is a need to predict the time when theconcentration of specific contaminants at specificlocations will decline to acceptable levels (e.g.,natural flushing).

F M M

8. When there is concern that at some time in the pastindividuals were exposed to elevated levels ofcontamination and it is desirable to reconstruct thedoses.

F M F

Table 2-1. (Continued)

Opportunities for Modeling Scoping1Site

Characterization1 Remediation1

1. M Denotes an important role.F Denotes a less important role. 2-5

9. When there is concern that contaminants may bepresent but below the lower limits of detection.

F M F

10. When field measurements reveal the presence ofsome contaminants and it is desirable to determine ifand when other contaminants associated with thesource may arrive, and at what levels.

F M F

11. When field measurements reveal the presence ofcontaminants and it is desirable to identify the sourceor sources of the contamination.

M M F

12. When there is a need to determine the timing of theremedy; i.e., if the remedy is delayed, is there apotential for environmental or public health impactsin the future?

F F M

13. When there is a need to determine remedial actionpriorities.

F F M

14. When demonstrating compliance with regulatoryrequirements.

M M M

15. When estimating the benefit in a cost-benefit analysisof alternative remedies.

F F M

16. When performing a quantitative dose or riskassessment.

F M M

17. When designing the site characterization programand identifying exposure pathways of potentialsignificance.

M F M

18. When there is a need to compute or predict theconcentration distribution in space and time ofdaughter products from the original source ofradionuclides.

M F F

19. When there is a need to quantify the degree ofuncertainty in the anticipated behavior of theradionuclides in the environment and the associateddoses and risks.

M F F

20. When communicating with the public about thepotential impacts of the site and the benefits of theselected remedy.

M F M

Source: EPA93

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Recognizing the need for modeling, and identifyingand applying the models that meet these needs, unfoldsas the project matures. Modeling decisions are basedon site-specific information pertaining to each of theabove five factors and the combined judgement ofregulatory and technical specialists. Modelingdecisions cannot be made in a "cookbook" fashion.Accordingly, during the initial phases of a remedialproject and throughout the remedial process, theremediation manager must continually assess the needto employ models. Table 2-1 can be useful indetermining when these needs exist or may arise.

Once the modeling needs are recognized, it isappropriate to determine or define the form of theresults or output of the modeling exercise. Thefollowing presents the various types of output resultingfrom a given modeling exercise for sites containingradioactive material.

! The time-averaged and time-varying radionuclideconcentrations in air, surface water, ground water,soil, and food items. These are usually expressed inunits of pCi/L of water or pCi/kg of soil or fooditem. The time-averaged values are used todetermine the annual radiation doses and risksand/or compliance with ARARs that are expressedas average, as opposed to peak values. The time-varying values are useful in determining arrivaltimes of contaminants at receptor locations, whichcan help in prioritizing sites, or the impacts ofaccidental releases, which are often one-time, short-term occurrences.

! The radiation field in the vicinity of radioactivematerial, expressed in units of µR/hr. Estimates ofexposure rate, whether measured or predicted, areuseful in protecting members of the public orworkers who may be present in, or need to enter, theradiation field.

! The transit time or time of arrival of a radionuclideat a receptor location. This measure is useful indetermining at what point in the future a source ofcontamination has the potential to adversely affectreceptors.

! The volume of water contained within or movingthrough a hydrogeological setting.

! Potentiometric surfaces (i.e., heads) are commonlyoutput from ground-water flow models from whichground water/contaminant flow paths and/or capture

zones can be determined.

! Radiation doses to individual members of the publicunder quasi-steady state and changing conditionsand following accidents. The doses are evaluatedfor the site in its current condition (i.e., the noaction alternative) and during and following a broadrange of feasible alternative remedies. These areusually expressed in units of mrem/yr effective doseequivalent (EDE) for continuous exposures andmrem per event (EDE) for transients and postulatedaccidents. Most radiation protection standards areexpressed in units of the dose to individuals.

! Radiation risks to individual members of the publicunder expected and transient conditions andfollowing accidents. The risks are evaluated for theno action alternative and during and following abroad range of feasible remedies. These are usuallyexpressed in units of individual lifetime risk of totaland fatal cancers. In addition to individual dose,individual risk is used to characterize the impacts onpublic health and is required by the NationalContingency Plan (NCP).

! Cumulative radiation doses to the population in thevicinity of the site under expected and transientconditions and following accidents. The cumulativedoses are evaluated for the no action alternative andduring and following a broad range of feasibleremedies. These are usually expressed in units ofperson rem/yr (EDE) for continuous exposures andperson rem per event (EDE) for transients andaccidents.

! Cumulative radiation risks to the population in thevicinity of the site under expected and transientconditions and following accidents. The cumulativepopulation risks are evaluated for the no actionalternative and during and following a broad rangeof feasible remedies. These are usually expressedin units of total and fatal cancers per year forcontinuous exposures or per event for transients andaccidents in the exposed population.

! Radiation doses and risks to remedial workers for abroad range of alternative remedies. The units ofdose and risk for individual and cumulativeexposures are the same as those for members of thepublic.

! Uncertainties in the above impacts, expressed as arange of values or a cumulative probability

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distribution of dose and risk.

The specific regulatory requirements that apply to theremedial program determine which of these "endproducts" is needed. In general, these modeling resultsare used to assess impacts or compliance withapplicable regulations; however, information regardingflux, transport times, and plume arrival times is alsoused to support a broad range of remedial decisions.

These modeling endpoints must be clearly defined,since the type of endpoint will help to determine thetype of ground-water flow and transport model thatwill support the endpoint of interest. For example, abaseline risk assessment at a site contaminated withradioactive material is used in determining the annualradiation dose to an individual drinking water obtainedfrom a potentially contaminated well. The endpoint inthis case is the dose to an individual expressed in unitsof mrem/yr. In order to estimate this dose, it isnecessary to estimate the average concentration ofradionuclides in the well water over the course of ayear. The models, input parameters, and assumptionsneeded to predict the annual average radionuclideconcentration are different than those needed to predictthe time-varying concentration at a given location.The latter usually requires much more input data andmodels capable of simulating dynamic processes.

2.3.2 Sources of Assistance

Once the remediation manager has identified the rolemodeling will play on the remedial project (see Table2-1) and the forms of the results of the modelingexercise, resources must be put into place to meet theseneeds. These resources include access to technicalexpertise and a broad range of ground-water flow andtransport models.

In response to the need for ground-water flow andtransport modeling in support of remedial decisionmaking, guidance and assistance are becomingincreasingly available. Appendix B brieflysummarizes some of the resources available to aremediation manager, organized according to thefollowing categories:

! Branches and Divisions within Agencies! Expert Systems! Electronic Bulletin Boards! Electronic Networks

2.3.2.1 Branches and Divisions Within Agencies

Environmental Protection Agency

Technical assistance available to EPA remediationmanagers is described in "Technical AssistanceDirectory," CERI-91-29, July 1991.

Nuclear Regulatory Commission

Technical assistance to NRC personnel with regulatoryoversight responsibility for the decontamination anddecommissioning of licensed facilities is availablefrom the Office of Nuclear Material Safety andSafeguards (NMSS).

Department of Energy

Technical guidance for DOE and DOE contractorpersonnel with responsibility for environmentalrestoration and waste management at DOE facilities isprovided through the Office of Environmental, Safety,and Health. In addition, since many of the DOE sitesare on the NPL, EPA technical assistance can also beaccessed.

2.3.2.2 Electronic Media

Electronic communication media are becoming acommon means by which individuals participate inforums where expertise is freely shared. Institutionswhose mandate includes the dissemination of expertadvice and information also use these media. Theseforms of communication result from the directtransmittal of computer media (e.g., tape, diskette, CD-ROM, etc.) or utilize remotely accessed computersystems consisting of dedicated hardware andassociated software. In remote systems, the user canaccess the system via modem or some other hard-wiredconnection and retrieve from or transmit to the systeminformation as required.

Electronic media offer great potential to assist ground-water model users and reviewers. It is possible toclassify these media into three types, namely bulletinboards (restricted access), networks (general access),and expert systems. Although the first two systemsoperate similarly and share some approaches toproviding their services, they differ in the way thatthey are used. A brief overview of these instrumentsfollows. Specific examples of these resources arepresented in Appendix B.

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Bulletin Boards

Bulletin boards exist at a specific location maintainedby an identifiable individual or institution. Bulletinboards usually contain facilities for posting electronicmail and allow the user to participate in one or moreconferences - more-or-less structured discussions onspecific topics. In addition, most bulletin boardscontain archives of files consisting of various databases, executable programs, and notices.

Networks

A computer network consists of a number (in somecases many thousands) of individual computers (nodes)tied together by hardware and some network softwarethat regulates access to the system and the transfer ofinformation between nodes. Most network discussiongroups are moderated by an individual or group ofindividuals. Networks can be and are used to postelectronic mail in much the same way as one wouldpost mail on a bulletin board. However, they have theadditional capability of "broadcasting" information toa much more general audience. Networks are a goodway to get answers to problems when the user isunsure of who might possibly provide those answers.An even more powerful aspect of some networks is theability to run software on one of the network nodesin real-time from aremote location with immediate feedback. Mostbulletin boards don't allow that level of access.

Expert Systems

Expert systems are software packages which guide auser through the solution of a problem by asking aseries of questions and/or by providing a series of pre-programmed answers to those questions. An exampleof such a system that can be used in the selection of anappropriate code for air, surface, or ground-watermodeling is the Integrated Model Evaluation Systemavailable from the Environmental Protection Agency.

Both bulletin boards and networks are effective inobtaining non-urgent help on focused issues and forkeeping up with fast-changing subjects - they are notparticularly useful if the user needs informationquickly or cannot phrase a question succinctly andclearly. Many bulletin boards and networks are free tothe user while others are based on some fee system.Nearly all remotely accessed electronic media requiresome form of registration before use, either by writtenrequest and registration or by on-line registrationduring the user's first session. Expert systems willusually offer the fastest and most in-depth answers tospecific problems. But expert systems can be quicklyoutdated if the data (knowledge) base on which theydepend changes. The "learning curve" for all threetypes of electronic information exchange is fairly quick- a user can request and/or obtain useful information ina matter of minutes to hours.

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SECTION 3

CONSTRUCTING AND REFINING THE CONCEPTUAL MODELOF THE SITE

For sites on the NPL, the development of a conceptual model of the site is identified as a specific step in the scopingstage of the RI/RS process (see EPA88). However, the need for conceptual modeling applies to any site undergoingremediation. Figure 3-1, taken from EPA88, is an example of a conceptual model. It identifies the various pathwaysthat may contribute to the potential current and future impacts of the site on public health and the environment.Accordingly, the construction of a conceptual model of a site is the first step in determining modeling needs andidentifying models that meet these needs. This section presents a brief discussion of basic concepts pertinent to theconstruction of a conceptual model of the site with respect to the ground-water pathway for sites contaminated withradionuclides.

Figure 3-1. Example Conceptual Model

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3.1 BASIC QUESTIONS THAT WILL NEED TOBE ANSWERED

For sites where ground-water contamination isidentified as a potentially important exposure pathway,the planning effort should attempt to answer thefollowing typical questions:

! Do the radionuclides have relatively long or shorthalf-lives and do they have radioactive daughters?

! Do the contaminants enter the ground-water flowsystem at a point, or are they distributed along aline or over an area (or volume)?

! Does the source consist of an initial pulse ofcontaminant or is it constant over time?

! Is there a thick unsaturated zone?

! Is the lithography relatively homogeneous or doesit contain multiple layers?

! How will the hydrogeology affect flow andtransport?

! At what rate will the radionuclides be transportedrelative to ground-water flow?

! Are there nearby wells or other hydraulicboundaries that could influence ground-waterflow?

! What is the nature of the system boundaries?

! Where are the current or future receptors located?Can they influence ground-water flow?

The answers to these questions will help to identify thetypes of processes that may need to be modeled at thesite, which, in turn, will help in screening the types ofmodels and computer codes appropriate for the site. Adiscussion of the various flow and transport processesand the site characteristics that influence theseprocesses is provided in EPA88.

During the scoping phase, it will not be possible, nornecessary, to answer these questions with certainty.However, as site characterization proceeds,information will become available that will help todevelop more complete answers to these questions. Infact, a well-designed site characterization program will

obtain data that will help answer these questions.

3.2 COMPONENTS OF THE CONCEPTUALMODEL FOR THE GROUND-WATERPATHWAYS

The components that make up the initial conceptualmodel of the site include:

1. the contaminant/waste characteristics,

2. the site characteristics, and

3. land use and demography.

As the remedial process progresses from initial scopingand planning to detailed characterization toremediation, the site characterization becomes moreprecise and complete. The following sections discusseach of these components of a conceptual model andhow they can influence model selection.

3.2.1 Contaminant/Waste Characteristics

To the extent feasible, the site conceptual model shouldaddress the following characteristics of the waste:

! Types of radionuclides

! Waste form and containment

! Source geometry (e.g., volume, area, depth,homogeneity)

! Physical and chemical properties of theradionuclides

! Geochemical setting

Within the context of ground-water modeling, thesecharacteristics are pertinent to modeling the sourceterm, i.e., the rate at which radionuclides aremobilized from the waste and enter the unsaturatedand saturated zones.

Types of Radionuclides

One of the most important characteristics indeveloping a conceptual model of the site is identifyingthe type and approximate quantities of theradionuclides present. This will not only determinethe potential offsite impacts of the site, it will also help

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to identify the potential magnitude of the risks toworkers, the mobility of the radionuclides, and thetime period over which the radionuclides may behazardous. The types of radionuclides will alsodetermine whether radioactive decay and the ingrowthof daughters are important parameters that will need tobe modeled.

Waste Form and Containment

Radioactive contaminants are present in a wide varietyof waste forms that influence their mobility. However,in most cases, the radionuclides of concern are long-lived, and the integrity of the waste form or containercannot be relied upon for long periods of time.Therefore, the source term is often conservativelymodeled as a uniform point, areal, or volume source,and no credit is taken for waste form orcontainerization (EPA92).

If it is desired to model explicitly the performance ofthe waste form (e.g., rate of degradation of solidifiedwaste or containerized waste) or transport in acomplex geochemical environment (changing acidity,presence of chelating agents or organics), complexgeochemical models may be needed. Depending onthe waste form and container, such models would needto simulate the degradation rate of concrete, thecorrosion rate of steel, and the leaching rate ofradionuclides associated with various waste forms (i.e.,soil, plastic, paper, wood, spent resin, concrete, glass,etc.). These processes depend, in part, on the localgeochemical setting. However, it is generallyacknowledged that it is not within the current state-of-the-art to explicitly model the geochemical processesresponsible for the degradation of the waste containersor the waste itself (NRC 90).

Physical and Chemical Properties of theRadionuclides

If feasible, the conceptual model of the site shoulddescribe the radionuclides and their physical andchemical characteristics. These parameters may bepertinent to model selection because certainradionuclides have properties that are difficult tomodel. For instance, most of the NPL and SDMP sitesare contaminated with thorium and uranium, both ofwhich decay into multiple daughters which may differfrom their parents both physically and chemically.Some of the radionuclides (e.g., uranium) exhibitcomplex geochemistry and their mobility is dependent

upon the redox conditions at the site. Though thechemical form of the radionuclides and thegeochemical setting can have a profound effect on thetransport of the radionuclides, it is generallyacknowledged reliable modeling of the variousgeochemical processes is not often feasible.Accordingly, during the construction of a siteconceptual model, detailed information regarding thechemical composition of the radionuclides may not benecessary. The degree to which this type ofinformation will be needed to support remedialdecision making will surface as site characterizationproceeds.

Geochemical Setting

In addition to the standard chemical properties ofradionuclides, it is important to understand thegeochemical properties and processes that may affecttransport of the radionuclides that are specific to thesite. These properties and processes include thefollowing:

! Complexation of radionuclides with otherconstituents

! Phase transformations of the radionuclides

! Adsorption and desorption

! Radionuclide solubilities at ambient geochemicalconditions

If it is desired to model these processes explicitly, asopposed to using simplifying assumptions, such asdefault or aggregate retardation coefficients, morecomplex geochemical models may be needed.However, as discussed above, it is currently not oftenfeasible to explicitly model complex geochemicalprocesses.

3.2.2 Environmental Characteristics

The conceptual model of the site should begin toaddress the complexity of the environmental andhydrogeological setting. A complex setting, such as acomplex lithology, a thick unsaturated zone, and/orstreams or other bodies of water on site (i.e., a complexsite), generally indicates that the direction and velocityof ground-water flow and radionuclide transport at thesite cannot be reliably simulated using simple one-dimensional, analytical models (see Appendix C).

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At more complex sites, such as many of the defensefacilities on the NPL, the remedial process is gener-ally structured so that, as the investigation proceeds,additional data become available to support ground-water modeling. An understanding of the physicalsystem, at least at a sub-regional scale, may allow anearly determination of the types of models appropriatefor use at the site. Specifically, during the early phasesof the remedial process, when site-specific data arelimited, the following site characteristics may beextrapolated from regional-scale information and will,in part, determine the types and complexity of modelsrequired:

! Approximate depth to ground water

! Ground-water flow patterns

! Lithology of the underlying rocks (e.g., limestone,basalt, shale)

! Presence of surface water bodies

! Land surface topography

! Sub-regional recharge and discharge areas

! Processes or conditions that varysignificantly in time

Even at complex sites, complex computer models maynot be needed. For example, if a conservativeapproach is taken, where transport through theunsaturated zone is assumed to be instantaneous, thenthe complex processes associated with flow andtransport through the unsaturated zone would not needto be modeled. Such an approach would beappropriate at sites that are relatively small and wherethe extent of the contamination is well defined. Underthese conditions, the remedy is likely to be removal ofthe contaminated surface and near-surface material.Examples of these conditions are many of the SDMPsites and several of the non-defense NPL sites. Inthese cases, the use of conservative screening models,along with site data, may be sufficient to supportremedial decision making throughout the remedialprocess.

Depth to Ground Water

Sites located in the arid west and southwest (e.g.,Pantex, Hanford, and INEL) generally have greater

depths to ground water. The simulation of flow andtransport through the unsaturated zone will generallyrequire more complex computer codes due to the non-linearity of the governing equations. Modeling of theunsaturated zone is further hampered because thenecessary data are often difficult to obtain.

Ground-Water Flow Patterns

The intricacy of the ground-water flow patterns willhave a significant impact on the complexity of therequired modeling. The dominating factors thatcontrol the flow patterns are both the geology andhydraulic boundaries. Flow in the saturated zone willtend to be uniform and steady in hydrogeologicsystems that have uncomplicated geology andboundary conditions that are relatively stable withtime. Uniform flow refers to flow that is in onedirection and does not vary across the width of the flowfield. Steady flow does not change over time.Boundary conditions, such as constantpumping/injection and recharge from perennial lakesand streams, are generally constant over time.

Hydrogeological features that indicate that flow may beunsteady and nonuniform are areas where discretegeologic features are known to exist (e.g., faults,fractures, solution channels), as well as hydraulicboundaries which may consist of ephemeral streams,highly variable rainfall, and areas occasionallyindurated by flooding.

Sub-Regional Lithology

The lithology of the underlying rocks also providesinsight into the expected level of difficulty ofmodeling. A number of the NPL sites overlie areaswhere fractures are probably dominant mechanisms forflow and transport. These sites include Hanford, IdahoNational Engineering Laboratory (INEL), Maxey Flats,Jacksonville, Oak Ridge, West Valley, and PensacolaAir Stations. In some cases, such as at Hanford, thefractured zone is deep below the site, and concernsregarding ground-water contamination are limitedprimarily to the near-surface sedimentary rock.

It is unlikely that analytical models could be used toadequately describe flow and transport in the fracturedsystems because radionuclide transport and ground-water flow in fractured media are much more complexthan in unfractured granular porous media. For that

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matter, it generally requires very specialized numericalcodes to simulate flow and transport in fracturedmedia. This is because of the extreme heterogeneityand anisotropy associated with the fractures.

Surface Water Bodies

Virtually all of the NPL sites and many of the SDMPsites have surface water bodies at or in the immediatevicinity of the site. Bodies of water often have asignificant impact on the ground-water flow and canseldom be neglected in the modeling analysis. Ingeneral, analytical models are limited in their ability tosimulate properly the effect that surface water bodieshave on contaminant flow and transport, particularlyif the surface water body behaves episo-dically, such astidal or wetland areas. Several of the NPL sites areinundated with wetlands, including Oak Ridge, Himco,and Shpack Landfill. At least two sites, Pensacola andJacksonville, are close to estuaries, which suggests thattidal as well as density-dependent flow and transportmay be significant.

Sub-Regional Topography

The land surface topography is often overlooked indeveloping a site conceptual model but may be animportant factor in evaluating the need for, andcomplexity of, ground-water modeling. Topographymay significantly influence ground-water flowpatterns. For instance, Maxey Flats is situated atop arelatively steep-sided plateau with a stream located atthe bottom of the slope. The steep topo-graphystrongly controls the direction of ground-water flow,making it much more predictable. Furthermore,estimating the flux of ground water moving into thesystem from upgradient sources becomes much simplerif the area of interest is a local recharge area, such asa hill or mountain.

Steep topography can also complicate the modeling bymaking it more difficult to simulate hydraulic headsthat are representative of the hydrologic units ofinterest.

Regional Recharge/Discharge

The ground-water flow paths will largely be controlledby regional and sub-regional ground-water rechargeand discharge areas. It is generally necessary to ensurethat the conceptual model of flow and transport on alocal scale is consistent with the sub-regional and

regional scale. If the site is located in an aquiferrecharge area, the potential for widespread aquifercontamination is significantly increased, and reliablemodeling is essential.

3.2.3 Land Use and Demography

The site conceptual model will need to identify thelocations where ground water is currently being used,or may be used in the future, as a private or municipalwater supply. At sites with multiple user locations, anunderstanding of ground-water flow in two or threedimensions is needed in order to predict realisticallythe likelihood that the contaminated plume will becaptured by the wells located at different directions,distances, and depths relative to the sources ofcontamination.

Simple analytical ground-water flow and transportmodels typically are limited to estimating theradionuclide concentration in the plume centerlinedowngradient from the source. Accordingly, if it isassumed that the receptors are located at the plumecenterline, a simple model may be appropriate. Suchan assumption is often appropriate even if a receptor isnot currently present at the centerline location becausethe results are generally conservative. In addition, riskassessments often postulate that a receptor could belocated directly downgradient of the source at sometime in the future.

The need for complex models increases if there are anumber of public or municipal water supplies in thevicinity of the source. Under these circumstances, itmay be necessary to calculate the cumulativepopulation doses and risks, which requires modelingthe radionuclide concentrations at a number of specificreceptor locations. Accordingly, off-centerlinedispersion modeling may be needed.

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SECTION 4

CODE SELECTION - RECOGNIZING IMPORTANT MODEL CAPABILITIES

The greatest difficulty facing the investigator during the code selection process is not determining which codes havespecific capabilities, but rather which capabilities are actually required to support remedial decision making duringeach remedial phase at a specific site. This section is designed to help the remediation manager and support personnelrecognize the conditions under which specific model features and capabilities are needed to support remedial decisionmaking.

4.1 INTRODUCTION

The influence that site and code related characteristicshave on code selection can be both global in nature aswell as very specific and exacting. For this reason, thissection is divided into two distinct parts. The first partaddresses general considerations of the code selectionprocess. The discussion provides an overview of howthe code selection process is influenced by theinterdependency between the modeling objectives andthe site and code characteristics. The second part ofthe section focuses primarily on specific considerationsrelated to the code selection process. The discussionprovides the information necessary to determine whichspecific site characteristics need to be explicitlymodeled and when attempting to model suchcharacteristics is impossible, unjustified, or possiblyeven detrimental to the modeling exercise.

4.2 GENERAL CONSIDERATIONS - CODESELECTION DURING EACH PHASE INTHE REMEDIAL PROCESS

Successful ground-water modeling must begin with theselection of a computer code that is not only consistentwith the site characteristics but also with the modelingobjectives, which depend strongly on the stage of theremedial process; i.e., scoping vs. site characterizationvs. the selection and implementation of a remedy.There are no fail-safe methods for selecting the mostappropriate computer code(s) to address a particularproblem. However, the entire process of code selectioncan be relatively straightforward if it is given adequateattention early in the project development.

One of the primary goals of mathematical modeling isto synthesize the conceptual model, as discussed insection 3, into mathematical expressions, which, inturn, are solved by selecting an appropriate computercode. This section discusses how the different

components of the conceptual model, in conjunctionwith the modeling objectives, influence the modelingapproach and ultimately the selection of the mostappropriate computer code.

The underlying premise of this section is that thevarious aspects of the conceptual model may besimulated in a variety of ways, but the selectedapproach must remain consistent with the objectives.That is, the physical system cannot be overlysimplified to meet ambitious objectives, and lessdemanding objectives should not be addressed withsophisticated models.

Table 4-1 presents an overview of how the overallapproach to modeling a site differs as a function of thestage of the remedial process. The most common codeselection mistakes are selecting codes that are moresophisticated than are appropriate for the availabledata or the level of the result desired, and theapplication of a code that does not account for the flowand transport processes that dominate the system. Forexample, a typical question that often arises is: whenshould three-dimensional codes be used as opposed totwo-dimensional or one-dimensional codes? Inclusionof the third dimension requires substantially more datathan one- and two- dimensional codes. Similarquestions need to be considered which involve theunderlying assumptions in the selection of a modelingapproach and the physical processes which are to beaddressed. If the modeler is not practical,sophisticated codes are used too early in the problemanalysis. In other instances, the complexity of themodeling is commensurate with the qualifications ofthe modeler. An inexperienced modeler may take anunacceptably simplistic approach.

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Table 4-1. General Modeling Approach as a Function of Project Phase

Attributes Scoping Characterization Remediation

Accuracy Conservative Approximations

Site-Specific Approximations

Remedial Action Specific

Temporal Representation ofFlow and Transport Processes

Steady-State Flow and Transport Assumptions

Steady-State Flow/TransientTransport Assumptions

Transient Flow and Transport Assumptions

Dimensionality One-Dimensional 1,2-Dimensional/Quasi-3-Dimensional

Fully 3-Dimensional/Quasi-3-Dimensional

Boundary and InitialConditions

UncomplicatedBoundary and UniformInitial Conditions

Non-Transient Boundaryand Nonuniform InitialConditions

Transient Boundary and Nonuniform InitialConditions

Assumptions Regarding Flowand Transport Processes

Simplified Flow andTransport Processes

Complex Flow andTransport Processes

Specialized Flow and Transport Processes

Lithology Homogeneous/Isotropic Heterogeneous/Anisotropic Heterogeneous/Anisotropic

Methodology Analytical Semi-Analytical/Numerical Numerical

Data Requirements Limited Moderate Extensive

One should begin with the simplest code that wouldsatisfy the objectives and progress toward the moresophisticated codes until the modeling objectives areachieved.

The remedial process is generally structured in a waythat is consistent with this philosophy; i.e., as theinvestigation proceeds, additional data becomeavailable to support more sophisticated ground-watermodeling. The data that are available in the earlystage of the remedial process may limit the modelingto one or two dimensions. In certain cases, this may besufficient to support remedial decision making. If themodeling objectives cannot be met in this manner,additional data will be needed to support the use ofmore complex models. The selection of more complexmodels in the later phases often depends on themodeling results obtained with simpler models duringthe early phases.

Generally in the later phases of the investigation,sufficient data have been obtained to meet moreambitious objectives through complex three-dimen-sional modeling. The necessary degree of sophistica-tion of the modeling effort can be evaluated in terms ofboth site-related issues and objectives, as well as thequalities inherent in the computational methodsavailable for solving ground-water flow and transport.

Modeling objectives for each stage of the remedialinvestigation must be very specific and well defined

early within the respective phase of the project. All toooften modeling is performed without developing aclear rationale to meet the objectives, and only after themodeling is completed are the weaknesses in theapproach discovered.

The modeling objectives must consider the decisionsthat the model results are intended to support. Theselected modeling approach should not be driven bythe data availability, but by the modeling objectiveswhich should be defined in terms of what can beaccomplished with the available data. It is importantto keep in mind that the modeling objectives should bereviewed and possibly revised during the modelingprocess. Furthermore, ground-water modeling shouldnot be thought of as a static or linear process, butrather one that must be capable of continuouslyadapting to reflect changes in modeling objectives,data needs, and available data.

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

The following discusses computer code selectionduring each phase of the remedial process. The emphasis is placed on the processes and assumptionsinherent in the mathematical models used in computercodes. The discussion is organized according to thefactors delineated in Table 4-1.

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4.2.1 Scoping

In the scoping phase, site-specific information is oftenlimited. Therefore, the modeling performed during theearly planning phase of most remedial investigationsis generally designed to support relatively simpleobjectives which can be easily tied to more ambitiousgoals developed during the later phases of theinvestigation. The very nature of the iterative processof data collection, analysis, and decision makingdictates that the preliminary objectives will need toevolve to meet the needs of the overall program. Thatis, it would be unreasonable to assume that simplifiedmodeling based upon limited data would do little morethan provide direction for future activities.

An important issue that often arises during the scopingphase is whether remediation and decommissioningstrategies can be selected during the scoping phaseusing limited data and simple screening models. Suchdecisions can be costly at complex sites where thenature and extent of the contamination and transportprocesses are poorly understood. How-ever, atrelatively simple sites, early remediation decisions canbe made, thereby avoiding the unneces-sary delays andcosts associated with a possibly pro-longed sitecharacterization and modeling exercise.

A large part of code selection in the early phase of theinvestigation is understanding the project decisionsthat need to be made, and, of these, which can beassisted through the use of specific codes under theconstraints of both limited data and an incompleteunderstanding of the controlling hydrogeologicprocesses at the site. It is not always necessary toselect a computer code or analytical method that isconsistent with all aspects of the conceptual model. Itis often useful to model only certain components of theconceptual model. In practice, early modeling focusesupon assessing the significance of specific parametervalues and their effects on flow and transport ratherthan modeling specific hydrogeologic transportprocesses. For instance, it is common during thescoping phase to evaluate transport as a function of arange of hydraulic conductivities; however, it isunlikely that more complex processes such as flow andtransport through fractures would be considered.

Because general trends, rather than accuracy, are mostimportant during the scoping phase, a computer codeor analytical method would need to be capable only ofaccommodating the following:

! Conservative Approximations

! Steady-State Assumptions

! Restricted Dimensionality

! Uncomplicated Boundary and InitialConditions

! Simplified Flow and Transport Processes

! System Homogeneity

These model attributes generally translate to modelingapproaches that are consistent with the available dataduring the scoping phase. They are discussed ingreater detail in the following sections.

4.2.1.1 Conservative Approximations

In the scoping phase of the investigation, the objectivesare generally focused on establishing order ofmagnitude estimates of the extent of contaminationand the probable maximum radionuclideconcentrations at actual or potential receptor locations.At most sites, the migration rates and contaminantconcentrations are influenced by a number ofparameters and flow and transport processes whichtypically would not have been fully characterized in theearly phase of the investigation. The parametersinclude recharge, hydraulic conductivity, effectiveporosity, hydraulic gradient, distribution coefficients,aquifer and confining unit thicknesses, and sourceconcentrations. Questions during the early phasesregarding flow and transport processes are typicallylimited to more general considerations, such aswhether flow and transport are controlled by porousmedia or fractures and whether the wastes areundergoing transformations from one phase to another(e.g., liquid to gas).

One of the most useful analyses at this point in theremedial program is to evaluate the potential effects ofthe controlling parameters on flow and transport. Oneobjective of the early analyses is to assess therelationship among the parameters. How do changesin one parameter affect the others and the outcome ofthe modeling exercise? A better understanding of suchinterdependencies would assist in properly focusing thesite characterization activities and ensuring that theyare adequately scoped. Obviously, it would also bedesirable to evaluate the effects that various processes

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would have on controlling flow and transport;however, this would generally have to be deferred untiladditional information is obtained during sitecharacterization. Furthermore, some caution is neededin that if simplistic assumptions have been made in themodel, the results may not be valid (i.e., transferable)to a more refined model that incorporates morerealistic or complex boundary conditions, initialconditions, or parameter variations.

In general, the uncertainty associated with each of theparameters is expressed by a probability distribution,which yields a likely range of values for eachparameter of interest. At this phase in the remedialprocess, it is important to select a modeling methodwhere individual parameter values can besystematically selected from the parameter range andeasily substituted into the governing mathematicalequations which describe the dominant flow andtransport processes at the site. In this manner, theeffects that a single parameter or a multitude ofparameters have on the rate of contaminant movementand concentrations may be evaluated. This techniqueof substituting one value for another from within arange of values is called a sensitivity analysis. It isimportant to ensure that the range of individualparameter values and parameter combinations selectedallow for a conservative analysis of the flow andtransport processes.

In many cases, the possible range of values ofimportant parameters is unknown or very large. As aresult, the analyst has little alternative but to evaluatethe sensitivity of the results to a very broad range ofpossible values for the parameters. Many of theseresults will be unrealistic but cannot be ruled out untilreliable site data are obtained during sitecharacterization. These types of analyses are usefulbecause they help to direct the field work. However,they can also be used incorrectly. For example,individuals not familiar with the scoping process couldcome to grossly inappropriate conclusions regardingthe potential public health impacts of the site based onthe results of scoping analyses. Accordingly, caremust be taken to assure that the results of scopinganalyses are used to support the decisions for whichthey were intended.

An alternative to the detailed sensitivity analysis is aconservative bounding approach. In this lessdemanding analysis, values are selected from theparameter range to provide the highest probability that

the results are conservative, i.e., that the contaminantmigration rates and concentrations would not beunderestimated. For example, high values of hydraulicconductivity combined with low effective porositiesand distribution coefficients would tend to maximizethe predicted contaminant migration rates although theconcentrations at receptors may be underestimated.

It is important to keep in mind that even though effortsare made to ensure a conservative analysis, a numberof natural as well as anthropogenic influences mayadversely affect the migration of radionuclides. Forinstance, distribution coefficients that are published inthe literature are frequently determined at neutral pHvalues. However, even values conservatively selectedfrom the low range could be too high if acid wasteshave been discarded with the radioactive material.Burrowing animals and construction activities havealso been responsible for moving radioactive wastesbeyond the boundaries predicted by ground-water flowand transport models.

Other processes that could render an otherwiseconservative analysis with erroneously optimisticresults include facilitative transport and discretefeatures, such as soil macropores. Facilitativetransport is a term used to describe the mechanism bywhich radionuclides may couple with either naturallyoccurring material or other contaminants and move atmuch faster rates than would be predicted by theirrespective distribution coefficients. Furthermore,discrete features are rarely considered in earlyanalyses, even though it is well known that discretefeatures, such as soil macropores, can allowcontaminant movement on the order of meters per yearin the vadose zone. The result could be a grossunderestimate of the time of arrival and concentrationof contaminants downgradient. Nonetheless, the lackof site-specific data will generally preclude themathematical modeling of anomalous flow andtransport processes during the project scoping phase.Therefore, the potential exists that what wouldnormally be considered conservative modeling resultsare actually underestimating the contaminant velocitiesand concentrations. This possibility highlights theneed for confirmation of modeling results with site-specific field data even if a conservative approach hasbeen undertaken.

As far as code selection is concerned, three basicchoices are available: analytical, semi-analytical, ornumerical codes (Appendix C). Analytical and semi-

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Figure 4-1. One-Dimensional Representation ofConceptual Model

analytical methods, which are limited to simplifiedrepresentations of the physical setting and flow andtransport processes, are ideally suited for performingsensitivity and conservative bounding analyses becausethey are computationally efficient (i.e., fast) andrequire relatively little data as input (Section 4.3.2.1).Several analytical models are set up specifically forperforming sensitivity analyses.

In contrast, numerical methods do not lend themselvesto the same kind of "simplified" applications. Theprimary reasons are that numerical models are difficultto set up, require a large amount of data input tocalibrate the model, and multiple parametersubstitutions are generally very cumbersome.However, the bottom line is that simply not enoughdata exist in the early phases of a remedial project toconstruct and perform defensible numerical modeling.

4.2.1.2 Steady-State Solutions

In the scoping phase, the data that are generallyavailable have been collected over relatively short timeintervals. Therefore, modeling objectives would belimited to those which could be met without a detailedunderstanding of the temporal nature of processesaffecting flow and transport. For example, a typicalanalysis that would not require detailed knowledge ofthe temporal nature of recharge, source release rates,and other flow and transport mechanisms would be theestimation of the distance that radionuclides havetraveled since the beginning of waste managementactivities. This analysis would use yearly averagevalues for the input parameters, such as ambientrecharge, stream flow stages, and source concentrationrelease rates. However, without accommodating thetransient nature of these processes, predictions of peakcontaminant concentrations arriving at downgradientreceptors would be associated with a high degree ofuncertainty.

Analytical transport solutions are generally able tosimulate only systems that assume steady-state flowconditions, but, because the available data rarelysupport transient simulations during the scopingphases, common analytical methods may often be usedmore effectively than numerical methods. It is mucheasier to conduct bounding and sensitivity analyseswith analytical rather than numerical models.

4.2.1.3 Restricted Dimensionality

Ground-water flow and contaminant transport areseldom constrained to one or two dimensions.However, during scoping, modeling objectives musttake into account that there is rarely sufficientinformation to describe mathematically the controllingflow and transport processes in three dimensions. Inreality, most of the modeling analysis in thepreliminary investigation will focus upon centerlineplume concentrations which are essentially one- andtwo-dimensional analyses. One-dimensional analysesof the unsaturated zone are customarily performed ina cross-sectional orientation because flow and transportare predominantly vertically downward. Similarly, inthe saturated zone, vertical gradients are generallymuch smaller than lateral gradients and, as a result,vertical transport need not always be explicitlymodeled. Therefore, two-dimensional areal analysesmay be appropriate.

Figures 4-1 through 4-4 may be useful in visualizingthe differences between one-, two-, and three-dimensional modeling. In one-dimensional modeling,the radionuclide concentration is predicted in theplume centerline in the x direction, and no informationis provided on the radionuclide concentration in the yor z direction (Figure 4-1).

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Figure 4-2. Two-Dimensional Cross-SectionalRepresentation of Unsaturated Zone inConceptual Model

Figure 4-3. Two-Dimensional ArealRepresentation of Saturated ZoneConceptual Model

Figure 4-4. Three-Dimensional Representation ofConceptual Model

In two-dimensional cross-sectional models for theunsaturated zone, the radionuclide concentration iscalculated for the x and z direction and it is assumedto be the same at any slice through the plume in the ydirection (Figure 4-2).

In saturated zone areal models, the radionuclideconcentrations are predicted for the x and y directions,but it is assumed the radionuclide concentration is thesame in any slice in the z direction (i.e., theconcentration at any location is the same at all depths)(Figure 4-3).

Cross-sectional modeling of the saturated zone inwhich flow is assumed to be in the lateral and vertical

directions (e.g., transverse flow is ignored) may also beperformed. A quasi-three-dimensional modelingapproach is also commonly used when verticalcomponents of flow within aquifers are deemedunimportant. This approach assumes that ground-water flow through any confining units that separateaquifers is in only one dimension (i.e., vertical).Furthermore, flow within the aquifers is twodimensional (i.e., vertical flow component is ignored).In this manner, the effects of the hydraulicinterconnection among interbedded aquifers andconfining units can be simulated without having to relyon fully three-dimensional models.

Three-dimensional models will calculate theradionuclide concentrations at any x, y, z coordinate,taking into consideration the variations in thelithography and hydrogeology in three dimensions(Figure 4-4).

A typical three-dimensional problem would be onewhich would be designed to evaluate the geometry ofhypothetical capture zones if one or more extractionwells were planned for the remediation of the groundwater. The vertical ground-water gradient that wouldbe artificially created by the pumping wells, as well asthe induced vertical leakage from overlying and underlying hydrogeologic units, would be veryimportant to consider in this analysis. If this leakagewere not accounted for, the effectiveness of theremedial system would be substantially overestimated

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Figure 4-5. Typical System Boundary Conditions

because the radii of the capture zones would be toolarge.

As a general rule, analytical methods, which can beperformed on a hand-held calculator, are developed forpredicting concentrations along the centerline of theplume and are limited to one dimension. Two- andthree-dimensional analyses are customarily performedwith the assistance of a digital computer. Althoughanalytical solutions are available for two- and three-dimensional analysis, the limitations that are placedupon the solution techniques are so severe that theycan be used only to simulate gross system behavior.Therefore, the three-dimensional example providedabove could not be satisfactorily addressed by ananalytical model because of computational limitations,such as simple boundary conditions and uniformgeology. However, attempts to circumvent thelimitations of analytical methods at this phase byadopting numerical methods would only complicatethe problem for reasons previously discussed, as wellas now having to provide parameter estimates in thesecond or third dimension.

At this phase, the question is not really whether to useanalytical or numerical methods but rather how manydimensions should be included in the analytical

modeling. The advantages of adding a second or thirddimension must be carefully weighed against thefurther complications of performing the sensitivityanalysis which provides the real strength behind theapplication of analytical methods.

4.2.1.4 Uncomplicated Boundary and UniformInitial Conditions

Boundary conditions are the conditions the modelerspecifies as known values in order to solve for theunknowns in the problem domain (Figure 4-5).Ground-water boundaries may be described in terms ofwhere water is flowing into the ground-water systemand where water is flowing out. Many different typesof boundaries exist, including: surface water bodies,ground-water divides, rainfall, wells, and geologicfeatures such as faults and sharp contrasts in lithology.Initial conditions are defined as values of ground-waterelevation, flow volumes, or contaminantconcentrations which are initially assumed to bepresent in the area of interest.

Governing equations that describe ground-water flowand contaminant transport and associated boundaryand initial conditions may be solved either analyticallyor numerically. Analytical solutions are preferablebecause they are easily adapted to sensitivity analyses;however, in most cases, analytical methods are notpossible because of irregularly shaped boundaries andheterogeneity of

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both the geology and flow field. If very few data areavailable for the site, it would be very unlikely thatreliable ground-water elevations and flow volumescould be assigned to calculate the unknowns in thedomain of a numerical model. Furthermore, theboundary conditions in the numerical model are notsupposed to be subject to radical adjustments and aregenerally excluded from detailed sensitivity analyses.In contrast to numerical methods, analytical methodsare conducive to testing and evaluating both theboundary and initial conditions. In fact, analyticalmethods do not require that boundary values be knownand assigned for the planes and surfaces that surroundthe modeled region. However, this is also a limitationof analytical methods in that, if boundary conditionsvary within the problem domain, they cannot beadequately simulated.

The lack of site-specific data available in the scopingphase will generally not allow a good definition of thesystem boundary and initial conditions; therefore, theobjectives will be confined to very limited calculationsof approximate travel distances and contaminantconcentrations.

Most analytical models will not accommodate non-uniform boundary or initial conditions. Therefore, ifthe domain includes areas where recharge is variableor a lake or stream exhibits strong effects on the flowfield, analytical modeling will not provide goodagreement with the overall system behavior. It followsthat, if the flow field is uniform, which can generallybe described with simple uniform boundary conditions,analytical models provide a better method for testingthe boundary conditions than do numerical methods.However, the true nature of the flow field cannot bedetermined until the site is characterized.

4.2.1.5 Simplified Flow and Transport Processes

Site-specific information describing the flow andtransport processes which dominate the migration ofradionuclides would not be available before detailedsite characterization activities are conducted.Therefore, modeling objectives would need to bedefined as those that could be addressed with onlylimited knowledge of the site hydrogeology andgeochemistry. In practice, this means that uniformporous media flow would be assumed, and that all ofthe geochemical reactions that affect the radionuclidetransport would be lumped together as a singleparameter termed the distribution coefficient.

However, the effects of dilution due to the lateralspreading of the plume over a uniform flow field canbe considered as well as the radionuclide half-lives.

Discrete features, such as macropores, fractures, andfaults, would generally have to be neglected for theflow and transport analysis, and distributioncoefficients would be selected from literature valuesjudged to be conservative. Movement through theunsaturated zone would be simulated with simplifiedversions of more complex equations describing theunsaturated flow and transport.

Unless there were sufficient data to prove to thecontrary, it would be assumed that the flow field wasuniform, and, at this time, there would be fewadvantages to selecting a numerical model over ananalytical one. Analytical methods do exist thatdescribe the flow and transport of radionuclidesthrough fractures. However, the fracture-flowmodeling would have to be performed as a sensitivityanalysis, as the information to adequately describe thegeometry of the fractures would seldom be availablebefore site characterization.

4.2.1.6 Uniform Properties

Homogeneity describes a system where all of thecharacteristics are uniform within the aquifer, whereasisotropy means that the hydraulic properties areidentical in all directions. A homogeneous system mayhave anisotropic flow properties, if, for example, anotherwise homogeneous sandstone aquifer has agreater hydraulic conductivity in the horizontaldirection than in the vertical. Therefore,hydrogeologic units may have anisotropic qualities butstill be considered uniform throughout, provided theanisotropy does not vary within the unit.

Prior to site characterization, only the most generalassumptions may be made regarding the relative flowproperties of the aquifers. For example, as a rule ofthumb, it is often assumed that the hydraulicconductivity in the horizontal direction is ten timesgreater than that in the vertical direction forsedimentary deposits.

Except for some radial flow problems, almost allavailable analytical solutions belong to systems havinga uniform steady flow. This means that the magnitudeand direction of velocity throughout the system areinvariable with respect to time and space, which

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requires the system to be homogeneous and isotropicwith respect to thickness and hydraulic conductivity.Therefore, analytical methods will not allow thesimulation of flow and transport through layers ofaquifers and aquitards. Furthermore, if there is adivergence from these uniform properties within theaquifer, such as direction flow properties of buriedstream channels, analytical models would be unable tosimulate the effect that these features would have onflow and transport. However, it is unlikely that thisdetailed information would be available prior to thesite characterization program.

4.2.2 Site Characterization

The primary reasons for ground-water modeling in thesite characterization phase of the remedial process areto: (1) refine the existing site-conceptual model; (2)optimize the effectiveness of the site characterizationprogram; (3) support the baseline risk assessment; and(4) provide preliminary input into the remedialapproach. To accomplish these goals, it is generallynecessary to apply relatively complex ground-watermodels to simulate flow and transport in the saturatedzone and, in many instances, the unsaturated zone.

A properly designed site characterization program willexpand the data base to enable very specific and oftendemanding objectives to be addressed. To meet themore rigorous requirements, the simplified modelingapproaches undertaken in the scoping phase give wayto more sophisticated means of data evaluation.However, this added sophistication and heightenedexpectations also convey far more complications inselecting the proper modeling approach. As discussedpreviously, the two general types of modeling optionsthat could be selected during the site characterizationprogram include analytical and numerical modelingmethods.

In many instances, several different modelingapproaches will be taken to accomplish the objectivesat a particular phase in the investigation. For example,the output of analytical modeling of the unsaturatedzone, in the form of radionuclide concentrations at theinterface between the saturated and unsaturated zone,may be used as input to numerical models of thesaturated zone. It must always be kept in mind that,regardless of the phase of the remedial process, thesimplest modeling approach that meets the modelingobjectives should be taken.

The site characterization program is the first time inthe investigation where flow and transport processesare identified and investigated. Prior to sitecharacterization activities, the investigator could onlyevaluate the effects of various parameter values on flowand transport. In the scoping phase, the modelingfocuses on parameter estimations rather than on theeffects that geochemical and physical flow mechanismscould have on the fate and transport of contaminants.Examples of these mechanisms include processesrelated to fractures, density dependence, phasetransformations, and changes in the geochemicalenvironment.

It is important during the site characterization to gainan appreciation for the governing geochemicalprocesses, as these reactions may have a significantimpact on the transport of contaminants and can besimulated indirectly in the analysis by assuming aspecified amount of contaminant retardation. Directmeans (computer codes) for simulating geochemicalprocesses are available; however, a detailed discussionof these methods is beyond the scope of this report.

As additional data are acquired during the sitecharacterization program and a better understanding ofthe hydrogeology is achieved, the modeling approachand code selection become more involved. Without thedata limitations that constrained the choice of methodsto those of an analytical nature in the scoping phase,the number of possible alternatives in the modelingapproach and code selection process increasessignificantly.

Rather than examine many of the available computercodes and their inherent limitations and capabilities,the following discussion addresses the rationale foradopting a modeling approach that will be consistentwith the objectives. This is important because it isrelatively easy to determine the various attributes of theexisting computer codes; however, it is far moredifficult to understand the relevance of these attributesas they apply to a specific site and the modelingobjectives.

The following subcategories, keyed to Table 4-1, areanalogous to those presented in the scoping phase.Because the modeling objectives of the sitecharacterization phase differ from those of the scopingphase, the approach to modeling is also different.

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Basically, analytical methods will be replaced bynumerical methods in order to use less restrictive andmore realistic assumptions. The following discussionsprovide an overview of the concepts, terminology, andthought processes necessary to facilitate the model andcomputer code selection process. The modelingapproach in the site characterization program willgenerally be based upon the following:

! Site-Specific Approximations

! Steady-State Flow/Transient Transport

! Multi-Dimensional

! Constant Boundary and Non-uniform InitialConditions

! Complex Flow and Transport Processes

! System Heterogeneity

Obviously, if the site characterization activitiesdiscover that the system is very simple and theobjectives can be addressed with analytical modeling,an approach similar to that outlined in the scopingphase can be taken.

4.2.2.1 Site-Specific Approximations

In the scoping phase of the investigation, the datalimitations impose a simple modeling approachwhich uses conservative parameter estimates. One ofthe primary objectives of the site characterizationprogram is to obtain sufficient data to enable theconservative modeling approach to be replaced by adefensible and more realistic approach whichincorporates site-specific data.

Many of the objectives defined for the sitecharacterization phase of the investigation cannot bemet solely with conservative analyses. If parametervalues are not known, it may be necessary to makeconservative estimates; however, the implications thata conservative approach may have on other aspects ofthe remedial program must also be considered. Forexample, if, during the baseline risk assessment,conservatively high hydraulic conductivities are usedin order to ensure that the downgradient contaminantarrival times are not underestimated, several problemsmay occur. First, it would be difficult to calibrate themodel to known parameters (e.g., potentiometric

surface), and adjustments to other parameters would berequired in order to match measured field values. Theend result would be a model that poorly predictssystem responses to hydraulic stresses (e.g., extractionwells). A second problem would involve contaminantconcentrations. A conservative increase in hydraulicconductivity would predict more ground-water flowthrough the system than is actually occurring and mayunderestimate the contaminant concentrations atdowngradient receptors. Furthermore, problems mayarise during the remedial design. If the modelingresults are used to estimate clean-up times, the modelmay predict that water and contaminants are flowingfaster than they actually are and at lowerconcentrations. This would result in an underestimateof both the amount of time required for remediation aswell as the contaminant breakthrough concentrations.

The major impact that the formulation of a morespecific site-conceptual model will have on themodeling approach is that now parameter ranges havebeen narrowed by additional data acquisition, andsensitivity analyses can become more focused. Thisparameter value refinement diminishes the need toperform a multitude of sensitivity analyses. Inconjunction with the increased demand to moreaccurately simulate the controlling flow and transportprocesses, the primary advantages of analytical modelsare superseded by their inability to simulate morecomplex conditions. Therefore, the model selectionprocess is reduced to determining which numericalmodel will best suit the objectives.

4.2.2.2 Steady-State Flow/Transient Transport

The data obtained during the site characterizationprogram are generally collected over relatively shorttime intervals and frequently do not reflect thetemporal nature of the hydrogeologic system.Unfortunately, objectives that need to be addressedduring the site characterization phase often involve theprediction of temporal trends in the data. For instance,the risk assessment would generally include ananalysis of the peak arrival times of radionuclides atdowngradient receptors. This incompatibility betweenthe objectives and data availability gives rise to someof the greatest uncertainties associated with the entireremedial investigation. However, one of the principalutilities of mathematical models is their ability toextrapolate unknown values through time.

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The modeling approach during site characterizationwill generally assume a steady-state flow field andaccommodate the transient nature of the systemthrough the contaminant transport analysis. Steady ortransient leaching rates would be used in conjunctionwith the existing plume concentrations for initialconditions. Therefore, the system is actually modeledas a steady flow system and possibly a transient orpulse-like source term. However, the transient natureof the plume is generally used as a model calibrationparameter and is not carried forward into thepredictive analysis for future radionuclideconcentrations. That is, rarely are there sufficient datato describe the temporal nature of the source release.Exceptions to this are when records are availablepertaining to the volumes of radioactive liquids thatwere dumped over time into absorption trenches orwhen correlations between rainfall events and sourceleaching rates may be extrapolated.

Analytical methods are able only to simulate systemsthat assume steady-state flow conditions, althoughsome analytical codes will allow for the simulation ofa transient source term. Therefore, analytical methodscan be used to simulate the temporal nature of thecontaminant plumes to predict probable maximumconcentrations and contaminant arrival times.However, other limitations within the analytical codesoften preclude their use during the site characterizationphase.

Almost all of the numerical transport codes written forradioactive constituents are able to simulate constantradionuclide source terms with radioactive decay.However, if the simulation of a pulse-like source termis desired, special care is needed to ensure that thiscapability has been written into the code. Otherwise,the source release would have to be manuallysimulated using a code that models a single pulse in aniterative fashion for each separate pulse.

4.2.2.3 Multi-Dimensional

The site characterization program should be designedto gather sufficient data to develop a three-dimensionalconceptual model. It is only after the three-dimensional system is relatively well understood thatit can be determined whether one-, two-, or three-dimensional modeling is necessary. If one or twodimensions are eliminated from the analysis, carefulconsideration needs to be given to what impactrestricting the dimensions will have on the model'scapability to simulate existing field conditions.

The magnitude of flow and transport in any directionrelative to the other directions provides the rationalefor which dimension(s) should be included orexcluded. In most instances, flow and transport in theunsaturated zone are assumed to be predominantlydownward with smaller horizontal components. If theflow components are found to have two dominant flowdirections, a two-dimensional cross section may allowa representation of the flow field.

Modeling and field validation studies of the vadosezone (the unsaturated zone) have yielded mixed resultsboth in model calibration and in the comparison oftransport predictions against measured field values. Inmodeling the vadose zone, as well as the saturatedzone, the question is always how much uncertainty inthe results is acceptable to meet the objectives.

Two-dimensional simulations of the saturated zone areusually performed when the horizontal flowcomponents are far greater than the vertical flowcomponents, allowing the vertical components to beignored. However, much of the modeling performedfor site characterization will be on a scale where thevertical components of flow are usually importantbecause many natural features, such as surface waterbodies, often have strong vertical flow componentsassociated with them. Furthermore, particular caremust be taken in eliminating the third dimensionbecause attempts to simulate three-dimensionalprocesses in two dimensions can lead to difficulties inmodel calibration as well as in producing defensiblemodeling results.

Water-level data collected from closely spaced wellsthat penetrate the same aquifer at different depthsprovide excellent information on the vertical gradients.This information may be used during the sitecharacterization program to determine the effective

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hydraulic basement of any contamination present, aswell as recharge and discharge areas. If there arestrong vertical gradients, the capability to simulate thevertical movement of ground water within thehydrogeologic system becomes very important indefining the nature and extent of the contaminantplume.

It should also be kept in mind that two-dimensionalplanar modeling will average the contaminantconcentrations over the entire thickness of the aquifer,and the vertical definition of the contaminant plumeswill be lost. This vertical averaging of contaminantswill result in lower downgradient concentrations andmay not support a base-line risk assessment. Again,this example illustrates that the decision on how manydimensions to include in the modeling must be tiedback to the objectives and the need to be aware of thelimitations imposed upon the results if one or moredimensions are eliminated.

The recent development of more sophisticated pre- andpost-processors greatly facilitate data entry andprocessing. These advances, in conjunction with therapid increase in computer speeds over the past severalyears, have greatly reduced the time involved inperforming three-dimensional modeling. In general,there are far more concerns associated withconstraining the analysis to two dimensions thanincluding the third dimension, even if many of theparameters in the third dimension have to beestimated.

Two-dimensional analyses during the sitecharacterization program are most valuable formodeling the unsaturated zone and for performingsensitivity analyses of selected cross-sections througha three-dimensional model. Two-dimensionalapproaches are also useful for performing regionalmodeling from which the boundary conditions for amore site-scale modeling study may be extrapolated.

The objectives for most characterization programs willbe met only by modeling approaches and models thatare multi-dimensional. Analytical models do exist thatare two- and three-dimensional, but they have verylittle versatility and would rarely suffice in meetingcomplicated objectives. Furthermore, the likelihoodthat analytical methods could be effectively used in theremedial design and evaluation are even more remote.Therefore, numerical methods should almost always be

chosen if detailed analysis is required to meet the sitecharacterization objectives.

There are numerous two- and three-dimensional flowand transport codes to describe the saturated zone.However, only a handful of three-dimensional codesexist that describe flow and transport through theunsaturated zone. A number of codes exist that aregenerally three-dimensional; however, certaintransport properties (e.g., dispersion) within thesecodes are simulated in only two dimensions. Specialattention should be given to ensure that the controllingflow and transport processes are described in thenumber of dimensions desired to meet the objectives.

Code selection should not only take into account therequired dimensionality of the site characterizationanalysis, but also the projected modeling needs of theremedial design and evaluation phase. It is mucheasier to use a code with three-dimensional capabilityfor a two-dimensional analysis and later expand to thethird dimension than it is to set up a three-dimensionalcode from output obtained from a separate two-dimensional model.

4.2.2.4 Constant Boundary and Non-uniformInitial Conditions

In general, boundary conditions are known orestimated values that are assigned to surfaces andplanes that either frame the perimeter of the modeledarea or define the nature of release from thecontaminant source. The different types of flowboundary conditions are: (a) head (ground-waterelevation) is known for surfaces or planes bounding themodeled region; (b) ground-water flow volumes areknown for surfaces or planes bounding the modeledregion; (c) some combination of (a) and (b) is knownfor surfaces or planes bounding the region. Boundaryconditions could also be assigned to interior features ofthe modeled region where ground-water elevations orflow volumes are known, such as lakes, rivers ormarshes.

The most common contaminant-source type boundarieseither specify the source concentration or prescribe themass flux of contamination entering the system. Theconcentration is generally prescribed when the releaserate is largely controlled by the solubility limits of thecontaminant. The mass flux type boundary is typicallyused when a leaching rate is known or estimated.Specialized source boundaries have also been

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formulated which allow the source to radioactivelydecay. The ability of the code to treat source decaymay not be important if the parents and daughters havea relatively long half-life when compared to theexpected travel time to the nearest receptor.

One of the primary objectives of the sitecharacterization program is to identify the presenceand location of ground-water flow and contaminantsource boundaries so that they may be incorporatedinto the conceptual model. These boundaries aregenerally quantified in terms of the volume of groundwater and contamination moving through the system.The physical boundaries are then translated intomathematical terms as input into the computer model.

Initial conditions are defined as values of ground-waterelevation, flow volumes or contaminantconcentrations, which are initially assigned to interiorareas of the modeled regions. At least for the flowmodeling performed during the site characterization,the initial conditions are generally set to uniformvalues. This is because the temporal nature of the flowsystem is usually poorly defined. In addition, if theflow analysis is performed to steady-state, which isusually the case, the initial conditions assigned to themodel domain are irrelevant as identical solutions willbe reached for these values regardless of the valuesinitially assigned. This occurs because these steady-state values are solely dependent on the valuesassigned to the boundaries of the model.

Non-uniform initial values (i.e., contaminantconcentrations) are routinely used in the contaminanttransport analysis to depict the geometry and varyingcontaminant concentrations within plume, as well as todefine the contaminant concentrations leaching fromthe contaminant source. The ability of a code to allownon-uniform initial conditions would be essential tofully describing and simulating the contaminantplume(s).

Analytical models are written for very specificboundary conditions and uniform initial conditions. Inessence, this means that the boundary conditionscannot vary spatially and, in most instances, only onetype of boundary condition can be accommodated.Furthermore, analytical methods do not allow for thecontaminant source concentrations to change throughtime and the measured plume values (i.e., non-uniforminitial conditions) cannot be input directly to themodel. Understandably, these restrictions would

impose significant limitations on analyzing the datacollected during the site characterization program.

Numerical models are broadly designed to adapt tomany different types of boundary geometries andinitial conditions. Non-uniform initial conditions fora single contaminant plume can almost always bevaried spatially, depending upon the dimensionality ofthe code.

The ability of numerical models to handle complexboundaries and non-uniform initial conditions bestowa versatility to the analysis which should be compatiblewith the objectives. This approach is consistent withthe principles behind coupling the sophistication of themodeling with that of the existing knowledge base.

4.2.2.5 Complex Flow and Transport Processes

Site-specific information describing the flow andtransport processes which dominate the migration ofradionuclides would not have been available during thescoping phase of the investigation. As the sitecharacterization activities progress, greater attention isfocused upon the physical, chemical, and biologicalprocesses that are affecting ground-water flow andcontaminant transport. Up until this time, theattention has been placed primarily upon estimatingparameter ranges and variances within these rangesvia the sensitivity analyses. This approach haslimitations and needs to be broadened during the sitecharacterization phase if ground-water flow andcontaminant transport are to be well described. Themeans by which this parameter-based approach isexpanded is by using computer codes thatmathematically accommodate the dominant flow andtransport processes. These processes could includeflow and transport through fractures, density-drivenflow, matrix diffusion, fingering, surface water/groundwater interactions, and geochemical reactions. Ifpresent, each of these processes can invalidate theoutput of models that are based on the assumption thatuniform flow and transport are occurring through ahomogenous porous media.

It is still likely that all of the geochemical reactionsthat affect the radionuclide transport would be lumpedtogether into the single parameter termed thedistribution coefficient. However, a better delineationof any geochemical facies would allow for thedistribution coefficient to vary from layer to layer aswell as within the units themselves. If this simplified

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means of simulating geochemical processes is found tobe inadequate, it may be necessary to utilizegeochemical models in order to explicitly addressspecific geochemical reactions by relying uponthermodynamically based geochemical models.

Movement through the unsaturated zone could besimulated in a number of different ways dependingupon the objectives. If the unsaturated zone isrelatively thin and travel times are short, it may be thatsimplified versions of more complex equationsdescribing the unsaturated flow and transport wouldsuffice. However, if the travel time through theunsaturated zone is significant and accurate flow andtransport predictions are required, then mathematicalmethods, which account for complex processesassociated with flow and transport through theunsaturated zone, may be necessary.

The modeling objectives need to be defined prior to thecharacterization; only in this fashion can it be assuredthat data are sufficient to perform modeling at thenecessary level of complexity. All too often,limitations within the data, rather than the modelingobjectives, drive the sophistication of the modeling.

Analytical methods are not well suited to simulatecomplex flow and transport processes. Further, evennumerical methods do not satisfactorily describe someflow and transport processes. These processes includefacilitative transport and non-Darcian flow, which arediscussed in section 4.3.

4.2.2.6 System Heterogeneity

One of the primary objectives of the sitecharacterization program is to identify heterogeneitywithin the system and to delineate zones of varyinghydraulic properties. System heterogeneity is one ofthe leading causes of a poor understanding of thephysical system controlling flow and transport.

If the accurate simulation of heterogeneous rocks isrequired to meet the modeling objectives, analyticalmethods would be inappropriate as they assume therocks to all have the same properties. In contrast, mostnumerical codes allow for zones with different porousrock properties; however, relatively few codes cansimulate discrete features, such as faults, fractures,solution features, or macropores. Numerical codesvary from one another in their ability to simulate sharpcontrasts in rock properties. For example, many codeswould have a problem arriving at a solution (i.e.,

convergence) if very impermeable rocks dissectedhighly permeable rocks. Therefore, if the site wassituated in an alluvial flood plane bordered by lowpermeability bedrock, special care would be needed toselect a code that will not have numerical convergenceproblems caused by permeability contrasts.

In selecting a computer code to be applied during thesite characterization, consideration should also begiven to what scenarios may be modeled during theremedial investigation. If a low-permeability slurrywall or sheet pile cut-off walls may be installed, itwould be important that the computer code be able tosimulate these features through permeability contrasts.

4.2.3 Remedial Phase

As the site investigation proceeds into the remedialphase, data are acquired that will assist in theidentification of feasible remedial alternatives. Thesedata, in combination with models, are used to simulatethe flow and transport in support of the selection,design, and implementation of the remedialalternatives. The data and models are used to predictthe behavior of ground-water flow and the transport ofradionuclides and thereby aid in the selection anddesign of the remedy and demonstrate that the selectedremedy will achieve the remedial goals.

The modeling objectives associated with remedialalternative design are generally more ambitious thanthose associated with the site characterization phase ofthe remedial process. Therefore, it is often necessaryeither to select a computer code with more advancedcapabilities, or modify the existing model in order tosimulate the more complex conditions inherent in theremedial design. The following are specific examplesof processes that may not be important to the baselinerisk assessment and site characterization, but are oftenessential 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 (in-situ vitrification/freezing);

! sharp contrasts in hydraulic conductivity(barrier walls);

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! multiple aquifers (barrier walls);

! the capability to move from confined tounconfined conditions (pump and treat); and

! ability to simulate complex flow conditions(pumping wells, trenches, injection wells).

From a modeling standpoint, the remedial design is themost challenging phase of the remedial investigation.Frequently, it is the first time in the process thatsufficient data are available to enable the modelpredictions to be verified. The very nature of many ofthe potential remedial actions (e.g., pump and treat)provide excellent information on the temporal responseof the flow and transport to hydraulic stresses. Thesedata allow continuous refinement to the calibration andenable the model to become a very powerfulmanagement tool.

The following describes modeling during the remedialphase of the investigation. The modeling approachestaken at various sites would generally have thefollowing characteristics in common:

! Remedial Action Specific

! Transient Flow and Transport

! Multi-Dimensional

! Prescribed Boundary and Non-uniformInitial Conditions

! Specialized Flow and Transport Processes

! System Heterogeneity

4.2.3.1 Remedial Action Specific

As the site characterization process comes to an endand the Remedial Design and Selection Phase isentered, data have been acquired which will define theremedial alternatives. The various remedialalternatives can be conveniently grouped into thefollowing three categories:

! Immobilization

! Isolation

! Removal

This section briefly describes each category, the typesof processes that need to be modeled to support eachcategory, and the special information needs for each ofthese categories. The information is required not onlyfor implementation of the remedial design but also toevaluate its effectiveness through numerical modeling.

Immobilization

Immobilization of the radioactive wastes refers tophysical, chemical, and/or biological processes used tostabilize the radionuclides and preclude their transport.A number of treatment options exist, each having theirown associated modeling needs, including:

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

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

! Biotic• 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, andbiological processes that may need to be modeled tosupport 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

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• oxidation-reduction reactions• system thermodynamics• chemical speciation• ion-exchange phenomena• precipitation• natural colloidal formation• radiolysis• organic complexation• anion exclusion

! Biotic Properties and Processes• biofixation

It would be ideal if these processes and propertiescould be reliably described and modeled withconventional and available models. However, many ofthese properties and processes are not well understood,and, in these instances, models do not exist that yieldreliable results.

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

! Determination of temperature-dependentflow and transport parameters

! Characterization of geochemicalenvironment

! Determination of the alteration of thephysical rock properties that govern flow andtransport

! Characterization of the microbialenvironment

Isolation

A common remedial alternative is to emplaceprotective barriers either to prevent contaminatedground water from migrating away from acontaminated site or to divert incoming (i.e., clean)ground water from the source of contaminants.Several types of materials are being used to constructsuch barriers, including soil and bentonite, cement andbentonite, concrete, and sheet piling. An alternative tothe physical emplacement of protective barriers is theuse of hydraulic containment which involvescontrolling the hydraulic gradient through the use ofinjection and/or withdrawal wells or trenches in order

to contain and treat the contaminant plume. Examplesof potential barriers include the following:

! Physical• hydraulic containment• grout curtains, sheet piling, bentonite

slurry walls• low permeability caps (clay and/or

synthetic)

! Chemical• ion-exchange barriers

! Biotic• microbial barriers

If properly designed and emplaced, such barriers canlast for several decades, barring any geologicaldisturbances, such as tremors, ground settling,significant changes in hydraulic gradients, etc.Accordingly, such barriers can be useful in mitigatingthe impacts of relatively short-lived radionuclides, orto control the migration of long-lived radionuclidesuntil a more permanent remedy can be implemented.

Several mechanisms or processes can affect the long-term integrity of such barriers. Once the installationis complete, failures can be due to cracking,hydrofracturing, tunnelling and piping, and chemicaldisruption. Changes in the site's geological orhydrological characteristics can also lead tocatastrophic failures, such as partial collapse, settling,and breaking. If a barrier should fail followinginstallation, water may infiltrate the site, andcontaminated leachates may move beyond the site.This type of failure could result in the dispersion ofcontaminants in the environment.

The modeling approaches that would be consistentwith simulating the effects that flow barriers wouldhave on the fate and transport of radionuclides areclosely tied to the ability of the code to accommodatea number of factors, including: high permeabilitycontrasts, transient boundary conditions, and possiblychemical and biological reactions. Theseconsiderations will be discussed in greater detail in thefollowing sections.

The following are the types of physical, chemical, andbiological processes that may need to be modeled tosupport alternative remedies based on isolation. Manyof these processes are very complex, and attempts atmodeling will meet with varying degrees of success:

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! 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

Typical characterization data needs related to barrieremplacement include:

! Barrier dimensions

! Barrier hydraulic conductivity

! Geochemical environment

! Structural integrity of barrier/barrierdegradation

! Microbial environment

! Detailed hydrogeology

Removal

Radioactively contaminated soil can result from thedisposal of both solid and liquid waste. Solid wastesmay have been buried in the past without sufficientintegrity of containment so that, eventually,radioactivity intermingled with the contiguous soil.Percolation of rain water through shallow burial sitescan contribute further to the migration of radionuclidesto lower depths as well as to some lateral movement.Wider areas of contamination have occurred whenwaste, stored temporarily at the surface, has lostcontainment and has been disbursed by the wind. Thetechnologies that are most commonly applied toremove solid, liquid, and vapor (e.g., tritium)radionuclides include the following:

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

! Biotic• injection and removal of biomass foam

The following are the types of physical, chemical, andbiological processes that may need to be modeled tosupport alternative remedies based on removal. Mostof these processes and properties are readily describedin mathematical terms and can be modeled relativelyreliably. Obviously, modeling the biological activityassociated with the injection of a biomass will have thesame limitations that are common to other types ofbiological modeling.

! Physical Properties and Processes• transient source term• unsaturated zone flow and transport• matrix diffusion• desaturation and resaturation of the

aquifer• vapor transport

! Biotic Properties and Processes• physical injection and withdrawal of the

biomass• microbial population modeling

Typical characterization needs related to radionuclideremoval include:

! Air permeability of the unsaturated zone! Unsaturated zone flow and transport

parameters! Areal extent of contaminated wastes! Depth to ground water! Saturated zone flow and transport properties

The degree to which these factors are addressed in themodeling relies heavily upon the objectives as well asthe availability of the required data. Specific examplesof how these considerations are tied into the modelingapproach are provided in the sections that follow.

4.2.3.2 Transient Solutions

The data that are available by the time the remedialdesign phase is entered usually span a relatively longtime frame, which often allows the temporal nature of

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the hydrogeologic system to be relatively well defined.If this is the case, the remedial design objectives couldinvolve many criteria that could not have been metduring the modeling activities in the sitecharacterization phase. Many of these additionalcriteria of the design phase objectives may require thatthe code have the capability to perform transient flowand transport simulations. This capacity would benecessary to evaluate the effectiveness of a number ofremedial alternatives. One such alterna-tive would bethe placement of earthen covers and a broad range ofnatural and synthetic barriers, which are engineered toestablish a cap over surface and subsurface soil. Oneof the objectives of the cover is to prevent rainwaterfrom percolating through contaminated soil andcarrying radionuclides to the ground water. In the sitecharacterization program, the objectives were such thatthey could probably have been met by assumingconstant areal recharge over the modeled area.However, this steady-state approach would not accountfor recharge rates which vary through time, whichwould be needed to simulate the deterioration of thecap and the subsequent effect on the radionuclideleaching rates.

Soil excavation of radioactively contaminated soil willresult in some amount of residual radioactivityremaining in the soil contiguous to the removaloperations. It could also result in the redistribution ofcontaminants in the unsaturated zone. Without theability to perform transient simulations, with thesource now largely removed, it would not be possibleto determine how long it would take for the remedialactions to have a noticeable effect on downgradientreceptors.

4.2.3.3 Multi-Dimensional

The need to perform three-dimensional modelingduring the remedial phase will largely depend uponwhat remedial alternatives are under consideration andhow the effectiveness of the selected alternative will beevaluated.

The remedial alternatives that are most commonlysupported by three-dimensional and quasi-three-dimensional modeling are those that impart a strongartificial stress to the hydraulic flow field, such aspumping wells and extraction trenches. Under manycircumstances, the vertical ground-water gradients,prior to these imposed stresses, would be several ordersof magnitude less than the horizontal gradients and,

therefore, could be ignored in a one- or two-dimensional flow analysis. However, when thehydraulic gradients are significantly altered byimposed stresses, three-dimensional flow fieldsgenerally develop. Without the capability to simulatethe actual flow field in three dimensions, it would bevery difficult to effectively determine capture zonesand influent contaminant concentrations. This islargely because vertical leakance from units above andbelow the screened interval of the extraction wellwould be ignored as well as vertical concentrationgradients.

Another remedial alternative that generally createsthree-dimensional flow fields are physical barriers toground-water flow. Whether the barriers consist ofgrout injection techniques, sheet pile cutoff walls, orbentonite slurry walls, all of these procedures will havea common problem which is that the hydraulic headwill build up behind the structures and induce verticalgradients allowing ground water to flow under thebarriers. In these cases, the analysis of vertical flow isessential in determining probable leakage rates and thevolume of water that would potentially flow throughthe structure.

4.2.3.4 Transient Boundary and Non-UniformInitial Conditions

Most of the modeling analysis up until the remedialphase can be performed with constant boundaryconditions. This means that physical features withinthe modeled area, such as the water elevations ofsurface water bodies and areal recharge, can besimulated with values that remain constant with time.Once the remedial phase is reached, however, themodeling objectives may require that the transientnature of these boundaries are incorporated into theanalysis, and time-weighted averages may no longer beapplicable. For instance, water bodies, such asradioactively contaminated waste lagoons, wouldprobably have been treated as constant boundariesduring the site characterization modeling, and theirwater-surface elevations would have been heldconstant. However, if one of the remedial activitiesinvolved withdrawing contaminated water from one ormore of the lagoons, the effect that the change inwater-surface elevations would have on the ground-water gradients could be evaluated only by simulatingthe drop in surface elevations through time. Thiswould be done by prescribing the boundaries of the

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lagoon(s) to change with time in order to simulate theexpected extraction rates.

The ability to prescribe boundaries within the modelwould also be important in the evaluation of in-situsoil flushing techniques, which are used to enhance themobility of contaminants migrating towards recoverypoints. In this case, recharge would be varied throughtime to reproduce the effects that various rates offlushing would have on the ground-water flow andcontaminant transport.

Protective barriers to ground-water flow areconstructed of very low permeability material andemplaced either to prevent contaminated ground waterfrom migrating away from a site or to divert incomingclean ground water from the source of contaminants.If properly designed and emplaced, barriers to flow canlast for several decades, barring any geologicaldisturbances, such as tremors, ground settling,significant changes in hydraulic gradients, etc.However, if a barrier should fail following installation,water may infiltrate the site, and contaminatedleachates may move beyond the site. Therefore, theeffects that the failure of a barrier would have oncontaminant flow and transport should be evaluatedthrough modeling. There are a number of ways thatthe failure of the barrier could be simulated. The moststraightforward method is to use transient boundariesto simulate additional flow through the barrier as wellas a reduction in the difference between water-levelelevations in front and behind the barrier. Therefore,a code selected for this simulation should have thecapability to incorporate transient boundaries.

4.2.3.5 Specialized Flow and Transport Processes

The design and evaluation of remedial alternativesfrequently involve the consideration of flow andtransport processes that were probably not explicitlymodeled during the site characterization program.These processes include: complex geochemicalreactions, matrix diffusion, heat flow, and possiblybiological reactions.

As mentioned previously, numerical models thatsatisfactorily couple ground-water flow andcontaminant transport to complex geochemicalreactions simply do not exist. The complexgeochemical models are based upon the laws ofthermodynamics, which means that they predictwhether the potential exists for a particular reaction to

occur within a closed system. Despite manyshortcomings inherent within the methods foranalyzing complex geochemical reactions, it isimportant that the controlling geochemical reactionsbe examined, possibly in laboratory benchscale or fieldstudies. This is particularly important whenphysical/chemical stabilization processes are underconsideration whereby physical or chemical agents areadded to, and mixed with, a waste (typically sludge inpits, ponds, and lagoons), with the objective ofimproving the handling or leaching characteristics ofthe waste destined for land disposal.

A detailed understanding of the geochemistry can alsobe very useful in estimating leach rates for uraniummill tailings which otherwise would be associated withpossibly unacceptably high uncertainties.

Matrix diffusion is the process by which concentrationgradients cause contaminants either to move into or bedrawn out of low-permeability rocks where diffusiongoverns contaminant transport rather than advectionand dispersion. Pump and treat systems will tend todraw water from the more permeable units, which mayleave large volumes of contaminants stored in the claysand other fine-grained materials, which will eventuallydiffuse out. Many computer codes do not adequatelysimulate this very slow process. If matrix diffusion isnot accounted for, the contaminant movement will bebased solely upon ground-water velocities rather thanthe diffusion term. Ground-water velocity willgenerally move the contaminant much more rapidlythan diffusion, and clean-up times may be dramaticallyunderestimated.

In-situ vitrification (ISV) of soils is a thermaltreatment and destruction process that achievesstabilization by converting contaminated soil andwastes into chemically inert, stable glass andcrystalline products, resembling obsidian. Predictingthe effectiveness of ISV and its implementability wouldrequire a number of specialized processes to bemodeled. One such process would be vapor transportof radionuclides, such as tritium, which would be animportant health consideration if the media were to beheated.

A mechanism that appears to affect the transport ofradionuclides under some conditions is microbialfixation. Radionuclides may be immobilized and/ormobilized by organisms or plants. Immobilizationmay occur if radionuclides are incorporated in the cell

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structure of microorganisms or plants that arerelatively stationary. On the other hand, radionuclidesmay be mobilized by forming biocolloids with bacteria,spores, and viruses. Modeling of microbial processesrequires a code that, at a bare minimum, allows adegradation rate to be assigned to the contaminant(s).

4.2.3.6 System Heterogeneity

The ability of a code to accommodate severe contrastsin soil and rock properties is particularly importantduring the design and evaluation of physical barriersfor protecting ground water. If the applicationinvolves extending the barrier down to a lowpermeability strata to form a seal and deter underflowleakage, it would be important that the code allow theincorporation of multiple stratigraphic layers as well assharp hydraulic conductivity contrasts. Only in thismanner could the effect on contaminant flow andtransport due to the effects of leakage through thebarrier wall and basement strata be evaluated.

4.3 SPECIFIC CONSIDERATIONS

The purpose of this section is to guide the RemediationManager and support personnel in determining whatspecific capabilities are needed from a computer codeto address the modeling objectives. The discussionfocuses on explanations as to how specific site andcode characteristics will provide the informationnecessary to decide whether various code attributescould potentially assist in the analysis or bedetrimental to the analysis, or whether they are simplyunnecessary.

After the conceptual model is formulated and themodeling objectives are clearly defined in terms of theavailable data, the investigator should have a relativelygood idea of the level of sophistication that theanticipated modeling will require. It now becomesnecessary to select one or more computer code(s) thathave the attributes necessary to describemathematically the conceptual model at the desiredlevel of detail. This step in the code selection processrequires detailed analysis of the conceptual model todetermine the degree to which specific waste and sitecharacteristics need to be explicitly modeled.

Fundamental questions that need to be answered at thisstage in the code selection process are presented inTable 4-2. In answering these questions, theinvestigator must decide whether a particular code has

the required capabilities and the importance ofindividual aspects of the conceptual model in themodeling analysis. It is generally relativelystraightforward to ascertain whether a code has aspecific capability, and many documents are alreadyavailable which provide this kind of information. It isfar more difficult to decide whether or not a certainattribute of a model is needed to accomplish themodeling objectives. Furthermore, other factors mustbe considered in the code selection process which areindependent of the waste, site characteristics, andmodeling objectives. These factors are inherent in theindividual computer codes and include: solutionmethodology, availability of the code, hardwarerequirements, usability of the code, and the degree towhich the code has been tested and accepted.

Accordingly, this section has two goals:

1. to describe the detailed waste and sitecharacteristics and flow and transport processesthat may need to be explicitly modeled in order toachieve the modeling objectives, and

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Table 4-2. Questions Pertinent to Model Selection

Site-Related Features of Flow and Transport Codes

Source Characteristics

Does the contaminant enter the ground-water flow system at a point, or is it distributed along a line orover an area?

Does the source consist of an initial pulse of contaminant, is it constant over time, or does it vary overtime?

Is the contaminant release solubility controlled?

Soil/Rock Characteristics

Are anisotropy and heterogeneity important?

Will fractures or macropores influence the flow and transport?

Are discrete soil layers relevant to the analysis?

Aquifer System Characteristics

What type of aquifers does the model need to simulate? Confined, unconfined, or both?

Does the model need to simulate complete dewatering of a confined aquifer?

Does the model need to simulate aquitards?

Does the model need to simulate the dewatering and resaturation of an aquifer?

Do multiple aquifers need to be accounted for?

Transport and Fate Processes

Which transport and fate processes need to be considered in the analysis (e.g., retardation, chain decayreactions, matrix diffusion)?

Multiphase Fluid Conditions

Are all of the wastes miscible in water?

Is the gas phase important to the analysis?

Are density effects important?

Flow Conditions

Will flow be under fully saturated or partially saturated conditions?

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Table 4-2. (Continued)

Code-Related Features of Flow and Transport Codes

Time Dependence

Are the fluctuations in the hydrogeologic system significant, requiring transient analyses, or can they beignored and simulated as steady state?

Solution Methodology

How will the various mathematical methods used to solve the flow and transport equations affect themodel results and therefore code selection?

What will be the hardware requirements?

Code Geometry

In how many dimensions is the code capable of modeling the representative flow and transport processes?

Source Code Availability

Is the code publicly available?

If not, how much does it cost and is the source code available?

Code Testing

Has the code been verified?

Has the code been field-validated?

Has the code been independently peer reviewed?

Code Input and Output

What input data parameters are required?

Does the code have a pre- or post-processor?

Will the code provide breakthrough curves?

How will the output depict plume extent?

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2. to describe the characteristics inherent in acomputer code that could influence the practicalusefulness of the code, including the usability ofthe code and the extent to which the code has beentested.

Once these two objectives are accomplished, the codeselection process becomes simply identifying the codesthat meet the modeling needs.

In light of these goals, this section is divided into twoparts, one addressing the site-related characteristicsand the other addressing code-related characteristicsthat must be considered when selecting a code. Table4-3 presents a matrix relating various sitecharacteristics and an example of codes that explicitlymodel those characteristics. Table 4-4 presents amatrix relating various code characteristics and anexample of codes that have those characteristics. Thefollowing sections discuss the conditions andcircumstances under which the various characteristicsare important.

Referring to Tables 4-3 and 4-4, it is not the intentionof this section to construct comprehensive referencetables listing all available codes, but rather to providetables that clearly illustrate the criteria generallyconsidered in the identification of candidate computercodes. Each of the criteria is discussed individually incontext to its relevance in answering the questionsidentified in Table 4-2.

Once one or more computer code(s) are identified aspotential candidates, the codes should undergo furtherreview as a cross-check to ensure that the code has thecapabilities that are specified in the literature.Furthermore, a more detailed review can providevaluable insight into the nuances of the code which aregenerally not available from cursory code reviews.

4.3.1 Site-Related Characteristics

The general components of the conceptual model thatneed to be considered when selecting an appropriatecomputer code are the following:

! Source Characteristics! Aquifer and Soil/Rock Characteristics! Transport and Fate Processes! Fluid Conditions! Flow Conditions

Each of these topics is presented as a major heading inTable 4-3. These broad subjects are further dividedinto their individual components both in the table andin the discussion that follows.

The objective of the subsequent presentation is not onlyto discuss the relevance that each of the site- relatedcharacteristics may have to the code selection process,but also to provide criteria to determine whether aparticular attribute of a code will be important in theanalysis.

4.3.1.1 Source Characteristics

The accurate portrayal of the contaminant source termis one of the most difficult tasks in the modelingprocess. All too often there is a general lack of datathat characterize the nature and extent of thecontamination as well as the release history. Computercodes can accommodate the spatial distribution of thecontaminant source in several ways. The mostcommon are the following:

! Point source! Line source! Areal source

Each of these source types can have an associatedrelease mechanism in which either the mass flux orconcentration is specified. The two general types ofsource-term boundary conditions include thefollowing:

! Concentration is prescribed! Contaminant mass flux is prescribed

Source Delineation

The determination of how the spatial distribution ofthe source term should be modeled (i.e., point, line, orarea) depends on a number of factors, the mostimportant of which is the scale at which the site will beinvestigated and modeled. If the region of interest isvery large, when compared with the contaminantsource area, even sizable lagoons or landfills could beconsidered point sources.

Typically, a point source is characterized bycontaminants entering the ground water over a verysmall area relative to the volume of the aquifer (e.g.,injection well). Line sources are generally used

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Table 4-3. Site-Related Features of Ground-Water Flow and Transport Codes

Section 4.3.1.1 Source CharacteristicsPoint SourceLine SourceAreally Distributed Source Multiple SourcesSpecified ConcentrationSpecified Source RateTime-Dependent Release

Section 4.3.1.2 Aquifer and Soil/Rock CharacteristicsConfined AquifersConfining Unit(s)Water-Table AquifersConvertible AquifersMultiple AquifersHomogeneousHeterogeneousIsotropicAnisotropicFracturesMacroporesLayered Soils

Section 4.3.1.3 Fate and Transport ProcessesDispersionAdvectionMatrix DiffusionDensity-Dependent Flow and TransportRetardationNon-linear SorptionChemical Reactions/SpeciationSingle Species First Order DecayMulti-Species Transport with Chained Decay Reactions

Section 4.3.1.4 Multiphase Fluid ConditionsTwo-Phase Water/NAPLTwo-Phase Water/AirThree-Phase Water/NAPL/Air

Section 4.3.1.5 Flow ConditionsFully SaturatedConvertible AquifersVariably Saturated/Non-HystereticVariably Saturated/Hysteretic

Section 4.3.1.6 Time DependenceSteady-StateTransient

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Table 4-4. Code-Related Features of Ground-Water Flow and Transport Codes

Section 4.3.2.1 Geometry1-D Vertical/Horizontal2-D Cross Sectional2-D ArealQuasi 3-D (Layered)Fully 3-D

Section 4.3.2.2 Source Code AvailabilityProprietary

Section 4.3.2.3 Code Testing and ProcessingVerifiedField-ValidatedPC-Version 386-SR486Pre and Post Processors

Section 4.3.2.3 Model OutputContaminant Mass/Rate of Release to Ground WaterContaminant Plume ExtentContaminant Concentration as a Function of DistanceAs a Function of Depth from SurfaceContinuously Distributed in SpaceAverage at Selected Points or CellsProfiles at Selected Points Over Time

Appendix C Solution MethodologyAnalytical

Approximate AnalyticalExact AnalyticalSemi-Analytical

NumericalSpatial Discretization

Finite DifferenceIntegrated Finite-DifferenceFinite ElementMethod of Characteristics

Temporal DiscretizationExplicitImplicitMixed Implicit-Explicit

Matrix SolversADIPDirect SolutionIterative ADIPSOR/LSOR/SSORSIP

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when the contaminants are entering the aquifer overareas where the length of the source greatly exceeds itswidth, such as leaking pipes or unlined trenches.Areal sources are often associated with agriculturalapplications of fertilizers and pesticides. Uranium milltailings would also frequently be treated as an arealsource for modeling purposes.

In some instances, it may be desirable to modelmultiple contaminant source areas. This would beparticularly important if cumulative health effects areto be determined or if the extent and nature (e.g.,commingling of various contaminant plumes) ofcontamination will have a significant impact on theremedial design. It is possible, however, to performmultiple-source modeling with codes that do notinherently allow the incorporation of multiple sources.The most common approach to accomplishing thisobjective is to perform a series of simulations in whicheach model run assumes only one source. The outputfrom each of the successive model runs is subsequentlycumulated into a representative multiple-source sitemodel.

The number of dimensions (i.e., one, two, or three)that will be explicitly modeled will tend to imposelimitations on how a contaminant source can bemodeled.

A point source can be simulated with either a one-,two-, or three-dimensional model, whereas a line orareal source must be modeled with either a two- orthree-dimensional model. One-dimensional codes areconstrained to simulating contaminant sources aspoints. The following four factors will determinewhether the source should be modeled as a point, line,or area source:

! Modeling objectives

! History of waste disposal activities

! Distribution of contaminants

! Fate and transport processes

The modeling objectives are probably the single mostimportant factor in determining the way in which thesource term should be modeled. One-dimensionalsimulations of point sources will yield generallyconservative approximations of contaminantconcentrations because of limited dispersion.

Therefore, if the modeling objective is to determinemaximum peak concentrations arriving atdowngradient receptors, area and line sources could besimulated as point sources comprised of average orpeak concentrations. However, if more realistic valuesof concentrations and plume geometry are required, itwill generally be necessary to simulate the source termcharacteristics more accurately.

Some knowledge of the history of the waste disposalactivities can often provide valuable insight into theprobable nature of the contaminant source term. Ingeneral, the longer the site has been active, the morelikely it is that the wastes have been dispersed over alarger area and discarded in many different forms.The presence of product and waste lines immediatelysuggests that line sources are present. Absorption bedsand storage tanks indicate potential point sources,whereas mill tailings, large lagoons, and air emissionsthat carried and subsequently deposited contaminantsin the site vicinity would generally represent areasources.

The distribution of measured contaminants in the soiland ground water will also provide clues as to thenature of their source. Contaminants that are wide-spread and of similar concentrations suggest an areasource, while narrowly defined areas of contamina-tionindicate a more localized or point source.

Dominating fate and transport processes should also beconsidered when assigning source term characteristics.If flow and transport properties are strongly confinedto one or two dimensions, as in the unsaturated zone(i.e., liquids flow down vertically due to gravity in theunsaturated zone), it may be possible to use a moresimplified approximation of the source geometry (e.g.,point).

Release Mechanism

Computer codes can simulate the introduction ofcontaminants to the ground water as an instantaneouspulse or as a continuous release over time. Acontinuous release may either be constant or vary withtime. The two most common means of simulatingcontinuous or pulse releases are by either specifyingrelease concentrations or by specifying thecontaminant mass entering the system. In general,both approaches have drawbacks and limitations andrequire considerable thought and possibly a number ofindependent calculations prior to selecting and

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implementing the most appropriate method for themodeling exercise. Furthermore, most ground-waterflow and transport codes do not explicitly account forthe physical degradation of waste containers and,therefore, anticipated release rates must be estimatedthrough other means (e.g., waste package codes) andinput as boundary conditions into the flow andtransport model.

It is generally preferable to pose the source-termrelease in terms of contaminant mass flux, rather thanspecified concentrations. This is true even if theconcentration at the source is known. The primaryproblem with specifying the concentration of thecontaminants entering the system is that care must betaken to ensure that the total mass that enters thesystem does not exceed that which would actually beavailable from the source. Furthermore, specifiedconcentrations tend to over-predict contaminantconcentrations near the source because the effects ofdilution and dispersion are not properly accounted for.However, it is not uncommon for specifiedconcentrations to be used if the release of thecontaminant is controlled by its solubility limit; that is,if the contaminant is relatively insoluble. Therationale for this approach is that specifiedconcentrations would tend to describe leaching ratesthat are solubility controlled.

Not all computer codes allow the concentration ormass of a continuous release to change with time. Thisquality is particularly important if it is suspected thatconditions in the past or future are not approximatedby those of the present. A specific example would bemodeling the performance of an engineered barrierwhose performance is expected to change with time.

Radioactive source terms present special considera-tions in that the mass fraction of the parent isotopeswill diminish with time due to radioactive decay.However, if the radionuclide mass release is solubilitycontrolled, the concentration of the leachate mayremain constant despite the decay of the source term.The release concentrations may remain constant untilthe source term has decayed to concentrations wheresolubility limits no longer dictate the amount ofradionuclides that may go into the solution.

4.3.1.2 Aquifer and Soil/Rock Characteristics

Computer codes have been developed that can simulatesingle or multiple aquifers which may behave asconfined, unconfined, or change from one condition toanother. Intrinsic characteristics of the aquifers andaquitards, which control flow and transport, are alsosimulated to various degrees by computer codes. Themost common code selection criteria with regard toaquifers and their characteristics include the following:

! Confined aquifers

! Water-table (unconfined) aquifers

! Multiple aquifers/aquitards

! Heterogeneous

! Anisotropic

! Fractures/macropores

! Layered soils/rocks

Water-Table and Confined Aquifers

The ground water flowing within a water-table aquiferis in immediate contact with the atmosphere and isdirectly recharged through the overlying unsaturatedzone. This water-table surface is equal to atmosphericpressure and is free to rise and fall within the aquiferin response to varying amounts of recharge (e.g., rain).The water-table aquifer generally follows land-surfacetopography and is frequently revealed in the form ofsurface-water bodies such as lakes and rivers (Figure4-6).

A confined aquifer is one in which the ground water isisolated from the atmosphere by some geologic feature(e.g., confining unit). As a result, the ground water isunder pressure greater than that of atmospheric, and,if a well penetrates a confined aquifer, the water in thewell will rise above the top of the aquifer.

In most circumstances, the water first encounteredbeneath the site will be under water-table conditions.However, this does not always mean that water levelsmeasured in wells are indicative of the water-table

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Figure 4-6. Water Table and Confined Aquifers

surface. This discrepancy may occur when a well isscreened below the water table in an unconfinedaquifer with large vertical gradients (or a well with avery long screen in an unconfined aquifer with largevertical gradients). In many instances, particularlywith domestic wells, water in the shallow water-tableaquifer has been cased off and a deeper unit, that maybe under confined conditions, is supplying water to thewell. The importance of this is that the water in a wellthat taps a confined aquifer can rise significantlyhigher in the well than the true water-table surface. Ifthis is the case, the thickness of the unsaturated zonemay be significantly underestimated.

The mathematical description for ground-water flow ina water-table aquifer is more complex than that forflow in a confined aquifer. This is largely because thesaturated thickness of a water-table aquifer will varywith time and, therefore, the transmissivity (which isthe quantity of volume of water flowing through theaquifer, mathematically calculated as the product ofthe hydraulic conductivity and the vertical thickness ofthe aquifer) is also time dependent. Confined aquifersalways remain saturated and, therefore, themathematics do not have to account for a varyingtransmissivity.

Computer codes that simulate confined aquifers canalso be used to simulate water-table conditions if thesaturated thickness of the aquifer is not expected tovary by more than ten percent over the time of interest.This assumption would generally be appropriate if the

modeling objectives can be met by assuming steady-state conditions. If significant changes (greater thanten percent) in the water-table elevation are expectedover the time of interest, not only would a steady-statemodeling approach be of uncertain value, but thevalidity of applying a computer code designed tosimulate confined flow to problems that involveunconfined flow would be questionable.

The importance of whether the system is under steadystate or transient conditions dictates that the length ofthe time of interest needs to be carefully considered incontext of the code applicability. In general, theshorter the time of interest the more likely it is thatfluctuations of the water table will exceed ten percentof the saturated thickness. As the length of the time ofinterest increases, long-term averages tend to dampenout the extremes within the water-table fluctuations.

Examples of conditions where a code developed forconfined conditions would probably not be applicableto simulate ground-water flow in water-table aquifersinclude:

! Highly variable recharge rates

! Ephemeral effects of surface-water bodies

! Remediation activities

! Physical properties of the contaminants

Shallow ground-water flow systems that are rechargedprimarily from percolating precipitation tend to bestrongly influenced by seasonal fluctuations of thelocal climate. Summer droughts and spring snowmelts can cause dramatic shifts in the water-tableelevation. For reliable seasonal predictions, computercodes would have to be able to simulate changes in theaquifer transmissivity through time. Such is not thecase if the use of long-term recharge averages could bejustified, as when estimating average annual radiationdoses associated with the drinking water pathway.

In many cases, water-table aquifers are closely tied tosurface-water bodies which are ephemeral in nature.These surface-water bodies may include intermittentand ephemeral streams, waste lagoons, and tidalmarshes. It is important that the transient effect ofthese features on the water table be considered whenselecting an appropriate computer code.

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Remediation activities may also create largeoscillations of the water table. Activities that includeactive remediation, such as pump and treat, artificialrecharge, and ground-water injection will generallyhave the greatest impact on the ground-water table.Relatively passive remediation activities, such asceasing the disposal of liquids into lagoons or streams,may also affect the shallow aquifer by causing thewater table to find a new equilibrium which may ormay not be significantly different from the initialposition.

A special consideration for modeling water-tableaquifers, particularly when the aquifer is beingsignificantly dewatered, as in pump and treatoperations, is that not all computer codes with thecapability to simulate water-table aquifers have thecapacity to resaturate the aquifer if it becomescompletely dewatered. This could pose a seriouslimitation if one of the objectives is to evaluate theeffectiveness of a pump and treat system that isoperated intermittently.

In determining whether a computer code that does notsimulate water-table conditions is appropriate, someconsideration needs to be given to the nature of thecontaminants. For example, the flow of LNAPL(contaminants less dense than water, such as oil) iscomplicated by the rise and fall of the water tablewithin the seasons. As the water table falls, the layerof mobile contaminant also falls. When the water tablerises, the contaminant also rises. However, residualcontamination is left behind in the saturated zone. Ifthe water table rises faster than the contaminant canrise, "pockets" of free contaminants might become leftbelow the water table. The flow of water andcontaminants is controlled by Darcy's law and dependsupon the effects of density, viscosity, and relativepermeability. Depending upon these factors, either thecontaminant or the water could have a greater velocityas the water table rises and falls. Therefore, in orderto predict remediation times accurately, the volume ofthe contaminant remaining in the unsaturated zoneneeds to be estimated. If the code does not allow thewater table to rise freely within the aquifer, theinteraction between the contaminant and the watertable cannot be simulated.

Relatively few computer codes have been developedthat will simulate conditions within an aquifer that arechanging from confined conditions to water-tableconditions. This capability is particularly useful for

simulating a ground-water system where a confinedaquifer will be heavily pumped and potentiallydewatered.

Multiple Aquifers/Aquitards

Computer codes have been developed that can simulateeither single or multiple hydrogeologic layers (Figure4-6). Generally, a single-layer code is used if the bulkof the contamination is confined to that layer or if thedifference of the flow and transport parametersbetween the various layers is not significant enough towarrant the incorporation of various layers.

In deciding whether there is a significant difference inthe flow and transport properties between variouslayers, the investigator should keep in mind that theparameter values that could vary from layer to layerinclude: hydraulic conductivity, effective porosity,distribution coefficients, and bulk densities. In mostinstances, effective porosities, distribution coefficients,and bulk densities are estimated from the literature andcould have a large associated error. Hydraulicconductivities, which are typically measured in thefield, also may be off by an order of magnitude.Therefore, it generally does not make much sense tomodel discrete layers if estimated parameter values,separating different layers, fall within probable errorranges. Furthermore, unless the discretehydrogeologic units are continuous over the majorityof the flow path, it is often possible to model thesystem as one layer using average flow and transportproperties.

The greater the depth to which the system is modeled,the more likely it will be that aquifers of varyingcharacteristics will be encountered. Ideally, the depthto which the system should be modeled is the depth atwhich ground-water gradients become consistentlyvertically upward. This depth will define the basementflow of the shallow system, and most contaminationwould be confined to shallower depths unlesscontaminants are being driven downward against theambient ground-water flow by density gradients.

If very little information is available on the distributionof vertical gradients, a general rule that is often usefulin estimating the relative base of the flow system isthat discharge areas (e.g., perennial streams, lakes, andswamps) are associated with upward gradients, whilerecharge areas (e.g., mountains and uplands) aretypified by downward gradients. Thus, it is more

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likely that the vertical extent of contamination isgreater when the contaminant source is located in arecharge area than in a discharge area.

Layered Soils/Rocks in the Vadose Zone

Rarely would soils and rocks within the vadose zonenot exhibit some form of natural layering. The firstconsideration as to how this natural layering should betreated in the modeling analysis is related to whetherthe various soil layers have significantly different flowand transport properties. If these properties do notvary from layer to layer, then there would be little needfor the code to have multiple-layer capability. On theother hand, if the layers have distinctive properties thatwould affect flow and transport, a decision needs to bemade how best to achieve the modeling objectives; i.e.,should each layer be discretely treated or should all ofthe layers be combined into a single layer?

In most instances, it would be appropriate to combinethe layers into a single layer for all phases of theremedial program with the following notableexceptions:

! Vapor-phase transport

! Model calibration

! Conceptual model development

Vapor-phase transport within the vadose zone, whichcan occur with tritiated water vapor, will be largelycontrolled by the various flow properties of the soilswithin the unsaturated zone. Vapors will tend tocongregate beneath layers with low air permeabilitiesand freely move through more permeable layers. Thedirection of movement of the vapor is often governedby the dip and orientation of the soil beds above thewater table and are independent of the ground-watergradients.

Percolating rainwater may induce a phase-transformation of radionuclide vapor back to a liquidphase, thus allowing transport to the saturated zone.If this process occurs in beds through whichradionuclide vapors have migrated, both away from thesource and up the ground-water gradient, it is possiblethat significant amounts of radioactivity may bedetected in the ground-water upgradient of the sourcearea.

This phenomenon is particularly important to considerwhen determining how far upgradient backgroundmonitoring wells should be placed to ensure that theambient ground water has not been contaminated viavapor transport from the contaminant source. In manysystems, with relatively thin vadose zones (< 10 m), itmay be more practical to approach this problemempirically and simply measure radionuclide vaporconcentrations in the unsaturated zone. However, theexpense of investigating relatively thick vadose zones(> 50 m) is often significant, and modeling could bevery useful in estimating the likely distance that vapormay have moved.

An evaluation of expected vapor movement andconcentrations could also be of considerable valuedepending upon remedial measure alternatives. Forinstance, it may be desirable to predict the potentialmovement of vapor out from under a remedial cap orthe movement of water vapor under a capped area.Without the ability of the code to accommodatediscrete layers, the effect that a low permeability capwould have on vapor transport could not be simulated.Under other circumstances, maintenance- relatedissues could be addressed, such as the build- up ofhydrogen gas within landfills that contain pyrophoricuranium (i.e., spontaneously combustible). In landfillswhere pyrophoric forms of uranium metal were placedin drums and submerged in petroleum-based orsynthetic oils to prevent rapid oxidation, there is thepotential for the uranium and petroleum to react toform hydrogen gas which, at high enoughconcentrations, is an explosion hazard.

Models are generally calibrated against measured fieldvalues. However, unless the field characteri-zationprogram was designed to characterize the unsaturatedzone, data are frequently insufficient to calibrate avadose zone model. Soil sampling would have had toprovide vertical, and in many instances horizontal,profiles of radionuclide concentrations, soilpermeability, and moisture content data. Therefore, itis important to decide prior to site characterizationwhether a fully calibrated vadose zone transport modelwill be required to meet the modeling objectives. Afterthe characterization is completed, it can be determined,from the data, whether a code is needed that will allowthe simulation of discrete layers.

Calibration of flow and transport through theunsaturated zone generally becomes important in areaswith relatively thick unsaturated zones (> 100 m). In

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Figure 4-7. Perched Water

these areas, deep boreholes are both very expensive toinstall and difficult to instrument. Under thesecircumstances, a calibrated model may be useful inperforming mass-balance calculations to determine thedepth that contaminants could have potentiallymigrated, and to provide an estimate of contaminantvolumes requiring remediation.

An accurate portrayal of the site-conceptual model isessential for all phases of the remedial program. Acomputer code with the capability to allow layeringmay facilitate the evaluation of various aspects of theconceptual model. For example, infiltration throughthe vadose zone may move laterally over significantdistances, particularly when there are soil layers of lowpermeability which impede vertical migration andallow saturated flow to occur in perched-water zones(Figure 4-7). This transport process is particularlyimportant in areas where a relatively thick unsaturatedzone is bisected by deep-cut streams, and the perchedwater movement in the unsaturated zone ispredominantly horizontal rather than verticalinfiltration to the water table. Under thesecircumstances, the radionuclides may short-circuit theground-water pathway and discharge to seeps andsprings along the river wall. Therefore, it could beimportant to evaluate the potential for horizontalmovement in the unsaturated zone to ensure that allexposure pathways are properly accounted for in theconceptual model.

Anisotropic/Isotropic

In a porous medium made of spheres of the samediameter packed uniformly, the geometry of the voidsis the same in all directions. Thus, the intrinsicpermeability of the unit is the same in all directions,and the unit is said to be isotropic. On the other hand,if the geometry of the voids is not uniform, and thephysical properties of the medium are

dependent on direction, the medium is said to beanisotropic.

Anisotropy can play a major role in the movement ofground water and contaminants. In most sedimentaryenvironments, clays and silts are deposited ashorizontal layers. This preferential orientation of themineral particles allows the horizontal hydraulicconductivities to greatly exceed those in the verticaldirection. As a general rule, for sedimentaryenvironments, it is assumed that horizontal hydraulicconductivities are 10 to 100 times greater than those inthe vertical direction.

If the modeling analysis does not account foranisotropy, the contaminants will be predicted to bemore dispersed in the vertical direction than wouldprobably be occurring in the real world. One of theprimary drawbacks to this taking place is that thepredicted concentrations would be significantlyreduced due to this artificial vertical dispersion andresulting dilution.

Macropores/Fractures

Modeling flow through the unsaturated zone is basedon the assumption that the soil is a continuousunsaturated solid matrix that holds water within thepores. Actual soil, however, has a number of cracks,root holes, animal burrows, etc., where the physicalproperties differ enormously from the surrounding soilmatrix (Figure 4-8). Under appropriate conditions,these flow channels have the capacity to carryimmense amounts of water at velocities that greatlyexceed those in the surrounding matrix.

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Figure 4-8. Macropores and Fractures

At present, there is no complete theory describingwater flow through these structural voids ormacropores. There is uncertainty regarding thesignificance of subsurface voids in water flow, since, iflarge, they should fill only when the surrounding soilmatrix is close to saturation. Nonetheless, studies haveshown that contaminants can migrate to substantialdepths with only a small amount of water input.

Many water flow processes of interest, such as ground-water recharge, are concerned only with areallyaveraged water input. Therefore, preferential flow ofwater through structural voids does not necessarilyinvalidate the code formulations that assume uniformflow and do not directly account formacropores. However, preferential flow is of criticalimportance in solute transport because it enhancescontaminant mobility and can significantly increasepollution hazards.

Since codes do not exist that directly simulate flowthrough macropores, it is important to select a codewith features that will allow an indirect simulation ofthe effects of macropores on flow and transport. Anumber of factors should be considered whendetermining whether macropores are important in themodeling analysis, including:

! Presence, geometry, and spatial distributionof macropores

! Location of the waste relative tomacropores

! Rainfall duration, intensity, and runoff

Determining the presence of macropores may soundrelatively straightforward; however, in many instances,the formation of macropores is an ephemeral processwhere the desiccation and shrinkage of clays will occuronly during the summer months or after long periodsof drought. Therefore, if it is suspected that conditionsare suitable for the formation of macropores, a specialeffort should be made to tour the site during theperiods when macropores are most likely to be present.After establishing the existence of macropores, thenext step would be to gain some understanding of theirgeometry and spatial distribution. If macropores arerelatively shallow (< 1 m), it is highly unlikely thatthey would have a significant effect on the flow andtransport even if they are closely spaced. However, ifthe macropores are relatively deep compared to thethickness of the unsaturated zone, on the order of tenpercent, their effect on flow and transport should beconsidered in the modeling exercise.

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The location of the wastes relative to any macroporesplays a significant role in determining theirimportance. Obviously, if the contaminated area isdissected by numerous relatively deep macroporesextending well below the wastes, it would raiseconcerns that flow and radionuclide transport may befacilitated due to their presence. On the other hand, ifthe wastes are buried below the maximum depth of themacropores, or if the site has been capped or coveredwith a material that is not prone to macroporedevelopment, their presence would play a lesser role.The direct effect that the macropores will have on themobility of the wastes is closely tied to whether themacropores are located beneath the waste. If so, theymay be providing an avenue for radionuclide transportor, if they terminate above the waste, they may beindirectly enhancing transport by allowing greateramounts of recharge to come in contact with thecontaminants.

The rainfall duration, intensity, and runoff also play amajor role in evaluating the relative importance ofmacropores on radionuclide transport. If an area isprone to high-intensity, short-duration storms(convective precipitation) with low runoff, the rainfallrates may exceed matrix infiltration rates, and it is notnecessary for the soil to become saturated before watercan flow within the macropores. In this manner, waterand/or contaminants can move well in advance of thewetting front and be carried beyond the maximumsaturation extent of the soil matrix. In contrast, in anarea which is typically subjected to long-durationrainfall events with low intensities, it is more likelythat flow will not occur in the macropores but will beconfined to the soil matrix. This is because the soilmatrix infiltration rate will exceed the rainfall ratescharacteristic of this cyclonic precipitation.

As mentioned previously, there are no codes thatdirectly simulate flow and transport throughmacropores in the unsaturated zone. Therefore, if it isdetermined that macropores are present and maypotentially have an important effect on flow andtransport, several approaches could be used to accountindirectly for the flow and transport within themacropores. These approaches are based upon thegeometry of the macropores, location of the wastes,and rainfall characteristics. Each of the approacheswill require a code with the proper attributes, asoutlined below.

If the maximum depth of the macropores is above thetop of the wastes and rainfall occurs at such anintensity that flow will take place within themacropores, it will be necessary to evaluate the effectthat additional water reaching the wastes will have oncontaminant transport. To account for thisphenomenon, the code will need the ability to regulaterecharge as well as infiltration rates. More precisely,the code must be very stable numerically and able toaccommodate areally variable and transient recharge,anisotropy, and heterogeneity. In essence, higherrecharge rates are applied over short time intervals toareas of the site with known macropores. However, inorder to enable the soil to absorb the additional waterand to simulate greater infiltration rates, the soil inthis area must also be assigned larger hydraulicconductivities with high vertical to horizontal ratios.To handle these sharp soil material contrasts, the codemust be well formulated and not be plagued withconvergence problems (see Appendix C).

In instances where macropores extend beneath thebottom of the buried wastes, several alternatives existfor modeling their potential effect on flow andtransport. The most straightforward approach is tosimulate the portion of the macropores that extendbelow the wastes by removing an equivalent thicknessfrom the modeled unsaturated zone. This essentiallyassumes instantaneous transport through themacropores and would result in very conservativevalues. This approach has a number of advantages, thegreatest of which is that the computer code does notneed any additional features than it would haveotherwise needed without the macropores. However,if this approach is thought to be overly conservative,which would probably be the case if more than half thethickness of the unsaturated zone would need to beremoved, an alternative could be employed whichinvolves methods that are used to simulate deepfractured networks in the vadose zone.

Determining the importance of fractures within theunsaturated zone generally presents more of a problemthan making the same determination for macroporesbecause: (1) fractures are usually not visible from thesurface and are difficult to characterize in thesubsurface; (2) if fractures are present, they will oftenextend through the entire unsaturated zone and intothe saturated zone; and (3) fractures may serve aseither conduits or barriers to flow. All of these issuesmust be addressed in the site characterization programto determine whether the fractures need to be

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considered in the modeling. In general, fractures thatcan be traced through the waste area are important andshould be considered, at least conceptually, in theanalysis.

Fracture modeling of the unsaturated zone cangenerally use computer codes with attributes verysimilar to those used for modeling macropores with afew notable exceptions. For the purposes of thisdiscussion, it is assumed that the fractures are found toextend through the unsaturated zone into the saturatedzone, and that an assumption of instantaneous flowthrough the entire vadose zone thickness would not beacceptable for the analysis. Unlike macropores, whichwill probably not extend to depths greater than 5meters, fractures may reach depths on the order ofhundreds of meters. This factor has a number ofimplications for both the flow of water and transport ofradionuclides.

Rainfall percolating through a fracture will slowlydiffuse into the soil matrix. Thus, eventually the watermoving in the fracture will become so depleted thatfracture flow will no longer develop unless othersources of water are intercepted (e.g., perched). Thedepth at which fracture flow would cease depends ona number of factors including fracture properties,rainfall characteristics, and soil matrix qualities, all ofwhich are closely interrelated and are difficult toquantify. Conceptually, this process of diffusion intothe matrix at depth suggests a direct correlationbetween the importance of the fractures and the depthof the unsaturated zone. That is, at some depth,fracture flow will no longer be important.

There will always be a large degree of subjectivityassociated with deciding the importance of fractures'effects on flow and transport within the vadose zone.However, it would probably be safe to assume that inmost unsaturated systems, fracture flow below 200meters is insignificant unless a continuous source ofwater is available (e.g., overlying adsorption beds).

The features of computer codes that would benecessary to describe fracture flow would be similar tothose required to simulate macropores, except thatnow, because the pulse-like nature of the rechargewould be dampened at greater depths, it wouldprobably not be necessary for the code to accommodatetransient recharge, particularly if the depths of interestare greater than 50 meters. However, the codes muststill be very stable numerically and able to incorporate

anisotropy and heterogeneity, which are discussed ingreater detail in the following sections.

Almost all of the discussion to this point has focusedupon modeling flow and transport in porous media. Itis important to realize, however, that a number ofradioactively contaminated sites overlie areas wherefractures and solution channels are probably dominantmechanisms for flow and transport. The uncertaintyassociated with fracture zone modeling is generallyhigh, and if fracture modeling is to be successful, aconcentrated effort needs to go into the design of thefield investigation. Therefore, the benefits associatedwith modeling fractured flow and transport processeshave to be carefully weighed against a number ofdeterrents which include:

! An expanded field program is needed;! Significant uncertainties are associated with

fracture characterization methods;! High degree of expertise is required of the

modeler;! Codes available to simulate fracture flow are

difficult to use.

A number of analytical models are available that dosimulate ground-water flow and radionuclide transportthrough fractures. However, it is unlikely thatanalytical models could adequately describe flow andtransport processes in most fractured systems becausethese processes are much more complex than those inunfractured granular porous media. This is due to theextreme heterogeneities, as well as anisotropies, in thefractured systems. When a radionuclide is introducedinto a fractured porous medium, it migrates throughthe fracture openings by means of advection as well ashydrodynamic dispersion. The radionuclide alsodiffuses slowly into the porous matrix. Moleculardiffusion dominates flow and transport within theporous matrix because the fluid velocity in the porousmatrix is usually very small. Upon introduction of theradionuclide into a fractured aquifer, the radionuclidemoves rapidly within the fracture network. As timeprogresses, the zone of contamination will diffusefarther into the porous matrix. Since the porousmatrix has a very large capacity to store thecontaminant, it plays a significant role in retarding theadvance of the concentration front in the fractures. Ifthe source of contamination is discontinued and theaquifer is flushed by fresh water, the contaminant massin the fractures will be removed relatively quickly,whereas the contamin-ant in the porous matrix will be

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removed very slowly via diffusion back to the fractureopenings.

In general, data limitations and narrow objectiveswould preclude the modeling of fractured systems untilat least the Site Characterization phase. If it isdetermined that numerical modeling of a fracturedsystem will be performed during the SiteCharacterization, it becomes necessary to evaluate thedata needed to support fracture flow and transportnumerical modeling. In order to adequatelyunderstand the potential data requirements for fractureflow and transport modeling, the following textprovides a very basic understanding of modelingfractured systems.

At present there are two general numerical methods forsolving flow and transport in a fractured medium:modeling of the flow, accounting for the fractures oneby one, or modeling with an equivalent continuousmedium approach.

Flow and transport modeling in a fracture system by acontinuous porous medium approach is performed byassigning each family of fractures a directionalconductivity, thus constituting a hydraulic conductivitytensor. As the frequency and direction of theseconductivities are defined, the principal axes ofanisotropy of the tensor and the conductivities in thesedirections can be calculated. It is thus assumed thatthe fracture spacings are frequent enough that, whenviewed from the perspective of the entire physicalsystem, flow and transport processes would beconsistent with those associated with porous media.Therefore, computer codes developed for porous mediamay sometimes be used to simulate multiple fracturefamilies. This approach relies heavily upon thepresence of multiple fractures. However, if there are arelatively limited number of fractures, as is often thecase with solution channel(s) or faults, an alternativeapproach is necessary. This alternative approachconsists of three general methods, which are termeddual-porosity, dual-permeability, and discrete fracture.All of these methods need a computer code that isspecifically developed for modeling fracture flow. Thecode will have separate equations which are developedfor flow and transport in the rock matrix and arecoupled to equations describing flow and transport inthe fractures. This allows fractures to be assigned flowand transport properties which are discrete from thematrix properties. The dual-porosity method assumesthat fractures are relatively uniformly spaced and does

not allow flow to occur among matrix blocks.Contaminants leave and enter the fractures onlythrough diffusion. The dual-permeability approachalso assumes that fracture networks are well developedalthough this method does allow advective anddispersive flow through the matrix blocks and isconducive to simulating highly fractured systems inwhich both the matrix and the fractures are relativelypermeable. The discrete fracture approach is similarto the dual-permeability method although the discretefracture method allows single fractures to be modeledseparately as line elements.

In most instances, it is very difficult to obtain the fielddata necessary to perform detailed fracture flow andtransport modeling. Such modeling could require asubstantial dedication of resources, and anycommitment should be carefully weighed against thatwhich may be gained from the modeling.Circumstances that could lead to a decision to performfracture-flow modeling may include:

! Future risks cannot be assessed withoutexplicitly accounting for flow and transport ina fractured system;

! Sensitivity or bounding analyses cannot bedesigned to meet objectives; and

! Empirical data are either not available or cannot be effectively used to estimate risks,capture zones, influent concentrations, etc.

Homogeneous/Heterogeneous

A homogeneous unit is one that has the sameproperties at all locations. For a sandstone, this wouldindicate that the grain-size distribution, porosity,degree of cementation, and thickness are variable onlywithin small limits. The values of the transmissivityand storativity of the unit would be about the same atall locations. A plutonic or metamorphic rock wouldhave the same amount of fracturing everywhere,including the strike and dip of the joint sets. Alimestone would have the same amount of jointing andsolution openings at all locations.

In heterogeneous formations, hydraulic propertieschange spatially. One example would be a change inthickness. A sandstone that thickens as a wedge isnonhomogeneous, even if porosity, hydraulicconductivity, and specific storage remain constant.

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Most numerical computer codes have the ability toassign varying hydraulic conductivities and storageproperties to the hydrostratigraphic units beingsimulated. Furthermore, computer codes have alsobeen developed that have the ability to simulateconstant or variable thicknesses.

Analytical methods are constrained to modelingaquifers that do not change significantly in thicknessor other aquifer characteristics. Numerical codes mayor may not have been developed for problemsinvolving an aquifer of variable thickness. Numericalcodes that do not allow the thickness of the aquifer tovary significantly use transmissivity as the model inputparameter which indirectly describes aquifer thickness(hydraulic conductivity multiplied by thickness).However, numerical codes that specify hydraulicconductivity and aquifer thickness as input parametersindependently calculate aquifer transmissivitythroughout the model domain and, therefore, allowaquifer thickness to vary. If advective-dispersivecontaminant transport calculations are expected to beperformed at some time in the analysis, it is importantthat hydraulic conductivities and aquifer thicknessesare known even when their product (i.e.,transmissivity) is only required as model input. Thisis because the quantity of ground-water flow throughaquifers of identical transmissivity will be the sameunder equal gradients. Therefore, an aquifer which isvery thick and has a low hydraulic conductivity canhave an identical transmissivity to that of anotheraquifer which is thin but has a high hydraulicconductivity. As far as the bulk movement ofgroundwater is concerned, the two systems will behavein a similar fashion when comparative boundaryconditions are applied. However, the transport ofradionuclides would behave very differently within thetwo systems, in that velocities would generally bemuch greater in systems with higher hydraulicconductivities.

A few finite-element computer codes use what aretermed curvilinear elements. These are specializedelements that can be spatially deformed to mimic theelevations of the upper and lower surfaces of thehydrogeologic units. Curvilinear elements areparticularly useful when aquifers and aquitards havehighly variable thicknesses.

In general, if it is expected that the aquifer thicknesswill vary by more than ten percent, it is recom-mendedthat the computer code be capable of simulating

variable thicknesses. If a code does not properlysimulate the aquifer thicknesses, the contaminantvelocities will be too large in areas where thesimulated aquifer is thinner than the true aquiferthickness and too small in those regions that have toogreat a simulated thickness.

The ability to simulate aquifer heterogeneities may alsobe very important during the remedial design phase ofthe investigation. If engineered barriers of lowpermeability are evaluated as potential remedialoptions, it would be necessary to determine theiroverall effectiveness. In this scenario, it would beimportant not only to select a computer code that cansimulate highly variable hydraulic conductivities, butalso to ensure that the sharp contrasts in hydraulicconductivities do not cause instabilities in themathematical solutions.

4.3.1.3 Transport and Fate Processes

The transport of radionuclides by flow through eithera porous matrix or a fractured system will, in eachcase, be affected by various geochemical andmechanical processes. Among the chemical processesare adsorption on mineral surfaces (both internal andexternal to the crystal structure), including the kineticsof adsorption, and processes leading to precipitation.The mechanical processes are advection, dispersiveeffects (hydrodynamic dispersion, channeling), anddiffusion. Radioactive compounds can also decay. Asa result of sorption processes, some solutes will movemore slowly than the ground water that is transportingthem; this effect is called retardation. Biologicaltransformation, radioactive decay, and precipitationwill decrease the concentration of the solute in theplume but may not necessarily slow the rate of plumemovement. The following are the primary processesthat affect the mobility and concentrations ofradionuclides being transported by ground water:

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! Advection

! Dispersion

! Matrix Diffusion

! Retardation

! Radioactive Decay

Advection

The process by which solutes are transported by thebulk movement of water is known as advection. Theamount of solute that is being transported is a functionof its concentration in the ground water and thequantity of the ground water flowing.

Computer codes that account only for advectivetransport and ignore dispersion and diffusion processesgenerally take one of two approaches. The firstapproach uses a semi-analytical method (Appendix C)to solve the ground-water flow and transport equations,whereas the second approach uses fully numericalmethods to determine the ground-water velocity fieldfrom which directions and rates of solute movementare calculated by the code.

The semi-analytical method frequently fails whenaquifers are of complicated shape and nonhomogen-eous. In these instances, it is better to use the secondoption which utilizes a fully numerical code for deter-mining the velocity distributions and particle (i.e.,solute) paths. This may be accomplished with eitherfinite-differences or finite-elements (Appendix C).

Computer codes that consider only advection are idealfor designing remedial systems (e.g., pump and treat)because the model output is in the form of solutepathlines (i.e., particle tracks) which delineate theactual paths that a contaminant would follow.Therefore, capture zones created by pumping wells arebased solely on hydraulic gradients and are not subjectto typical problems that occur when solvingcontaminant transport equations which includedispersion and diffusion in the aquifer. Theseproblems are numerical dispersion and artificialoscillation. Numerical dispersion arises becausecomputers have a limited accuracy, thus some round-off error will occur in the computations. This errorresults in the artificial spreading of contaminants due

to the amplification of the dispersivity. Hence, thecontaminant will disperse farther than it should with agiven physical, or "real" dispersivity. This extradispersion will result in lower peak concentrations andmore spreading of the contaminant. Methods exist tocontrol numerical dispersion, but the methodsthemselves may introduce artificial oscillation.Artificial oscillation is the over- or under-shooting ofthe true solution by the model and results in inaccuratesolutions and may give erroneously high and lowconcentrations.

There are other ground-water solute modeling situa-tions where the phenomenon of dispersion, togetherwith its many uncertainties, is only a minor factor indescribing the transport of radionuclides in groundwater and can be ignored. For example, the flux ofcontaminants entering a river that is recharged from acontaminated aquifer is much less sensitive todispersion than the concentration in a particular well.In the former case, the contaminated ground waterwould enter over a wide area, which would tend tosmear out the effects of dispersion. For similar reasons,the transport from nonpoint sources of con-tamination,such as mill tailings and large landfills, would diminishthe sensitivity of the modeled results to dispersion. Inthese instances, computer codes that consider onlyadvection may be appropriate.

As mentioned previously, advective codes are alsoexcellent in the remedial design stage for determiningthe number and placement of extraction or injectionwells and in evaluating the effect that low permeabilitybarriers may have on the flow system. However, thereare a number of drawbacks that must be carefullyconsidered when selecting a code that ignoresdispersion and diffusion. The most significant of theseis that matrix diffusion, which is discussed below, canbe one of the most important processes that willdetermine the length of time that a pump and treatsystem must operate before clean-up goals will be met.Without the ability to evaluate the effects of diffusion onsolute transport, it would be very difficult to estimateremediation times accurately.

A second potential problem with advection-based codesis that dispersion will tend to spread contaminants overa much wider area than would be predicted if onlyadvective processes are considered, therebyunderestimating the extent of contamination. However,because dilution is under-accounted for, unrealisticallyhigh peak concentrations are generally obtained, which

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Figure 4-9. Hydrodynamic Dispersion

may be appropriate if conservative estimates aredesired.

Advective codes also tend to yield more accuratetravel-time determinations of unretarded contaminantsbecause the solution techniques are inherently morestable, and numerical oscillations, which artificiallyadvance the contaminant front, are minimized.

Another important advantage of advective codes is thatthe output (i.e., particle tracks) is a very effectivemeans of ensuring that ground-water gradients, bothvertical and horizontal, are consistent with theconceptual model.

Hydrodynamic Dispersion

In the previous discussion, advective processes oftransport in porous media were presented. In reality,the transport of contaminants is also influenced bydispersion and molecular diffusion, which is caused bythe tendency of the solute to spread out from the path that it would be expected to follow if onlytransported by advection (Figure 4-9). This spreadingof the contamination over an ever-increasing area iscalled hydrodynamic dispersion and has twocomponents: mechanical dispersion and diffusion.Hydrodynamic dispersion causes dilution of the soluteand occurs because of spatial variations

in ground-water flow velocities and mechanical mixingduring fluid advection. Molecular diffusion, the othercomponent of hydrodynamic dispersion, is due to thethermal kinetic energy of solute particles and alsocontributes to the dispersion process. Thus, ifhydrodynamic dispersion is factored into the solutetransport processes, ground-water contamination willcover a much larger region than in the case of pureadvection, with a corresponding reduction in themaximum and average concentrations of thecontaminant.

Because hydrodynamic dispersion is the sum ofmechanical dispersion and diffusion, it is possible todivide the hydrodynamic dispersion term into the twocomponents and have two separate terms in theequation. Under most conditions of ground-water flow,diffusion is insignificant and is frequently neglected inmany of the contaminant transport codes. However,this artificial exclusion of the diffusion term may createproblems in certain instances as will be discussed underthe topic of matrix diffusion.

There is concern as to how adequately dispersion can berepresented in computer codes because it is related tospatial scale and variations in aquifer properties whichare generally not explicitly simulated in the code (e.g.,tortuosity). Furthermore, dispersion coefficients arevery difficult to measure in the field

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Figure 4-10. Matrix Dispersion

and are usually obtained during the model calibrationprocess.

These limitations suggest that not too much confidencebe placed in dispersion values, and that it is generallybest to use advection-dispersion-based codes to boundthe maximum probable extent that contamination mayhave spread. However, as mentioned previously, peakconcentrations will tend to be underestimated.

Matrix Diffusion

Diffusion in solutions is the process whereby ionic ormolecular constituents move under the influence oftheir kinetic activity in the direction of theirconcentration gradient (Figure 4-10). The diffusion ofradionuclides from water moving within fractures, orcoarse-grained material, into the rock matrix or finer-grained clays can be an important means of slowingthe transport of the dissolved radionuclides,particularly for non-sorbing or low-sorbing solublespecies. The apparent diffusion coefficient for a givenradionuclide depends on properties that are intrinsic tothe chemical species (e.g., mobility) as well asproperties of the rocks (such as porosity, tortuosity, andsorption ratios).

As stated previously, matrix diffusion is frequentlyinsignificant and is often neglected in many of thecontaminant-transport codes. However, potential

problems arise when matrix diffusion is ignored andcontaminant distributions are based solely onadvective-dispersive principles. For example, ground-water pump and treat remediation systems work on thepremise that a capture zone is created by the pumpingwell and all of the contaminants within the capturezone will eventually flow to the well. The rate at whichthe contaminants flow to the well may, however, bevery dependent on the degree to which thecontaminants have diffused into the fine-grainedmatrix (e.g., clays). This is because the rate at whichthey will diffuse back out of the fine-grained materialsmay be strongly controlled by concentration gradients,rather than the hydraulic gradient created by thepumping well. Therefore, matrix diffusion cansignificantly retard the movement of contaminants,and, if the computer code does not explicitly accountfor this process, the overall effectiveness of theremediation system (i.e., clean-up times) could begrossly underestimated.

Other instances where matrix diffusion processes canlead to erroneous model predictions is in thedetermination of travel times, peak concentrations, andflushing volumes. The fact that diffusion can play asignificant role in slowing the transport ofradionuclides suggests that, if it is ignored, travelrates, as well as peak concentrations, will beoverestimated. Frequently, clean-up times areestimated based on the flushing of a certain number ofpore volumes. However, matrix diffusion

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processes, if unaccounted for, can cause the numberof required pore volumes to be greatly underestimated.This is because pore volume calculations generallyassume that water moves freely through all of the poresand does not account for the relatively stagnantconditions of fine-grained rocks in which contaminantsmay have diffused.

Retardation

In addition to the physical processes, the transport ofradionuclides is affected by chemical processes. Thefollowing summary of geochemical processes thatcould potentially play a role in the transport ofradionuclides has been provided in order to offer anappreciation of their wide variety and complexity:

! Sorption -- the attachment of chemicalspecies on mineral surfaces, such as ionexchange, chemisorption, van der Waalsattraction, etc., or ion exchange within thecrystal structure.

! Ion exchange phenomena -- that type ofsorption restricted to interactions betweenionic contaminants and geologic materialswith charged surfaces which can retard themigration of radionuclides.

! Speciation -- the distribution of a givenconstituent among its possible chemical formsof the radionuclide which can influence itssolubility and therefore its rate of transport bylimiting the maximum concentration of theelement dissolved in the aqueous phase.

! Precipitation -- the process by whichdissolved species exceed solubility limits,resulting in a portion precipitating out ofsolution.

! Natural colloidal formation -- the attachmentof radionuclides to colloids resulting in amode of radionuclide transport or retardationwhich involves the movement or mechanicalretardation of radionuclides attached to largecolloidal particulate matter suspended in theground water or the formation of colloidalclusters of radionuclide molecules.

! Radiolysis -- the change in speciation due toradiation or recoil during radioactive decay,

which can affect the solubility ofradionuclides.

! Biofixation -- the binding of radionuclides tothe soil/organic matrix due to the action ofsome types of microorganisms and plants,thus affecting mobility of the radionuclide.

! Natural organic matter interactions -- soilorganic matter can play a significant role inmobilizing, transporting, sorbing, andconcentrating certain radionuclides.

! Anion exclusion -- negatively charged rocksurfaces can affect the movement of anions,by either retarding the movement of anionsby not allowing negatively chargedradionuclides to pass through the poreopening, or by enhancing the transport ofions by restricting the anion movement to thecenter of the pore channel where ground-water velocities are higher.

Obviously, a wide range of complex geochemicalreactions can affect the transport of radionuclides.Many of these reactions are poorly understood and areprimarily research topics. From a practical view, theimportant aspect is the removal of solute from solution,irrespective of the process. For this reason, mostcomputer codes simply lump all of the cumulativeeffects of the geochemical processes into a single term(i.e., distribution coefficient) which describes thedegree to which the radionuclide is retarded relative tothe ground water. Thus, the distribution coefficientrelates the radionuclide concentration in solution toconcentrations adsorbed to the soil. Because thedistribution coefficient is strongly affected by site-specific conditions, it is frequently obtained from batchor column studies in which aliquots of the solute, invarying concentrations, are well mixed withrepresentative solid from the site, and the amount ofsolute removed is determined.

If the sorptive process is rapid compared with the flowvelocity, the solute will reach an equilibrium conditionwith the sorbed phase, and there is a greater likelihoodthat the distribution coefficient approach will yieldreasonable values. However, if the sorptive process isslow compared with the rate of fluid flow, the solutemay not come to equilibrium with the sorbed phaseand geochemical (i.e., based on thermodynamics andkinetics) models are generally required.

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Most computer codes assume that the distributioncoefficient is constant over all solute concentrationranges (i.e., linear isotherm). However, thisassumption may place a serious limitation on thepredictive capability of the code, in that a linearrelationship between the concentration of solute insolution and the mass of solute sorbed on the solid doesnot limit the amount of solute that can be sorbed ontothe solid. In actuality, this is not the case; there mustbe an upper limit to the mass of solute that can besorbed, due to a finite number of sorption sites on thesolid matrix. This upper bound on sorption suggeststhat, in a natural system, retardation would decrease ascontaminant concentrations in the ground-waterincrease. This discrepancy between computer codesassuming linear sorption behavior when, in fact, non-linear sorption is more accurate, can have importantimplications when predicting the migration of thecenter of mass versus the leading edge of acontaminant plume, or when predicting requiredpumping times for a pump and treat remedial action.At high concentrations, the linear assumption willover-predict retardation and under-predict radionuclidetravel rates and contaminant concentrations.

A basic assumption in code development is that atdilute concentrations the errors associated with usinglinear sorption isotherms to predict non-linearrelationships will be minimal. However, radionuclidespresent a special problem in that frequently thereleases may be at dilute concentrations but overextended durations. These long time frames may allowall of the sorption sites to be filled, even at low releaseconcentrations, and model results will diverge fromactual values by under-predicting radionuclide travelrates and concentrations.

The ability of a code to accommodate retardationeffects is essential for evaluating radionuclide transportrates unless a special case is being considered, such asone involving tritium which moves unretarded or if theprimary objective is to determine the absoluteminimum travel times and maximum travel distances.It is possible to back out travel rates and distances fromcomputer codes that do not accommodate distributioncoefficients; however, if the species are decaying, thecalculations can become very tedious.

Radioactive Decay

Radionuclides decay to stable products or to otherradioactive species called daughters. For some

radionuclides, several daughter products may beproduced before the parent species decays to a stableelement. For some radionuclides, the daughter(s) maypresent a potentially greater health risk than theparent. Accounting for the chain-decay process isparticularly important for predicting the potentialimpacts of uranium, thorium, and transuranicmigration.

In considering this process over the transport path ofradionuclides, one transport equation must be writtenfor each original species and each daughter product toyield the concentration of each radionuclide (originalspecies and daughter products) at points of interestalong the flow path in order to estimate totalradiological exposures. However, not all computercodes that simulate radioactive decay allow foringrowth of the daughters, which may not cause aproblem if the daughter half-lives are very long (i.e.,they take a very long time to grow in) or if thedaughter products are of little interest. In addition, itis computationally difficult to account for ingrowth ofdaughters during transport. Codes that do addressdaughter ingrowth generally account for ingrowth inthe contaminated zone only. The difficulty arises inthe need to use the Kd of the daughter and changes inthe travel distance as the daughters grow duringtransport through the unsaturated and saturated zones.

4.3.1.4 Multiphase Fluid Conditions

The movement of contaminants that are immiscible inwater (i.e., non-aqueous phase liquids - NAPL)through the vadose zone and below the water tableresults in systems which have multiple phases (i.e., air,water, NAPL). This coexistence of multiple phasescan be an important facet in many contaminant-transport analyses. However, only the water and thevapor phase are of concern when evaluating thetransport of radionuclides. A limited number ofradionuclides can form volatile species that are capableof being transported in a moving vapor or gas. Amongthese are tritium, carbon-14, and iodine-129. Over alarge scale, factors that affect transport in flowingground water also affect transport in flow-ing gas (i.e.,the velocity of the gas determines the potential foradvective transport). In the absence of flow, diffusionis the only mechanism for transport in the gaseousstate. The processes of partitioning of the volatilespecies between the gaseous, liquid, and solid state andisotopic exchange must also be consi-dered whenassessing the impact of vapor transport.

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Currently a number of analytical and numerical codesallow the investigation of vapor transport in theunsaturated zone; however, almost all of these codesassume an immobile water phase. The limitation ofthis assumption is that one of the principal concernsregarding gaseous transport is its role in transportinggas-phase radionuclides through the unsaturated zoneto the water table where they may be dissolved andtransported by the ground water. Without thecapability to simulate the percolation of water throughthe unsaturated zone, tritium concentrations reachingthe water table will be greatly underestimated.Furthermore, remediation strategies cannot be fullydeveloped if the residual water held in the unsaturatedzone is assumed to remain stagnant. For instance, amethod that has been proposed to remediate tritiuminvolves pumping the tritiated water from withdrawalwells located downgradient from the source area. Thecontaminated water is subsequently reinjected intowells upgradient from the withdrawal wells. In thismanner, tritium is recycled continuously until it decaysto levels below the remedial criteria (e.g., the drinkingwater standards). Two aspects of this system thatcould not be evaluated without having the ability tosimulate mobile water and vapor in the unsaturatedzone are, first, whether vapor transport will carrytritium beyond the limits of the hydraulic capture zonecreated by the pumping wells, and second, what theexpected loading rates will be from the source term.

4.3.1.5 Flow Conditions

The ground-water environment can be divided into avariably saturated (vadose zone) and saturated regimes.The irregular surface that forms the boundary betweenthese two regimes is known as the water table. Belowthe water table, pressures are equal to or greater thanatmospheric and the pores and spaces within andbetween individual soil particles are filled with water.Above the water table, in the partially saturated zone,water is generally under negative pressure or tension(less than atmospheric). Some of the pore space isusually occupied by gases derived primarily from theatmosphere as well as pore water.

Radionuclide releases to the ground water may resultfrom a number of mechanisms. These mechanismscan affect ground water directly or indirectly, and theyinclude the following:

! Direct discharge (e.g., on-site release fromtreatment processes)

! Leachate generation (e.g., from buriedwastes, surface impoundments, andabsorption beds)

! Overland flow (e.g., from impoundmentoverflow or failure, drum leakage)

! Contaminated stream interaction withaquifers

The decision as to whether the vadose zone and/orsaturated zone will be modeled is directly related to themechanism by which the contamination was released.That is, if radionuclides are being released directly tothe water table, little would probably be gained bymodeling the vadose zone. However, if the riskassessment is based only on radionuclideconcentrations reaching the water table, it may not benecessary to model the saturated zone.

After a determination is made as to whether the vadosezone and/or saturated zone are to be modeled, itbecomes necessary to address a much more difficultquestion, i.e., the complexity at which each zoneshould be modeled. This question can be answeredonly by attaining a thorough understanding of themodeling objectives, as well as an appreciation of theadvantages and disadvantages of each prospectiveapproach.

The sophistication of the unsaturated zone modelingapproach will be based primarily on the overallmodeling objectives, although the complexity of thehydrogeology may also play a significant role. Forinstance, accurate predictions of radionuclide flow andtransport through a very complex unsaturated zonemay be irrelevant and unnecessary if credit is not takenfor it in the baseline risk assessment. On the otherhand, if the risk assessment is based solely uponarrival times and peak concentrations of radionuclidesarriving at the ground-water table, then a detailedanalysis of flow and transport through even a thin,uncomplicated unsaturated zone may be significantand require complex modeling.

Relative to saturated zone modeling, vadose zonemodeling is characterized (plagued) by significantnumerical difficulties and greater uncertaintyregarding conceptualization and parameter estimation.In many vadose zone modeling situations, it may beadvisable to use simple models and conservativeassumptions to estimate exposure concentrations. The

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appropriate level of modeling and data collection forrisk assessment at individual sites should bedetermined during the remedial process.

Situations may arise where reliable simulations of flowand transport of radionuclides through the unsaturatedzone may not be possible even with complex ground-water models. In particular, if the unsaturated zone isindurated with fractures or macropores with highpermeability, the flow and transport processes becomeso involved that mathematical formulations of porousmedia transport are poor representations of thephysical phenomena. Furthermore, localized zones ofhigher permeability may cause the wetting front toadvance at highly variable rates, which may introducesignificant disparities between the actual and predictedcontaminant concentrations.

Under single-phase flow conditions, an option to selecta vadose zone code which simulates hysteresis isprovided. Hysteresis is simply a term which describesthe fact that wetting and drying curves for a certainsoil (pressure head versus volumetric water content),under partially saturated conditions, are not the same.That is, the pressure head is not only dependent uponthe water content but also on whether water is beingremoved or added to the system. The effect is due toboth the geometric shapes of the pores and the contactangle between the water and the mineral surface,which is different depending on whether the water isadvancing and retreating. Of particular relevance inconsidering hysteric effects as a code-selection criteriais that hysteresis will have little effect on the flow andtransport of contaminants. The primary utility ofincluding hysteresis is to account for this processduring model validations studies. Therefore, if modelvalidation will not be performed, which will be thecase in the vast majority of modeling studies, thecapability of a code to simulate hysteresis will be oflittle importance.

4.3.1.6 Time Dependence

The most frequently performed ground-water modelingis that of the saturated zone. The parameter needs arewell defined and the field data collection activities arerelatively straightforward. The major factors thatprovide immediate insight into whether sophisticatedground-water modeling will be necessary are thecomplexity of the:

! Source term

! Dominant flow and transport processes! Hydrogeology (e.g., layers, heterogeneity)! Hydraulic boundaries

Previous discussions have addressed the relativeimportance of these issues in the code selectionprocess. However, one aspect that has not been fullyconsidered is the temporal nature of flow and transportwithin the system. As discussed previously,simulations can be performed in either a steady or atransient state. At steady-state, it is assumed that theflow field and contaminant releases remain constantwith time, whereas a transient system simply meansone that fluctuates with time. This fluctuation may beinduced by both natural (e.g., tides, rainfall) andmanmade influences (e.g., wells, hydraulic barriers).In many instances, transient systems, if observed overthe long term, will approach relatively steady-stateconditions.

As far as code selection is concerned, relative to thetemporal behavior of the system, it is a fairlystraightforward decision. Namely, most analyticalmodels do not simulate a transient flow system;therefore, if a transient flow system needs to bemodeled, analytical and semi-analytical methods aregenerally not available. Furthermore, if a steady-stateflow system is acceptable, but a transient transportcapability is required, both analytical and numericalcodes are readily available for these conditions and theselection criteria should be deferred to otherconsiderations.

4.3.2 Code-Related Characteristics

In addition to the site-related characteristics presentedin the previous section, the code selection process mustalso consider attributes that are integral components ofthe computer code(s), including:

! Geometry

! Source Code Availability

! Code Accessibility/Ease of Use

! Code Verification and Validation

! Code Output

! Solution Methodology (Appendix C)

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4.3.2.1 Geometry

The decision to model a site in a particular number ofdimensions should be based primarily upon both themodeling objectives and the availability of field data.Other considerations include whether a computer codeexists that can simulate the dominant processes in thedesired number of dimensions, and whether hardwarerequirements are compatible with those available.

In determining how many dimensions are necessary tomeet the objectives, it becomes necessary to gain abasic understanding of how ground-water flow andcontaminant concentrations are affected by theexclusion or inclusion of an additional dimension. Itshould be kept in mind that the movement of groundwater and contaminants is usually controlled byadvective and dispersive processes which areinherently three-dimensional. Advection is moreresponsible for the length of time (i.e., travel time) ittakes for a contaminant to travel from the source termto a downgradient receptor, while dispersion directlyinfluences the concentration of the contaminant alongits travel path. This fact is very important in that itprovides an intuitive sense for what effectdimensionality has on contaminant migration rates andconcentrations. As a general rule, the fewer thedimensions, the more the model results will over-predict concentrations and under- predict travel times.Concentrations will be over- predicted becausedispersion, which is a three-dimensional process, willbe dimension limited and will not occur to the samedegree as it actually would in the field. Travel timeswill be under-predicted, not because of a change in thecontaminant velocities, but because a more directtravel path is assumed. Therefore, the lowerdimensionality models tend to be more conservative intheir predictions and are frequently used for screeninganalyses.

One-dimensional simulations of contaminant transportusually ignore dispersion altogether, andcontamination is assumed to migrate solely byadvection, which results in a highly conservativeapproximation. Vertical analyses in one dimension aregenerally reserved for evaluating flow and transport inthe unsaturated zone.

Two-dimensional analyses of an aquifer flow systemcan be performed as either a planar representation,where flow and transport are assumed to be horizontal(i.e., longitudinal and transverse components), or as a

cross section where flow and transport components areconfined to vertical and horizontal components. Inmost instances, two-dimensional analyses areperformed in an areal orientation, with the exceptionof the unsaturated zone, and are based on theassumption that most contaminants enter the saturatedsystem from above and that little vertical dispersionoccurs. However, two-dimensional planar simulationshave a number of limitations. These include theinability to simulate multiple layers (e.g., aquifers andaquitards) as well as any partial penetration effects.That is, the contaminant source, wells, rivers, lagoons,and lakes are all assumed to penetrate the entirethickness of the aquifer. Furthermore, because verticalcomponents of flow are ignored, a potentially artificiallower boundary on contaminant migration has beenautomatically assumed which may or may not be thecase.

A two-dimensional formulation of the flow system isfrequently sufficient for the purposes of riskassessment, provided that flow and transport in thecontaminated aquifer are essentially horizontal. Theadded complexities of a site-wide, three-dimensionalflow and transport simulation are often believed tooutweigh the expected improvement in the evaluationof risk. Complexities include limited site-widehydraulic head and lithologic data with depth andsignificantly increased computational demands.

Quasi-three-dimensional analyses remove some of thelimitations that are inherent within two-dimensionalanalyses. Most notably, quasi-three-dimensionalsimulations allow for the incorporation of multiplelayers; however, flow and transport in the aquifers arestill restrained to longitudinal and transversehorizontal components, whereas flow and transport inthe aquitards are even further restricted to vertical flowcomponents only. Although partial penetration effectsstill cannot be accommodated in quasi-three-dimensional analyses, this method can sometimesprovide a good compromise between the relativelysimplistic two-dimensional analysis and the complex,fully three-dimensional analysis. This is the case,particularly if movement of contaminants from theshallow aquifer through a confining unit and into adeeper aquifer is suspected.

Fully three-dimensional modeling generally allowsboth the geology and all of the dominant flow andtransport processes to be described in threedimensions. This approach usually affords the most

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reliable means of predicting ground-water flow andcontaminant transport characteristics, provided thatsufficient representative data are available for the site.Fully three-dimensional analyses are often the onlydefensible means to evaluate the effectiveness of manypotential remedial scenarios. For example, extractionand injection wells may create strong verticalgradients, as well as three-dimensional capture zones.Without the ability to accommodate these gradientsand capture zones, dilution effects and capture zonescould be over- or underestimated. The ground-waterflow and contaminant transport beneath a barrier wallwould also be subject to serious predictive limitationswithout a three-dimensional analysis, again because ofthe strong vertical gradients that generally accompanythese features.

4.3.2.2 Source Code Availability

As a general rule, an effort should be made to usepublicly available computer codes, provided they havebeen well documented and tested and can meet all ofthe major requirements of the modeling objectives. Incertain instances, however, it may be necessary topurchase a proprietary code. A proprietary code maybe needed for a number of reasons, but, mostcommonly, proprietary codes are selected eitherbecause the user is familiar with the code or becausethe publicly available codes would not meet themodeling objectives.

The following is a list of factors that need to beconsidered during the selection process of bothproprietary and non-proprietary computer codes:

! Whether the code has been widely used and isgenerally accepted by the technicalcommunity;

! How well the code is documented andverified;

! Whether the code has been independentlypeer reviewed;

! Whether the purchase price of the codeprovides any technical support, and, ifadditional support is required, what it willcost;

! Whether the source code is provided, and, ifnot, under what conditions could it beobtained if necessary;

! Whether the code has ever been applied to asimilar problem with consistent objectives;

! Whether the code has been field tested onproblems directly relevant to the subject site;

! Whether the code has ever been used tosupport a case in litigation or regulatoryenforcement action;

! Whether any additional enhancements ormodifications to the code are planned in thefuture.

4.3.2.3 Code Testing and Processing

The verification process is generally undertaken duringthe developmental stages of the computer code. It is aprocedure in which analytical equations of knownsolutions are used to ensure that there is an agreementbetween the formulations and solutions of the samebasic equations, which are solved with more complexnumerical methods. In some instances, numericalmethods, which have been verified with analyticalsolutions, are used to check other newly formulated oreven more complex numerical solutions. The purposeof verification is to show only that the numericaltechniques work and that no errors exist in either themathematical formulation or in the actual coding ofthe formulation.

One important aspect of code verification is that it canusually be performed independently of the codedevelopment process. This allows the accuracy ofcodes to be checked even without access to the source-code documentation. It is not recommended, however,that codes be selected that were not verified during thedevelopment process and are not well documented.

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Calibration and validation are activities designed totest the realism of the ground-water flow and transportmodel. From a philosophical perspective, calibrationand validation are very different. When addressing thesubject of calibration, it is generally assumed that boththe conceptual model and numerical models arereasonably correct or adequate. Therefore, to calibratea model, model parameters are simply adjusted withinan acceptable range, based on site-specificmeasurements, to arrive at a best fit of the dependentvariable, which is usually hydraulic head or soluteconcentrations. Validation, on the other hand,examines in more detail the realism of both theconceptual model and the numerical model.

Model calibration of vadose zone models is verydifficult and rarely attempted primarily due to datalimitations, whereas calibration of saturated flow andtransport models is relatively straightforward, providedthere are sufficient field measurements of hydraulichead or solute-concentration data. One potentialproblem with calibration of saturated flow models isthat a unique solution for the hydraulic headdistribution is not available if all of the boundaryconditions are either no-flow or fixed head. In otherwords, if the model does not contain a flux conditionof significant magnitude (relative to total flux throughthe model), increasing or decreasing all the hydraulicconductivities in equal proportion will result in theexact same hydraulic head distribution. The onlydifference is that the amount of flux through the modelwill be increased or decreased in proportion to thechange in hydraulic conductivities. This is why itbecomes very important to not only narrow theprobable ranges of hydraulic conductivities throughmethods such as aquifer tests but also to use massbalance information to check the calibration results.

Model validation is, in general, a comparison of thesolutions of the mathematical equations from whichthe model is formulated with field-measured data.Compelling arguments have been made that ground-water models cannot be validated, only invalidated(KON92). Accordingly, validation is best thought ofas a process for determining the degree to which amodel can be relied upon to support a specificmodeling objective at a specific site. Validation, atbest, may consist of reasonable agreement betweensimulated results and actual field data at two or moretime periods.

Attempts to validate models must address the issue ofspatial variability when comparing model predictionswith limited field observations. If sufficient field dataare obtained to derive the probability distribution ofcontaminant concentrations, the results of a stochasticmodel can be compared directly. For a deterministicmodel, however, the traditional approach has been tovary the input data within its expected range ofvariability (or uncertainty) and determine whether themodel results fall within the bounds of field-measuredvalues.

Regardless of whether the solution is obtained byanalytical or numerical techniques, true validation orhistory matching can be done only through comparisonwith field measurements and, in some cases, laboratorydata. Furthermore, given the lack of comprehensivefield data sets that adequately describe the spatialparameter distributions, and our inability to directlymeasure water and solute fluxes which are morelogical variables for model validation, it is highlyunlikely that complete validation of any simulationmodel can be possible.

Such complete validation, however, is not necessaryfor most modeling approaches if model limitations areadequately recognized. It should also be kept in mindthat validation is site-specific and consequently itsutility, if achieved at one location, is limited whenconsidering application of the model at anotherlocation.

The need for the overall validation or history matchingoutlined above is directed at the creation of reasonablyreliable computational and forecast capabilities forstudies that would generally go beyond the baseline-risk assessment. It is acknowledged that the fieldtesting efforts outlined here usually occur concurrentlywith the remedial process; however, validation or fieldtesting is not simply applying models within theremedial investigation context. This is because theremedial investigation of a waste site may stronglyfocus on the calculation of risk. For example, if allcontaminants released at a waste site are immobile, theremedial investigation activities in support of thebaseline risk assessment may concentrate on thequantification of partitioning between the water andthe solid phase. As such, simplified flow and transportmodels may be used to support the baseline riskassessment under this situation. Within this context,it is recognized that flow and transport modeling isonly one component of the risk calculation, and those

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responsible for the quantification of the baseline riskassessment may employ a relatively unsophisticatedmodeling approach for the baseline and perhaps veryconservative simulations. On the other hand, for othersituations, detailed flow and transport analyses may berequired. Under these conditions, resolution of theflow and transport model validation issue will requireexamination of the waste site with models of somecomplexity or sophistication with regard to thegeologic structure and dominant processes.

4.3.2.4 Model Output

One aspect of the computer code that is frequentlyignored in the selection process is the form that themodel output will take. It is true, however, that inmost instances the actual output can be fashioned intothe desired format, provided the model itself isconsistent with required output. That is, output inthree dimensions cannot be obtained with a two-dimensional model.

In general, the model output is expressed in terms ofhydraulic head, pressure, or solute concentrations. Thespatial coverage of parameter output values is eitherdependent on the frequency of nodal spacing(numerical) or on the number of specified x and ycoordinates (analytical) which are included in themodel input files. Code output will also vary due tothe inherent nature of the code itself. For example,codes that simulate movement in the unsaturated zoneproduce what are termed saturation profiles. Theseprofiles indicate what percentage of the pore space isfilled with water, whereas saturated zone codes haveno need for this capability because all of the poresbelow the water table are assumed to be filled.

Some codes provide output in a format which is veryuseful and saves time during the post-processing of thedata. The best example of this is where the user canspecify nodes where concentration profiles are desiredwith time (i.e., breakthrough curves). These profilesallow arrival times, peak concentrations, andcontaminant mass changes to be easily evaluated.

The single most important code selection criteria,relative to the model output, would be that the codeprovides mass-balance information. A mass-balancedetermination is a check to ensure that at steady-state,the amount of water or contaminant mass entering thesystem equals the amount exiting the system. If inflowdoes not equal outflow for a steady-state simulation,there may be something wrong with the numericalsolution, although errors in the mass balance may alsoindicate that there are problems with the mass balanceformulation itself. Therefore, mass-balanceinformation not only provides a check on themathematical formulations within the code, but it alsoassists in ensuring that input parameter conversionsand other errors have not been made.

It is not uncommon for codes that do include mass-balance output to provide information (e.g., fluxes,heads) on specific boundaries as well as the sourceterm, all of which can be used in the interpretation andevaluation of the predicted flow and solute transportdirections and rates.

4.4 MODELING DILEMMAS

The previous sections have described how site- andcode-related features affect the model selectionprocess. What is not presented, however, is adiscussion of the processes that are very difficult, if notimpossible, to model with currently available models.Complex flow and transport processes present anotherdifficulty in that computer codes currently do not existthat explicitly accommodate a number of theseprocesses including:

! Turbulent Ground-Water Flow

! Facilitative Transport

! Unsaturated Fracture Flow

! Complex Geochemical Reactions

Although these processes are very complex, it isimportant that at least a basic understanding of thesemechanisms and concepts be grasped prior to initiatingfield or modeling investigations in which they may beimportant. The subsequent discussion will introducethe difficulties associated with modeling these complexprocesses. Of particular relevance is that the processesare not fully understood and are, therefore, not welldescribed mathematically. If modeling is not possible

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because of the overall complexity of the sitecharacteristics, it is common for a greater emphasis tobe placed on empirical rather than predicted data.This may involve establishing long-term monitoringprograms, which in effect, have objectives similar tothose of ground-water modeling.

Turbulent Ground-Water Flow. As ground-watervelocities increase, flow diverges from the laminar-type which is characteristic of low velocities andbecomes more turbulent. At the point in whichturbulent flow is reached, a basic law describing therelationship between hydraulic gradient and specificdischarge (i.e., Darcy's) breaks down and is no longervalid. Most ground-water flow, however, is notturbulent, except in the very close proximity of largepumping or recharging wells. In practice, however,turbulent flow over relatively small areas is generallyignored without introducing any severe limitations inthe modeling. On the other hand, in cases whereturbulent flow is observed over relatively large areas,such as cavernous limestone aquifers, Darcy's law maybe significantly violated and results from flow andtransport modeling would be of questionable value.

Facilitative Transport of Radionuclides. Field andlaboratory investigations have indicated that undercertain conditions contaminants are more mobile thanwould be predicted based on properties such assolubility, ion exchange, speciation, sorption-desorption and ground-water velocities. Thesepredictions, however, have not accounted for thepotential interactions between the inorganiccontaminants and mobile colloids. Colloidal-sizeparticles include humic substances, clay minerals, ironoxides and microorganisms. Colloids not only have ahigh surface area per unit mass and volume, but manytypes of colloids are also extremely reactive sorbantsfor radionuclides. Therefore, radionuclides that mightotherwise be sorbed to stationary material in theaquifer could be transported in the sorbed layers ofthese mobile colloids. Sorption in this case hasfacilitated transport.

A number of actinides, plutonium in particular, canform natural colloids under conditions of near-neutralsolutions of low ionic strength. It is also suspected thatamericium may form colloids under similar conditions.Colloidal particles (up to 0.5 micrometers in diameter)remain suspended for long periods and hence maymigrate with the ground water. As the solid wasteform is leached, particles containing radionuclides may

form by the sorption of dissolved radionuclides onnonradioactive particles. At this time it is believedthat plutonium and americium are most likely to betransported as colloids, although other radionuclidesmight be subject to this transport process under certainconditions. Transport of particulates in geologicmedia will depend on aqueous flow rate, on pore andfracture size in the rock, on ions carried in the water,and on the nature of the particulate matter. Severalmechanisms may remove colloidal particulates fromground water such as mechanical filtration by the rockmatrix, sorption on the surface of the rock pores (vander Waals), and neutralization of the repulsive chargeson the colloids, thus allowing them to coagulate.

Radiocolloids may arise from a variety of sources. Thecorrosion of metal containers can lead to the formationof absorbent colloids. Degradation of engineeredbackfills may also lead to colloidal formation. If thewaste form is leached by ground water, naturallyoccurring colloids derived from smectites,vermiculites, illites, kaolinite, and chlorite present inground water may also adsorb radionuclides.

The degree to which facilitative transport can bemodeled is largely dependent upon the objectives of themodeling and the extent of understanding of thetransport mechanisms active at the site. A site-specificevaluation may be required to determine the possibleimportance of colloidal transport on the mobility of theradionuclides. To estimate the amount ofradionuclides that could be transported by colloidalsuspension, it is first necessary to determine whethercolloidal-sized particles exist in the ground water.Then, the sorption ratios for waste elements on theseparticles must be measured or estimated from thecomposition of the particles. In addition, theconditions under which colloids could form from thewaste elements or from the waste and their stabilityafter formation must be determined. Finally, theconditions necessary for the filtration or sorption of theparticles by the rock matrix itself must be defined.

An alternative approach to detailed site investigationsto characterize the potential for colloidal transportwould be to undertake a conservative approach and setall of the distribution coefficients to zero. Thisapproach, however, may not always be conservative inthat it is possible that under certain circumstancescolloids may have a velocity greater than the averagelinear ground-water velocity. This may be due to bothsize-exclusion and charge-repulsion. Size-exclusion

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occurs when molecules or ions are so large that theycannot be transported through the smaller pores. As aresult, they are restricted to the larger pores, in whichthe ground-water velocity is greater than average. Thecharge-repulsion phenomenon occurs when thecolloids have a negatively charged surface which isrepelled by the negatively charged clays which line thepore channels. This process may confine the colloid tothe central part of the channel where the velocities arehighest and the ground-water velocity is greater thanaverage.

Attempts have also been made to model the transportof colloids which are more mobile than water bysetting the distribution coefficient to less than zero.This approach, however, has a number of problems.One of the most significant of these is that all of thewaste released from the source term would be assumedto be transported as colloids which may result in overlyconservative solutions.

Currently, ground-water models do not exist thatdescribe the constitutive relationships involved withcolloidal transport and explicitly account for thedominant geochemical interactions responsible forcolloidal transport.

Unsaturated Fracture Flow. As previously discussed,ground-water modeling of the unsaturated zone isbased upon developing sets of moisture-characteristiccurves, that is the functional dependence of liquid-water saturation and relative hydraulic conductivity onthe liquid-water potential within the rock matrix andfractures for each hydrogeologic unit. In unfracturedrocks, these relations refer to the storage andmovement of liquid water within and through theinterstitial pore space. In fractured rocks, allowancemust be made for the storage and movement of waterwithin the interconnected fracture openings as well asfor the movement of water between the fractureopenings and the rock-matrix pore space. Standardfield and laboratory methods are not yet available bywhich to determine the moisture-characteristicrelations for fractures within the unsaturated zone.

Liquid-water storage within fractures probably isinsignificant, but the flow of liquid water within andacross fractures is not yet well understood. Theoreticalmodels for liquid-water flow in single unsaturatedfractures have been developed but have not yet beenfield tested. Fractures may or may not impede liquid-water flow at low matrix saturations, and longitudinal

flow within the fractures may dominate liquid-waterflow above some critical matrix saturation.Consequently, at high matrix saturations, fracturesystems and fault zones may become highly efficientpathways for liquid-water flow. Liquid-water flowwithin fractures may or may not be Darcian (i.e.,laminar) and will be dependent on the gradient andhydraulic conductivity.

At low matrix saturations, little or no water moveslongitudinally within the fracture openings, and theeffective hydraulic conductivity is controlled by that ofthe fracture-bounded matrix blocks. As the matrixapproaches complete saturation, however, themovement of water within and along the fractureaperture rapidly becomes more efficient so that atcomplete saturation the fractures may be dominantcontributors to the net hydraulic conductivity. Therelative contributions of fractures and matrix to the neteffective hydraulic conductivity depend on the fracturefrequency, aperture-size distribution, and degree ofinterconnectivity. However, there is currently no wayto generate a complete set of fracture location andgeometry data.

In essence, a generally poor understanding of thephysics controlling fluid flow in fractured-unsaturatedsystems, in conjunction with an inability tocharacterize the fracture properties and locations,makes it nearly impossible to model these systemsreliably.

Complex Geochemical Reactions. Radionuclides areundergoing geochemical reactions. The principalgeochemical properties and processes of theradionuclides, which may be site-specific andimportant to understand, include the following:

! Complexation

! Phase transformations

! Adsorption and desorption

! Precipitation

As stated previously, if it is desired to model theseprocesses explicitly, as opposed to using simplifyingassumptions such as default or aggregate retardationcoefficients, geochemical rather than flow andtransport models may be required. As indicated, someof the more common radionuclides, such as uranium

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and plutonium, can exist in a number of chemicalstates, which can significantly affect their rate oftransport. Other radionuclides, such as tritium, arerelatively insensitive to the site geochemical conditionsbut undergo phase transformations which are difficultto simulate with existing codes. Explicit geochemicalmodels can be applied to assist in evaluating thegeneral effect that the geochemical environment willhave on the radionuclide fate and transport, but eventhese methods are often unreliable and the results mustbe interpreted carefully.

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SECTION 5

THE CODE SELECTION PROCESS

Section 4 described the various waste and site characteristics and processes and the code-related characteristicspertinent to the code selection process. The emphasis was placed on recognizing when specific waste, site, and codecharacteristics are important and therefore must be considered in order to meet the modeling needs of each phase ofthe remedial process. This section presents the basic procedure that should be followed in evaluating ground-waterflow and transport code(s) prior to making a final selection among two or more potential codes.

5.1 OVERVIEW OF THE CODE REVIEW ANDSELECTION PROCESS

Given that an investigator understands the variouswaste and site characteristics that need to be modeledin order to meet specific modeling objectives, therewill often be several suitable computer codes whichcould potentially be chosen from a large number ofcodes published in the scientific literature (BAC80,EPA91, and MOS92). As mentioned in Section 1,IMES "Integrated Model Evaluation System" providesan excellent computerized means by which codes maybe screened automatically for their respectivecapabilities. The user simply checks off the desiredcode capabilities within a screening module of IMES,and the program eliminates all of the codes without thespecified capabilities from an extensive internaldatabase. Furthermore, IMES will provide someinformation on the code itself although thesedescriptions are, in many instances, somewhat limited.Ideally, a detailed evaluation of each candidate codeshould be performed to identify the one mostappropriate for the particular site and modelingobjectives. The resources to complete a detailed studyare seldom available, and usually only one to two codesare selected based upon a cursory review of codecapabilities. Regardless of whether a detailed or morecursory review is performed, it is important for thereviewer to be cognizant of the following factors andhow they will affect final code selection:

1. Code Capabilities Consistent with: User needs Modeling objectives Site characteristics Contaminant characteristics Quality and quantity of data

2. Code Testing Documentation

Verification Validation

3. History of Use Acceptance

The first aspect of the review concentrates on theappropriateness of the particular code to meet themodeling needs of the project. This subject isdiscussed in depth in Sections 3 and 4. The reviewermust also determine whether the data requirements ofthe code are consistent with the quantity and quality ofdata available from the site. Next, the review mustdetermine whether the code has been properly testedfor its intended use. Finally, the code should havesome history of use on similar projects, be generallyaccepted within the modeling community, and bereadily available to the public.

Evaluating a code in each of the three categories wouldtake a significant effort, especially with respect to codetesting. Theoretically, the reviewer should obtain acopy of the computer code, learn to use the code, selectverification problem sets with known answers, andcompare the results of the model to the benchmarkproblems. This task is complicated, largely because nostandard set of benchmark problems exists, and themathematical formulation for each process describedwithin the code has to be verified through thebenchmarking process. Primarily for this reason,selection of codes that are already widely tested andaccepted is recommended. Code validation, whichinvolves checking the model predictions against actualfield investigations designed specifically to test theaccuracy of the model, would almost never be practicalduring the code evaluation and selection process.

The selection and evaluation process presented in thissection takes an approach which is consistent withindustry standards by relying on published reports anduser interviews as a substitute for actual hands-ontesting. The result is a code selection and evaluation

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process that provides a reasonable technical reviewthat is relatively straightforward and takes a relativelyshort time to complete (Figure 5-1).

The model evaluation process presented in subsequentsections involves the following steps:

1. Contact the author or curator of the code andobtain the following:

Documentation and other model-relatedpublications

List of users

Information related to code testing

2. Read all publications related to the model,including documentation, technical papers,and testing reports.

3. Contact code users to find out their opinions.

4. Complete the written evaluation using thecriteria shown in Table 5-1.

Much of the information needed for a thoroughevaluation can be obtained from the author ordistributor of the code. In fact, inability to obtain thenecessary publications can indicate that the code iseither not well documented or not widely used. Ineither case, inaccessibility of the documentation andrelated publications should be grounds for evaluatingthe code as unacceptable.

Most of the items in Table 5-1 should be described inthe code documentation, although excessive use ofmodeling jargon may make some items difficult tofind. For this reason, some assistance from anexperienced modeler may be required to complete theevaluation. Detailed conversations with users can alsobe used to decipher cryptic aspects of thedocumentation.

The evaluation process recommended in the followingsections relies on user opinions and publishedinformation to take the place of hands-on experienceand testing. User opinions are especially valuable indetermining whether the code functions as documentedor has significant errors (bugs). In some instances,users have performed extensive testing andbenchmarking or are familiar with published papers

documenting the use of the code. In essence, theproposed evaluation process substitutes second-handexperience for first-hand knowledge (user opinions) toshorten the time it takes to perform the review. It isalso important to keep in mind that code selection is avery dynamic process, and multiple codes may need tobe selected over the remedial lifetime of the site inorder not only to reflect the remedial phase of theproject, but also to remain current with existingtechnology.

Models attempt to simulate natural processes througha series of mathematical expressions. Because of thesimplifications and assumptions needed to simulatethese processes, all models will be inexact andimprecise. Thus, it is important to understand themagnitude of these deficiencies prior to the selectionand/or application of any model. As a first step in thisprocess, available documentation on the model must bereviewed and evaluated to determine if the documentedcapabilities of the model correspond with the objectivesof the study. Code documentation is, however, oftenbiased and in many cases incomplete. Furthermore,major inherent weaknesses of the code (e.g., omissionof a process such as daughter in-growth) may not behighlighted. For this reason, it is important to secureor prepare independent reviews of any code before it isselected. These reviews can be obtained from theliterature and supplemented with code-specificevaluations similar to those presented in this report.To the extent possible, the code should be exercisedwith representative data prior to its final selection.Failure to conduct such audits and benchmark testingmay result in the inappropriate selection of a code andin a waste of time and resources.

As the user friendliness of the codes increase, thepractical expertise of the user typically decreases. Thisis a potentially dangerous situation because of the largepotential for code misuse. In prior years when codeswere available only in mainframe-type environments,they were almost always used by "experts" who hadknowledge of the capabilities of a selected code. Basedon this knowledge, appropriate inputs would be usedin a modeling effort. Now,

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Figure 5-1. Code Selection Review Process

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Table 5-1. Model Selection Criteria

CRITERIA

Section 5.2.1 Administrative DataAuthor(s)Development Objective (research, general use, education)Organization(s) Distributing the CodeOrganization(s) Supporting the CodeDate of First ReleaseCurrent Version NumberReferences (e.g., documentation)Hardware RequirementsAccessibility of Source CodeCostInstalled User BaseComputer Language (e.g., FORTRAN)

Section 5.2.2 Remedial ProcessScopingCharacterizationRemediation

Section 5.2.3 Site-Related CriteriaBoundary/Source Characteristics

Source CharacteristicsMultiple SourcesGeometry

linepointarea

Release typeconstantvariable

Aquifer System Characteristicsconfined aquifersunconfined aquifers (water-table)aquitardsmultiple aquifersconvertible

Soil/Rock Characteristicsheterogeneity in propertiesanisotropy in propertiesfracturedmacroporeslayered soils

Transport and Fate Processesdispersionadvectiondiffusiondensity dependentpartitioning between phases

solid-gassolid-liquid

Table 5-1. (Continued)

CRITERIA

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equilibrium isotherm:linear (simple retardation)LangmuirFreundlichnonequilibrium isotherm

radioactive decay and chain decayspeciation

Multiphase Fluid Conditionstwo-phase water/NAPLtwo-phase water/airthree-phase water/NAPL/air

Flow conditionsfully saturatedvariably saturated

Temporal discretization (steady-state or transient)

5.2.4 Code-Related CriteriaSource Code AvailabilityHistory of UseCode UsabilityQuality Assurance

code documentationcode testing

Hardware RequirementsSolution MethodologyCode OutputCode Dimensionality

default values are available, and it is possible for a userwith only limited knowledge to produce a result. Thisresult may, however, be highly inaccurate, and the usermay be unaware of potential errors.

5.2 EVALUATION CRITERIA

The code(s) to be used for a particular application willsatisfy a combination of needs defined by theintersection of regulatory requirements, sitecharacteristics, and attributes of the code (Figure 5-2).The code review process outlined within the nextsections is based upon a complete and consistent set ofevaluation criteria. The evaluation process follows ascheme which groups evaluation criteria based on theirsimilarity to one another. That grouping is reflectedin the organization of Table 5-1. Yet the selectionprocess must also account for the interrelationshipsbetween evaluation criteria. For example, certaingroups of criteria will influence model selection andevaluation in different ways. Some criteria areimportant in choosing among codes, others in

controlling the way the code operates, and still othersin how the results can be interpreted and applied. Inthe discussion that follows, these criteria are describedin terms of the way in which they influence the codeselection process.

5.2.1 Administrative Data

Few administrative data are, in fact, discriminatorycriteria, yet some administrative data may be indicativeof factors that exert overwhelming control over the useof codes. Thus, codes must be available and obtainableif they are to be used. The pedigree of a code, while itdoes not prevent the use of older versions, may implythat newer versions should be used. Undocumentedcodes would impose different emphasis on some of theother criteria used in the evaluation. These and othersimilar data will often control whether or not a code isused at all rather than how a code is applied to modela given problem.

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Figure 5-2. General Classification of Selection Criteria

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5.2.2 Criteria Based on Phase in the RemedialProcess

In general, regardless of the nature of the on-sitecontamination or the regulations being followed, theremedial process for contaminated sites may generallybe divided into three discrete phases: the scopingphase, the site characterization phase, and theremediation phase.

The overall remedial process begins with the scopingphase, which is designed to assess the existing andpotential risks that the contaminated site poses tohuman health and to the environment, and to developsite characterization plans. The objectives of the sitecharacterization phase are to obtain sufficientinformation to support dose and risk assessment and toprovide specific-site data required to identify feasibleremedies and remedial action goals. The final phaseof the remedial process is the selection,implementation, and evaluation of a remedy. In eachphase of the remedial process, some information isavailable to assist in code selection. In the earlystages, only broad-based decisions can be supported bythe available data. However, as the process continues,the available information becomes more detailed, andthe code selection can be based upon very specificcriteria dictated by the following factors:

! Modeling objectives ! Waste characteristics! Hydrogeological characteristics! Fate and transport processes! Fluid and flow conditions! Local land use and demography

The influence that these criteria have on code selectionis fully described in Sections 3 and 4.

5.2.3 Criteria Based on Waste and SiteCharacteristics

Section 4 presents a detailed description of howspecific waste and site characteristics influence codeselection. This section summarizes these points withinthe context of completing Table 5-1.

Transport of radionuclides through subsurfacematerials is influenced by the physical and chemicalnature of both the transporting media (usually water)and the medium through which flow occurs (usuallysoil or rock). Criteria used to select or evaluate models

will be related to those processes that control the rateof flow of water through earth materials and thoseprocesses that either remove or deliver materials towater as it flows through earth materials. Subsurfaceflow is controlled by two master variables, hydraulicconductivity and driving force, and modified by thevariability or continuity among those two variables.The hydraulic conductivity of porous or fracturedsubsurface materials is determined by the volumetricextent of voids or porosity within the material and theease or rate with which fluids can move from one voidto another. Flow within and between void spaces is afunction of the properties of the fluid and theinteraction of that fluid with the walls of the porespaces. Since most ground-water flow consists of themovement of dilute water solutions at very lowvelocity, changes in fluid properties generally can beignored.

The properties of the media through which the waterflows and which are of overwhelming significance incontrolling the velocity, direction, and quantity of floware the relative degree of saturation of the materials,and the relative importance of fractured versus porousmedia flow. These site characteristics can generally bedetermined from a study of the type of soil and rockunderlying a site.

The driving force, summed up within the concept ofhydraulic head, for moving a fluid through subsurfacematerials is a combination of gravity and any externalforce applied to the ground-water flow system, such asareal recharge.

The factors that control flow through subsurfacematerials can be either uniformly or non-uniformlydistributed. When they are uniformly distributed, anumber of simplifying assumptions can be made aboutthe nature of flow and transport. These simplifyingassumptions have a great influence on the applicationof a mathematical model. When subsurface materialproperties are anisotropic and/or inhomogeneous, thedirection and rate of flow will vary with position.These site characteristics alone have a marked effecton differentiating among codes which tend to berelatively simple and generalized and those that tendto be relatively complex and focused.

As solutions move through the spaces withinsubsurface materials, solutes may either be added to orremoved from that solution. Which solutes areremoved or added, and the quantity and rate at which

5-8

they are added or removed, is controlled by thegeochemical nature of the solution and subsurfacematrix. These geochemical process may be verycomplex, and their understanding may require anextensive base of physical and chemical data which arerarely available. Because of their complexity,geochemical models are generally developed as stand-alone modules that assume equilibrium (i.e.,instantaneous reactions) and run independently of flowand transport models. The site characteristics that willtrigger the requirement to utilize geochemicalmodeling are unusual subsurface chemistry such assharp variations in chemical conditions (e.g., redox,pH) within soils and rocks.

Most subsurface transport models lump the effects ofall geochemical reactions into the concept of thedistribution coefficient (Kd) or related retardationfactors because, without assuming any retardation,there would be a tendency to over-estimate the mobilityof certain highly reactive radionuclides. There is,however, a very wide range of experimental- and field-determined values for distribution and retardationcoefficients, and, in practice, as with so many othercharacteristics, these parameters are usually bestdetermined on a site-specific basis. At many sites, itmay be unknown whether predicted changes in theconcentration of radionuclides in ground water can beadequately explained by the simplifying assumptionsthat underlay the Kd concept. As the assumption of aKd to calculate radionuclide partitioning istheoretically valid only if: (1) chemical equilibriumexists among all aqueous species containing the solute;(2) reversible, linear sorption is the dominant processcontrolling exchange of the solute between thegroundwater and the rock; and (3) transport of thesolute by particulates (colloids) is insignificant. Thesite characterization program would need to determineif these assumptions are valid for radioelementtransport in the ground water or if deviations fromthese conditions will produce significant errors.Consequently, focused geochemical modeling andlaboratory studies may be needed to address theseuncertainties.

The conceptual model is the set of hypotheses andassumptions about the physical characteristics (e.g.,aquifer properties and boundary type) and thephenomena (e.g., model of fluid flow) that describesand postulates the behavior of the actual system. Theapproach to formulating an appropriate conceptualmodel(s) of the site integrates the generalized

knowledge of physical processes with the availableinformation. Therefore, a conceptual model providesa simplifying framework in which information can beorganized and linked to processes that can besimulated with predictive models.

The mathematical model is the mathematicalrepresentation of the conceptual model. Amathematical model might include coupled algebraic,ordinary or partial differential, or integral equationsthat approximate the physical processes for a specifiedportion of the site conceptual model. The process bywhich the input and output of various mathematicalmodels may be linked to support the conceptual modelin order to meet the modeling objectives also plays animportant role in the selection of a computer code(s).For example, the conceptual model may include flowand transport processes in both the unsaturated andsaturated zones, in which case it would be possible toselect one code that would simulate the flow andtransport processes in the unsaturated zone at thedesired level of detail and to use this model output asinput into a second code which is capable of simulatingflow and transport within the saturated zone.Therefore, the code selection and evaluation processhas to reflect this availability to potentially dissect theconceptual model into discrete components.

The overall application of this approach willessentially be reduced to two considerations: (1) eachcomponent of the conceptual model is adequatelydescribed by the mathematical model; and (2) each ofthe separate mathematical models has beensuccessfully integrated to where the sum of the parts isequal to the whole. The second consideration is moreapplicable to the application of the code and will be farmore difficult to evaluate than the first.Each code, however, should individually meet thebasic criteria which are related to the sitecharacteristics and which have been outlined asgeneral components of the conceptual model that needto be considered when assessing the appropriateness ofa computer code (Figure 5-3).

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Figure 5-3. Physical, Chemical, and Temporal Site-Related Selection Criteria

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These broad subjects are further broken down intotheir individual components both in the table presentedas Appendix D and in the discussion presented inSections 3 and 4.

5.2.4 Criteria Based on Code Characteristics

A contaminant fate and transport model results fromthe application of a previously written or newcomputer code to a specific problem via the collectionof input data and the parameterization of sitecharacteristics. The resultant model is, therefore, amerger of a mathematical formulation, solutionmethodology, data, and ancillary information whichenhances or controls the use of the model. Therefore,in addition to selection criteria for the modelingobjectives which were presented in the previoussection, the code evaluation process must also considerattributes that are integral components of the computercode(s) including:

• Source Code Availability• History of Use• Code Documentation• Code Testing• Hardware Requirements• Code Output• Solution Methodology• Code Dimensionality

The development of selection criteria presented in thissection takes an approach consistent with industrystandards by relying on published reports pertaining tothe quality assurance and quality control in thedevelopment and application of computer codes.

Source Code Availability

To facilitate a thorough review of the generic code,detailed documentation of the code and itsdevelopmental history is required. Also, the sourcecode must be available for inspection (Figure 5-4). Inaddition, to ensure independent evaluation of thereproducibility of the verification and validationresults, the computer source code as well as thecompiled version of the code (i.e., computer code inmachine language) should be available for use by thereviewer, together with files containing the originaltest data used in the code's verification and validation.

History of Use

Much of the information needed for a thorough codeevaluation can be obtained from the author ordistributor of the code (Figure 5-4). In fact, inabilityto obtain the necessary publications can be anindication that the code is either not well documentedor that the code is not widely used. In either case, theinaccessibility of the documentation and relatedpublications should be strong grounds for deciding thatthe code is unacceptable.

The acceptance and evaluation process should rely onuser opinions and published information in addition tohands-on experience and testing. User opinions areespecially valuable in determining whether the codefunctions as documented or has significant errors orshortcomings. In some instances, users independent ofthe developer have performed extensive testing andbench-marking or are familiar with published papersdocumenting the use of the code. Users will also havefirst-hand knowledge about how easy it is to use thecode and what level of experience is required.

Quality Assurance

It is recommended that code selection criteria beclosely tied to the quality assurance criteria which werefollowed during the development of the computer code.These criteria will be associated with the adequacy ofthe code testing and documentation (Figure 5-5).

Quality assurance in modeling is the procedural andoperational framework put in place by the organizationmanaging the modeling study, to assure technicallyand scientifically adequate execution of all projecttasks included in the study, and to assure that allmodeling-based analysis is verifiable and defensible(TAY85).

The two major elements of quality assurance arequality control and quality assessment. Quality controlrefers to the procedures that ensure the quality of thefinal product. These procedures include the use ofappropriate methodology in

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Figure 5-4. Source Code Availability and History of Use Selection Criteria

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Figure 5-5. Quality Assurance Selection Criteria

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developing and applying computer simulation codes,adequate verification and validation procedures, andproper usage of the selected methods and codes(HEI92). To monitor the quality control proceduresand to evaluate the quality of the studies, qualityassessment is applied (HEI89).

Software quality assurance (SQA) consists of theapplication of procedures, techniques, and toolsthrough the software life cycle, to ensure that theproducts conform to pre-specified requirements(BRY87). This requires that in the initial stage of thesoftware development project, appropriate SQAprocedures (e.g., auditing, design inspection, codeinspection, error-prone analysis, functional testing,logical testing, path testing, reviewing, walk-through),and tools (e.g., text-editors, software debuggers, sourcecode comparitors, language processors) need to beidentified and the software design criteria bedetermined (HEI92).

Quality assurance for code development andmaintenance implies a systematic approach, startingwith the careful formulation of code design objectives,criteria and standards, followed by an implementationstrategy. The implementation strategy includes thedesign of the code structure and a description of theway in which software engineering principles will beapplied to the code. In this planning stage, measuresare to be taken to ensure complete documentation ofcode design and implementation, record keeping of thecoding process, description of the purpose andstructure of each code segment (functions,subroutines), and record-keeping of the codeverification process.

Records for the coding and verification process mayinclude: a description of the fundamental algorithmsdescribing the physical process(es) which are to bemodeled; the means by which the mathematicalalgorithms have been translated into computer code(e.g., Fortran); results of discrete checks on thesubroutines for accuracy; and comparisons among thecodes' numerical solutions with either analytical orother independently verified numerical solutions.

Code verification or testing ensures that the underlyingmathematical algorithms have been correctlytranslated into computer code. The verificationprocess varies for different codes and ranges fromsimply checking the results of a plotting routine tocomparing the results of the computer code to known

analytical solutions or to results from other verifiedcodes.

Traceability describes the ability of the computeranalyst to identify the software which was used toperform a particular calculation, including its name,date, and version number, while retrievability refers tothe availability of the same version of the software forfurther use.

Code Documentation

Detailed guidelines for the preparation ofcomprehensive software documentation are given bythe Federal Computer Performance Evaluation andSimulation Center (FED81). This publicationdiscusses the structure recommended for four types ofmanuals providing model information for managers,users, analysts and programmers. According toFEDSIM (1981), the manager's summary manualshould contain a model description, modeldevelopment history, an experimentation report, and adiscussion of current and future applications.Currently, ASTM (American Society for Testing andMaterials) is developing a standard ground-water codedescription for this specific purpose (HEI92).

As discussed in van der Heijde (1992), the codedocumentation should include a description of thetheoretical framework represented by the genericmodel on which the code is based, code structure andlanguage standards applied, and code use instructionsregarding model setup and code execution parameters.Furthermore, the documentation should also include acomplete treatment of the equations on which thegeneric model is based, the underlying mathematicaland conceptual assumptions, the boundary conditionsthat are incorporated in the model, the method andalgorithms used to solve the equations, and thelimiting conditions resulting from the chosenapproach. The documentation should also includeuser's instructions for implementing and operating thecode, and preparing data files. It should presentexamples of model formulation (e.g., grid design,assignment of boundary conditions), complete withinput and output file descriptions and include anextensive code verification and validation or fieldtesting report. Finally, programmer-orientateddocumentation should provide instructions for codemodification and maintenance.

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An integral part of the code development process is thepreparation of the code documentation. Thisdocumentation of QA in model development consistsof reports and files pertaining to the development ofthe model and should include (HEI92):

• A report on the development of the codeincluding the (standardized and approved)programmer's bound notebook containingdetailed descriptions of the codeverification process;

• Verification report including verificationscenarios, parameter values, boundary andinitial conditions, source-term conditions,dominant flow and transport processes;

• Orientation and spacing of the grid andjustification;

• Time-stepping scheme and justification;

• Changes and documentation of changesmade in code after baselining;

• Executable and source code version ofbaselined code;

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

• Notebook containing reference material(e.g., published papers, laboratory results,programmers rationale) used to formulatethe verification problem.

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

• record technical information that enablessystem and program changes to be madequickly and effectively;

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

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

• increase program sharing potential;

• facilitate auditing and verification ofprogram operations;

• provide managers with information toreview at significant developmentalmilestones so that they may independentlydetermine that project requirements havebeen met and that resources shouldcontinue to be expended;

• reduce disruptive effects of personnelturnover;

• facilitate understanding among managers,developers, programmers, operators, andusers by providing information aboutmaintenance, training, and changes in andoperation of the software;

• inform other potential users of thefunctions and capabilities of the software,so that they can determine whether itserves 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.

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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 internallywell documented; where possible, self-explanatoryparameter, variable, subroutine, and function namesshould be used.

Code Testing

Before a code can be used as a planning and decision-making tool, its credentials must be establishedthrough systematic testing of the code's correctness andevaluation of the code's performance characteristics(HEI89). Of the two major approaches available, theevaluation or review process is rather qualitative innature, while code-testing results can be expressedusing quantitative performance measures.

Code testing (or code verification) is aimed atdetecting programming errors, testing embeddedalgorithms, and evaluating the operationalcharacteristics of the code through its execution oncarefully selected example test problems and test datasets. ASTM84 defines verification as the examinationof the numerical technique in the computer code toascertain that it truly represents the conceptual model,and that there are no inherent problems with obtaininga correct solution.

At this point, it is necessary to point out the distinctionbetween generic simulation codes based on ananalytical solution of the governing equation(s)(Appendix C) and codes that include a numericalsolution. Verification of a coded analytical solution isrestricted to comparison with independently calculatedresults using the same mathematical expression, i.e.,manual calculations, using the results from computerprograms coded independently by third partyprogrammers. Verification of a code formulated withnumerical methods might take two forms: (1)comparison with analytical solutions, and (2) codeintercomparison between numerically based codes,representing the same generic simulation model, usingsynthetic data sets.

It is important to distinguish between code testing andmodel testing. Code testing is limited to establishingthe correctness of the computer code with respect tothe criteria and requirements for which it is designed(e.g., to represent the mathematical model). Modeltesting (or model validation) is more inclusive thancode testing, as it represents the final step indetermining the validity of the quantitativerelationships derived for the real-world system themodel is designed to simulate.

Attempts to validate models must address the issue ofspatial and temporal variability when comparingmodel predictions with limited field observations. Ifsufficient field data are obtained to derive theprobability distribution of contaminant concentrations,the results of a stochastic model can be compareddirectly. For a deterministic model, however, thetraditional approach has been to vary the input datawithin its expected range of variability (or uncertainty)and determine whether the model results satisfactorilymatch historical field measured values. This code-testing exercise is sometimes referred to as historymatching.

Konikow and Bredehoeft (KON92) present acompelling argument that computer models cannot betruly validated but can only be invalidated. Asreported by Hawking (HAW88), any physical theory isonly provisional, in the sense that it is only ahypothesis that can never be proven. No matter howmany times the results of the experiments agree withsome theory, there is never complete certainty that thenext test will not contradict the theory. On the otherhand, a theory can be disproven by finding even asingle observation that disagrees with the predictionsof the theory.

From a philosophical perspective, it is difficult todevelop selection criteria for a model validationprocess which may be intrinsically flawed. However,the average strategy presented in this chapter providessome assurance that the code selected has the highestprobability of most accurately representing theconceptual model.

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Hardware Requirements

In general, hardware requirements should rarely be adiscriminatory factor in the selection of a computercode (Figure 5-6). However, a number of the availablecodes require very sophisticated hardware, not so muchbecause of the intrinsic requirements of the code butbecause the simulated processes may be very complexand require time-consuming solution methods.Therefore, hardware requirements should be clearlyidentified for the code itself and be consistent with thehardware available to the user.

Mathematical Solution Methodology

Every ground-water or contaminant transport model isbased upon a set of mathematical equations. Solutionmethodology refers to the strategy and techniques usedto solve these equations. In ground-water modeling,the equations are normally solved for head (waterelevations in the subsurface) and/or contaminantconcentrations.

Mathematical methods can be broadly classified aseither deterministic or stochastic (Figure 5-7).Deterministic methods assume that a system or processoperates such that the occurrence of a given set ofevents leads to a uniquely definable outcome.Stochastic methods pre-suppose the outcome to beuncertain and are structured to account for thisuncertainty.

Most stochastic methods are not completely stochasticin that they often utilize a deterministic representationof soil processes and derive their stochastic naturefrom their representation of inputs and/or spatialvariation of soil characteristics and resulting chemicalmovement (i.e., Monte Carlo). While the deterministicapproach results in a specific value of a soil variable(e.g., solute concentration) at pre-specified points inthe domain, the stochastic approach provides theprobability (within a level of confidence) of a specificvalue occurring at any point.

Deterministic methods may be broadly classified aseither analytical or numerical. Analytical methodsusually involve approximate or exact solutions tosimplified forms of the differential equations for watermovement and solute transport. Simple analyticalmethods are based on the solution of applicabledifferential equations which make a simplifiedidealization of the field and give qualitative estimates

of the extent of contaminant transport. Such modelsare simpler to use than numerical models and cangenerally be solved with the aid of a calculator,although computers are also used. Analytical modelsare restricted to simplified representations of thephysical situations and generally require only limitedsite-specific input data. They are useful for screeningsites and scoping the problem to determine data needsor the applicability of more detailed numerical models.

Analytical solutions are used in modelinginvestigations to solve many different kinds ofproblems. For example, aquifer parameters areobtained from aquifer pumping and tracer teststhrough the use of analytical models, and ground-waterflow and contaminant transport rates can also beestimated with the use of analytical models.

Numerical models provide solutions to the differentialequations describing water movement and solutetransport using numerical methods such as finitedifferences and finite elements. Numerical methodsaccount for complex geometry and heterogenousmedia, as well as dispersion, diffusion, and chemicalretardation processes (e.g., sorption, precipitation,radioactive decay, ion exchange, degradation). Thesemethods almost always require a digital computer,greater quantities of data than analytical modeling, andexperienced modelers.

The validity of the results from mathematical modelsdepends strongly on the quality and quantity of theinput data. Stochastic, numerical, and analytical codeshave strengths and weaknesses inherent within theirformulations, all of which need to be considered priorto their selection.

Code Output

One aspect of the computer code that is frequentlyignored in the selection process is the form of themodel output (Figure 5-8). It is true, however, that inmost instances the actual output can be fashioned intothe desired format, provided the model itself isconsistent with required output (e.g., output in threedimensions cannot be obtained with a two-dimensionalmodel).

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Figure 5-6. Hardware Requirements Selection Criteria

Figure 5-7. Mathematical Solution Methodology Acceptance Criteria

5-19

Figure 5-8. Code Output Selection Criteria

5-20

In general, the model output is expressed in terms ofhydraulic head, pressure, velocities, or soluteconcentrations. The spatial coverage of parameteroutput values is either dependent on the frequency ofnodal spacing (numerical) or on the number ofspecified x and y coordinates (analytical) which areincluded in the model input files. Model output willalso vary due to the inherent nature of the code itself.For example, codes that simulate movement in theunsaturated zone generally produce saturation profiles.These profiles indicate the percentage of the pore spacethat is filled with water, whereas saturated zone codeshave no need for this capability because all of the poresbelow the water table are assumed to be filledcompletely with water. The single most importantcode selection criteria, relative to the model output,would be that the code provides mass-balanceinformation. A mass-balance determination is a checkto ensure that the amount of water or contaminantmass entering the system equals the amount exiting thesystem plus the change in the quantity stored in thesystem. If there is a significant discrepancy in themodel's mass balance, something may be wrong withthe numerical solution, although errors in the massbalance may also indicate problems with the mass-balance formulation itself. Therefore, mass-balanceinformation not only provides a check on themathematical formulations within the code, but alsoassists in ensuring that input parameter conversionsand other errors have not been made. It is notuncommon for codes that do include mass-balanceoutput to provide information (e.g., fluxes, heads) onspecific boundaries as well as the source term, all ofwhich can be used in the interpretation and evaluationof the predicted flow and solute transport directionsand rates.

Code Dimensionality

The determination as to the number of dimensions thata code should be capable of simulating is basedprimarily upon the modeling objectives and thedimensionality of the processes the code is designed tosimulate (Figure 5-9).

In determining how many dimensions are necessary tomeet the objectives, it becomes necessary to gain abasic understanding of how the physical processes(e.g., ground-water flow and transport) are affected bythe exclusion or inclusion of an additional dimension.It should be kept in mind that the movement of groundwater and contaminants is usually controlled by

advective and dispersive processes which areinherently three-dimensional. Advection is moreresponsible for the length of time (i.e., travel time) ittakes for a contaminant to travel from the source termto a downgradient receptor, while dispersion directlyinfluences the concentration of the contaminant alongits travel path. This fact is very important in that itprovides an intuitive sense for the effect dimensionalityhas on contaminant migration rates andconcentrations.

As a general rule, the fewer the dimensions, the morethe model results will over-estimate concentrations andunder-estimate travel times. In a model with fewerdimensions, predicted concentrations will generally begreater because dispersion, which is a three-dimensional process, will be dimension limited andwill not occur to the same degree as it actually wouldin the field. Similarly, predicted travel times will beshorter than the actual travel time, not because of achange in the contaminant velocities but because amore direct travel path is assumed. Therefore, thelower dimensionality models tend to be moreconservative in their predictions and are frequentlyused for screening analyses.

One-dimensional simulations of contaminant transportusually ignore dispersion altogether, andcontamination is assumed to migrate solely byadvection, which may result in a highly conservativeapproximation. Vertical analyses in one dimension aregenerally reserved for evaluating flow and transport inthe unsaturated zone. Two-dimensional analyses of anaquifer flow system can be performed as either aplanar representation, where flow and transport areassumed to be horizontal (i.e., longitudinal andtransverse components), or as a cross section whereflow and transport components are confined to verticaland horizontal components.

In most instances, two-dimensional analyses areperformed in an areal orientation, with the exceptionof the unsaturated zone, and are based on theassumption that most contaminants enter the saturatedsystem from above and that little vertical dispersionoccurs. However, a number of limitations accompanytwo-dimensional planar simulations. These includethe inability to simulate multiple layers (e.g., aquifersand aquitards) as well as any partial penetrationeffects. Furthermore, because vertical

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Figure 5-9. Code Dimensionality Selection Criteria

5-22

components of flow are ignored, an artificial lowerboundary on contaminant migration has beenautomatically assumed which may or may not be thecase.

A two-dimensional formulation of the flow system isfrequently sufficient for the purposes of riskassessment provided that flow and transport in thecontaminated aquifer are essentially horizontal. Theadded complexities of a site-wide, three-dimensionalflow and transport simulation are often believed tooutweigh the expected improvement in the evaluationof risk. Complexities include limited site-widehydraulic head and lithologic data with depth andsignificantly increased computational demands.

Quasi-three-dimensional analyses remove some of thelimitations inherent in two-dimensional analyses.Most notably, quasi-three-dimensional simulationsallow for the incorporation of multiple layers; however,flow and transport in the aquifers are still restrained tolongitudinal and transverse horizontal components,whereas flow and transport in the aquitards are evenfurther restricted to vertical flow components only.Although partial penetration effects still cannot beaccommodated in quasi-three-dimensional analyses,this method can sometimes provide a goodcompromise between the relatively simplistic two-dimensional analysis and the complex, fully three-dimensional analysis. This is the case, particularly ifvertical movement of contaminants or recharge fromthe shallow aquifer through a confining unit and intoa deeper aquifer is suspected.

Fully three-dimensional modeling generally allowsboth the geology and all of the dominant flow andtransport processes to be described in threedimensions. This approach usually affords the mostreliable means of predicting ground-water flow andcontaminant transport characteristics, provided thatsufficient representative data are available for the site.

Although the intrinsic dimensionality of the codeshould be an important consideration relative to theacceptance or rejection of the code, this determinationwill also be closely tied to the code application andmodeling objectives.

Ref-1

REFERENCES

AND92 Anderson, M.P., and W.W. Woessner, 1992. Applied Groundwater Modeling: Simulation of Flowand Advective Transport. Academic Press, Inc., San Diego, California.

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

BAE83 Baes, C.F., and R.D. Sharp, 1983. "A Proposal for Estimation of Soil Leaching Constants for Use inAssessment Models," Journal of Environmental Quality, 12 (1):17, January - March 1983.

BAC80 Bachmat, Y., J. Bredehoeft, B. Andrews, D. Holtz, and S. Sebastian, 1980. Ground-WaterManagement: The use of numerical models, Water Resources Monograph 5, American GeophysicalUnion, Washington, D.C., 127 pp.

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

DOE91 Department of Energy, 1991. Ground-Water Model Development Plan in Support of RiskAssessment, Decisional Draft, RL-91-62.

EPA88 Environmental Protection Agency, 1988. "Guidance for Conducting Remedial Investigations andFeasibility Studies Under CERCLA," EPA/540/G-89/004, OSWER Directive 9355.3-01, October1988.

EPA90 Environmental Protection Agency, OSWER, 1990. OSWER Models Management Initiative: reporton the usage of computer models in hazardous waste/superfund programs, Phase II Final Report,December 1990.

EPA91 Environmental Protection Agency, 1991. Integrated Model Evaluation System (IMES), prepared forOffice of Health and Environmental Assessment, Exposure Assessment Group, Washington, D.C.

EPA93 Environmental Protection Agency, "Environmental Pathway Models - Ground-Water Modeling inSupport of Remedial Decision Making at Sites Contaminated with Radioactive Material," EPA 402-R-93-009, March 1993.

FED81 Federal Computer Performance Evaluation and Simulation Center (FEDSIM), 1981. ComputerModel Documentation Guide. NBS Special Publ. 500-73, Inst. for Computer Science andTechnology, Nat. Bur. of Standards, U.S. Dept. of Commerce, Washington, D.C.

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

GIL88 Gilbert, T.L., M.J. Jusko, K.F. Eckerman, W.R. Hansen, W.E. Kennedy, Jr., B.A. Napier, andJ.K. Soldat. "A Manual for Implementing Residual Radioactive Material Guidelines" (RES-RAD),U.S. Department of Energy, 1988, 217 pp.

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GRA6-1 Environmental Protection Agency, 1992. Ground-Water Modeling Compendium, EPA/540/G-88/003.

GRA6-1 Environmental Protection Agency. Basics of Pump and Treat Ground-Water RemediationTechnology, EPA/600/9-90/003.

GRA6-1 Environmental Protection Agency, 1988. Guidance on Remedial Actions for Contaminated GroundWater at Superfund Sites, EPA/540/G-88/003.

GRA6-1 EPA, 1988. Superfund Exposure Assessment Manual, EPA/540/1-88/001.

HAW88 Hawking, S.W., 1988. A Brief History of Time: From the Big Bank to Black Holes. Bantam Books,New York, 1988.

HEI92 van der Heijde, P.K.M., and O.A. Elnawawy, 1992. Compilation of Ground-water Models. GWMI91-06. 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 Groundwater Modeling. GWMI 89-04. Internat. Ground Water Modeling Center, Holcomb Research Inst., Indianapolis,Indiana.

HEI88 van der Heijde, P.K.M., and M.S. Beljin, 1988. Model Assessment for Delineating WellheadProtection Areas. EPA 440/6-88-002, Office of Ground-Water Protection, U.S. EnvironmentalProtection Agency, Washington, D.C.

HUY91 Huyakorn, P.S., J.B. Kool and Y.S. Wu, October 1991. VAM2D - Variability Saturated AnalysisModel in Two Dimensions, Version 5.2 with Hysteresis and Chain Decay Transport. NUREG/CR-5352, Rev. 1. U.S. Nuclear Regulatory Commission, Washington, D.C.

KON78 Konikow, L., and J. Bredehoeft, 1978. Computer model of two-dimensional solute transport anddispersion in ground water, U. S. Geological Survey Water Resources Investigation, Book 7, ChapterC2.

KON92 Konikow, L.F., and J.D. Bredehoeft, 1992. Ground-Water Models Cannot be Validated. Advancesin Water Resources SWRENI 15(1): 75-83.

MCD88 McDonald, M.G., and A.W. Harbaugh, 1988. A Modular Three-Dimensional Finite-DifferenceGround-Water Flow Model. U. S. Geological Survey TWRI, Book 6, Chapter A1.

MER81 Mercer, J.W., and C.R. Faust, 1981. Ground Water Modeling, Nat. Water Well Assoc., Dublin,Ohio.

MOS92 Moskowitz, P., R. Pardi, M. DePhillips, and A. Meinhold, 1992. Computer models used to supportcleanup decision making at hazardous waste sites, Brookhaven National Laboratory.

NRC86 Nuclear Regulatory Commission, 1986. "Update of Part 61 Impacts Analysis Methodology,"Prepared by O.I. Oztunali, W.D. Pon, R. Eng, and G.W. Roles, NUREG/CR-4370, January 1986.

NRC90 Nuclear Regulatory Commission, 1990. "Background Information for the Development of a Low-Level Waste Performance Assessment Methodology. Computer Code Implementation andAssessment," Prepared by Sandia National Laboratory, NUREG/CR-5453, August 1990.

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NRC90a Nuclear Regulatory Commission, 1990. "Performance Assessment Methodologies for Low-LevelWaste Facilities," Prepared by Sandia National Laboratory, NUREG/CR-5532, July 1990.

PAR92 Pardi, R.R., Daum, M.L., and Moskowitz, P.D., 1992. Environmental Characteristics of EPA, NRC,and DOE Sites Contaminated with Radioactive Substances. U. S. Environmental Protection Agency,Office of Radiation Programs, Washington, D.C.

SHE90 Sheppard, M.I., and E.L. Gershey, 1990. "Default Solid Soil/Liquid Partition Coefficients, Kds, forFour Major Soil Types: A Compendium," Health Physics, 59 (4):471, October 1990.

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

ZHE90 Zheng, C., 1990. A Modular Three-Dimensional Transport Model for Simulation of Advection,Dispersion, and Chemical Reactions of Contaminants in Ground-Water Systems, Prepared for theUnited States Environmental Protection Agency, Robert S. Kerr Environmental Research Laboratory,Ada, Oklahoma.

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BIBLIOGRAPHY

Barney, G.S., J.D. Navratil, and W.W. Schultz, 1984. Geochemical Behavior of Disposed Radioactive Waste,American Chemical Society, Washington, D.C.

Bear, J., 1979. Hydraulics of Ground Water. McGraw-Hill Book Company.

Boonstra, J. and N.A. de Ridder, 1981. Numerical Modeling of Ground-Water Basins. ILRI Publication 29.

de Marsily, G., 1986. Quantitative Hydrogeology. Ground-Water Hydrology for Engineers, Academic Press, Inc.

Drever, J.I., 1982. The Geochemistry of Natural Waters. Prentice-Hall Inc., Englewood Cliffs, N.J.

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Environmental Protection Agency, 1987. "The Use of Models in Managing Ground-Water Protection Programs,"EPA/600/8-87/003, Robert S. Kerr Environmental Research Laboratory.

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APPENDIX A

GLOSSARY

A-2

GLOSSARY

ACTINIDES - Elements 90 through 103.

ADSORPTION - Physical attraction and adhesion of gas, vapor, or dissolved molecules to the surface of solidswithout chemical reaction.

ADVECTION - The process by which solutes are transported by the bulk motion of flowing ground water.

ALLUVIAL FLOODPLAIN - The lowland adjacent to a river, usually dry but subject to flooding when the riveroverflows its banks. It is that flat area constructed by the present river in the present climate. It is built ofalluvium carried by the river during floods and deposited in the sluggish water beyond the influence of the swiftestcurrent.

ANALYTICAL MODEL - A model based on known initial and boundary conditions which incorporates acontinuous exact solution of a simple flow or solute transport equation such as Darcy's Law. Analytical models areordinarily restricted to conditions of homogeneous, isotropic flow, and transport.

ANION EXCLUSION - Negatively charged rock surfaces can affect the movement of anions, by either retardingthe movement of anions by not allowing negatively charged radionuclides to pass through the pore opening or byenhancing the transport of ions by restricting the anion movement to the center of the pore channel where ground-water velocities are higher.

ANISOTROPIC - Having some physical property that varies with direction of flow.

AQUIFER - A unit of porous material capable of storing and transmitting appreciable quantities of water to wells.

AQUITARD - A saturated, but poorly permeable bed, formation, or group of formations that can store groundwater and also transmit it slowly from one aquifer to another.

ARTESIAN WELL - A well deriving its water from a confined aquifer in which the water level in the casingstands above the top of the confined aquifer.

BASALT - A general term for dark-colored iron- and magnesium-rich igneous rocks, commonly extrusive, butlocally intrusive. It is the principal rock type making up the ocean floor.

BEDROCK - A general term for the rock, usually solid, that underlies soil or other unconsolidated material.

BIOFIXATION - The binding of radionuclides to the soil/organic matrix due to the action of some types ofmicroorganisms and plants, thus affecting mobility of the radionuclide.

BULK DENSITY - The mass or weight of oven-dry soil per unit bulk volume, including air space.

CALIBRATION - The process by which a set of values for aquifer parameters and stresses is found thatapproximates field-measured heads and flows. It is performed by trial-and-error adjustment of parameters andboundary conditions or by using an automated parameter estimation code.

CAPTURE ZONE - The portion of the flow system that contributes water to a well or a surface water body suchas a river, ditch, or lake.

A-3

CHAIN DECAY - Form of radioactive decay in which several daughter products may be produced before theparent species decays to a stable element.

CLAY - (Clay particles are mineral particles < 0.002 mm. in diameter). In the grading of soils by texture, clay isthe extreme of fineness.

CONFINED AQUIFER - An aquifer which is overlain by a unit of porous material that retards the movement ofwater.

CURVILINEAR ELEMENTS - Specialized elements used by finite-element computer codes that can be spatiallydeformed to mimic the elevations of the upper and lower surfaces of the hydrogeologic units.

DARCY'S LAW - A derived equation that can be used to compute the quantity of water flowing through anaquifer assuming that the flow is laminar and inertia can be neglected.

DETERMINISTIC MODEL - A model whose output is fixed by the mathematical form of its equations and theselection of a single value for each input parameter.

DIP - The angle to the horizontal (slope) that a geologic unit may have.

DISCHARGE - The volume of water flowing in a stream or through an aquifer past a specific point in a givenperiod of time.

DISPERSION - A mixing phenomenon linked primarily to the heterogeneity of the microscopic velocities insidethe porous medium.

DISTRIBUTION COEFFICIENT - The slope of a linear Freundlich isotherm.

EFFECTIVE POROSITY - The volume of the void spaces through which water or other fluids can travel in arock or sediment divided by the total volume of the rock or sediment.

FACILITATIVE TRANSPORT - A term used to describe the mechanism by which radionuclides may couplewith either naturally occurring material or other contaminants and move at much faster rates than would bepredicted by their respective distribution coefficients.

FAULT - A fracture or a zone of fractures along which there has been displacement of the sides relative to oneanother parallel to the fracture.

FINITE DIFFERENCE - A particular kind of a digital computer model based upon a rectangular grid that setsthe boundaries of the model and the nodes where the model will be solved.

FINITE ELEMENT - A digital ground-water flow model where the aquifer is divided into a mesh formed of anumber of polygonal cells.

FLOCCULATION - The agglomeration of finely divided suspended solids into larger, usually gelatinous,particles; the development of a "floc" after treatment with a coagulant by gentle stirring or mixing.

FRACTURED LITHOLOGY - Porous media which is dissected by fractures.

FREUNDLICH ISOTHERM - An empirical equation that describes the amount of solute adsorbed onto a soilsurface.

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GEOCHEMICAL FACIES - A unit of material of similar physical properties that was deposited in the samegeologic environment.

GROUT CURTAIN - An underground wall designed to stop ground-water flow; can be created by injecting groutinto the ground, which subsequently hardens to become impermeable.

GROUTING - The operation by which grout is placed between the casing and the sides of the well bore to apredetermined height above the bottom of the well. This secures the casing in place and excludes water and otherfluids from the well bore.

HETEROGENOUS - Pertaining to a substance having different characteristics in different locations.

HYDRAULIC CONDUCTIVITY - A coefficient of proportionality describing the rate at which water can movethrough a permeable medium. The density and kinematic viscosity of the water must be considered in determininghydraulic conductivity. The rate of flow of water in unit volume per unit of time through a unit cross section ofarea of geologic material under a unit hydraulic gradient, at the prevailing temperature.

HYDRAULIC GRADIENT - The change in total head with a change in distance in a given direction. Thedirection is that which yields a maximum rate of decrease in head.

HYDRODYNAMIC DISPERSION - The process by which ground water containing a solute is diluted withuncontaminated ground water as it moves through an aquifer.

HYDROFRACTURING - The process in which fluid is added to an aquifer at sufficient pressures to where thepore pressure in the rock causes the rocks to fracture.

HYDROSTATIGRAPHIC UNIT - A formation, part of a formation, or group of formations in which there aresimilar hydrologic characteristics allowing for grouping into aquifers or confining layers.

HYSTERESIS - A term which describes the fact that wetting and drying curves for a certain soil (pressure headversus volumetric water content) under partially saturated conditions, are not the same.

IMMISCIBLE - Substances that do not mix or combine readily.

IN-SITU VITRIFICATION - Process by which electrodes are used to heat the soil-waste matrix to temperatureshigh enough to melt soils and destroy organics by pyrolysis.

INTRINSIC PERMEABILITY - Pertaining to the relative ease with which a porous medium can transmit aliquid under a hydraulic or potential gradient. It is a property of the porous medium and is independent of thenature of the liquid or the potential field.

INVERSE MODEL - The model in which values of the parameters and the hydrologic stresses are determinedfrom the information about heads.

ION EXCHANGE - A process by which an ion in a mineral lattice is replaced by another ion that was present inan aqueous solution.

LANGMUIR ISOTHERM - An empirical equation that describes the amount of solute adsorbed onto a soilsurface.

LAYERED LITHOLOGY - Interbedded geologic units (e.g., sand, clay, gravel).

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LEACH - The removal of soluble chemical elements or compounds by the passage of water through the soil.

LEACHATE - Water that contains a high amount of dissolved solids and is created by liquid seeping from alandfill.

LIMESTONE - A sedimentary rock consisting chiefly of calcium carbonate, primarily in the form of the mineralcalcite.

LITTORAL - Pertaining to the ocean environment between the high tide and the low tide.

LOADING RATES - The rate at which contaminants and/or water enters the model domain.

LOW PERMEABILITY BARRIERS - Vertical or horizontal obstructions that are of sufficiently lowpermeability to retard significantly the migration of water and/or contaminants.

MACROPORES - Large or noncapillary pores. The pores, or voids, in a soil from which water usually drains bygravity. Is differentiated from a micropore, or capillary pore space, which consists of voids small enough thatwater is held against gravity by capillarity. Sandy soils have a large macropore, or noncapillary pore space and asmall micropore, or capillary, pore space. Non-granular clayey soils are just the reverse.

MATRIX DIFFUSION - The diffusion of radionuclides from water moving within fractures, or coarse-grainedmaterial, into the rock matrix or finer grained clays.

METAMORPHIC ROCK - Any rock derived from preexisting rocks by mineralogical, chemical, and/orstructural changes, essentially in the solid state, in response to marked changes in temperature, pressure, shearingstress, and chemical environment, generally at depth in the Earth's crust.

MOLECULAR DIFFUSION - Dispersion of a chemical caused by the kinetic activity of the ionic or molecularconstituents.

NON-AQUEOUS PHASE LIQUIDS (NAPL) - Liquids that are immiscible in water.

NUMERICAL MODEL - One of five methods (finite-difference, finite element, integrated finite difference,boundary integral equation method, and analytical elements) used to approximate by means of algebraic equationsthe solution of the partial differential equations (governing equation, boundary, and initial conditions) thatcomprise the mathematical model. Numerical models can be used to describe flow under complex boundaryconditions and where aquifer parameters vary within the model area.

ORGANIC COMPLEXATION - The formation of organic complexes by the combination of organic material orradionuclides.

PARTICLE TRACK - The movement of infinitely small imaginary particles placed in the flow field.

PARTITIONING - The process by which a contaminant, which was originally in solution, becomes distributedbetween the solution and the solid phase.

PERCHED WATER - Unconfined ground water separated from an underlying main body of ground water by anunsaturated zone.

POROUS MEDIA - Rocks that are not dissected by discrete features (e.g., macropores, fractures).

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PROPRIETARY - A code in which the ownership rights are held by a company or organization.

RADIAL FLOW - The flow of water in an aquifer toward a vertically oriented well.

RADIOACTIVE DECAY - The change of a nucleus into another nucleus (or a more stable form of the samenucleus) by the loss of a small particle or a gamma ray photon.

RECHARGE - The addition of water to the zone of saturation; also, the amount of water added.

RETARDATION FACTOR/COEFFICIENT - A measure of the capability of adsorption within the porousmedia to impede the movement of a particular radionuclide being carried by the fluid.

SANDSTONE - A sedimentary rock composed of abundant rounded or angular fragments of sand set in a fine-grained matrix (silt or clay) and more or less firmly united by a cementing material.

SATURATED ZONE - The zone in which the voids in the rock or soil are filled with water at a pressure greaterthan atmospheric. The water table is the top of the saturated zone in an unconfined aquifer.

SECONDAY MINERALIZATION - Mineralization that occurred later than the rock enclosing it.

SEDIMENTARY ENVIRONMENT - An environment in which the rocks are formed by the accumulation andcementation of mineral grains transported by wind, water, or ice to the site of deposition or chemically precipitatedat the site of deposition.

SHALE - A fine-grained sedimentary rock, formed by the consolidation of clay, silt, or mud. It is characterized byfinely laminated structure and is sufficiently indurated so that it will not fall apart on wetting.

SILT - Soil particles between 1/256 and 1/2 mm in diameter, smaller than sand and larger than clay.

SOLUTION FEATURES - An opening resulting from the decomposition of less soluble rocks by waterpenetrating pre-existing interstices, followed by the removal of the decomposition products.

SOURCE TERM - The quantity of radioactive material released to the biosphere, usually expressed as activity perunit time. Source terms should be characterized by the identification of specific radionuclides and their physicaland chemical forms.

SPECIATION - The chemical form of the radionuclide, which can influence its solubility and therefore its rate oftransport by limiting the maximum concentration of the element dissolved in the aqueous phase.

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APPENDIX B

GROUND-WATER MODELING RESOURCES

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ELECTRONIC MEDIA-BASED SOURCES OF ASSISTANCE

Bulletin Boards

Access to bulletin boards is made via modem either by direct dialing or through a communication system like TELNETor TYMNET. Access to most systems is controlled by the use of login protocols and passwords obtained from thesystem operator. Examples of existing systems include:

Name: ORB-BBSPurpose: Information about ORD operations and software available through ORDMaintained by: U. S. Environmental Protection Agency

Office of Research and DevelopmentCincinnati, Ohio

System Operator: Charles W. GulonModem Phone(s): (513) 569-7610 (1200-2400 bps)

(800) 258-9605 (1200-9600 bps)(513) 569-7700 (1200-9600 bps)(513) 569-7272

Communication Parameters: 1200, 2400, 4800, 9600 - N-8-1Hours/Cost: 24 hours/7 days - Free

Name: CEAMPurpose: Supports the use of exposure assessment models, especially

those used to model the transport of agricultural chemicals.Maintained by: U. S. EPA

Office of Research and DevelopmentAthens, Georgia

System Operator: David DisneyModem Phone(s): (706) 546-3402

(FTS) 250-3549Voice Phone(s): (706) 546-3590

(706) 546-3136Communication Parameters: 1200, 2400 - N-8-1Hours/Cost: 24 hours/7 days - Free

Name: CSMoSPurpose: The Center for Subsurface Modeling Support (CSMoS) provides ground-water modeling

software and services to public agencies and private companies throughout the nation.Maintained by: U.S. Environmental Protection Agency

Center for Subsurface Modeling SupportR.S. Kerr Environmental Research Laboratory

System Operator: Dr. David S. BurdenVoice Phone(s): (405) 332-8800

Bulletin Boards (Continued)

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Name: CLU-INPurpose: Current events information for hazardous waste cleanup professionals,

innovative technologies, and access to databases.Maintained by: U. S. EPA

Office of Solid Waste and Emergency ResponseTechnology Innovation OfficeWashington, D.C.

System Operator: Dan PowellModem Phone(s): (301) 589-8366Voice Phone(s): (301) 589-8368Communication Parameters: 1200, 2400 - N-8-1Hours/Cost: 24 hours/7 days - Free

Name: USGS BBSPurpose: General information from USGSMaintained by: U. S. Geological SurveySystem Operator:Modem Phone(s): (703) 648-7127

(703) 648-4168Voice Phone(s): (703) 648-7000Communication Parameters:Hours/Cost: CD-ROM conference is Free

Name: ESDDPurpose: Earth Science Data Directory - list of nationwide databases of earth

science dataMaintained by: U. S. Geological Survey

Reston, VirginiaSystem Operator: Joe KemperModem Phone(s): (703) 648-4100

(703) 648-4200Voice Phone(s): (703) 648-7112\Communication Parameters: 300, 1200, 2400, 9600 - 7-M-1Hours/Cost: Free (call voice phone for ID number)

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Networks

In order to join a network conference, you must have access to a computer system that is a node in that network.Access to the network can then be made by subscribing to a LISTSERV or joining a newsgroup. Subscribing to aLISTSERV is accomplished using the e-mail facility of a local node. A simple mail message is sent, SUB name, wherename is one of the address names below. Mail from that network conference will then appear in the user's e-mailbox.Unsubscribing is accomplished by sending the message UNSUB name.

In addition, if the remote system permits, the user can access the remote node of the network via software like filetransfer protocol (FTP). Within a system like ftp, the user has direct access to the remote node as if it were a localcomputer, and in some cases, software on the remote system can be run and the results later transferred to the localnode.

To FTP a remote site, the user types ftp node from the local node where node is one of the address names below. Inmost cases, the remote node will require a login name and password if the ftp process is successful. The login nameis often anonymous and the password guest, although other login strings are often called for and can only bedetermined by contacting the individual in charge of the remote system.

Name: AQUIFER@BACSATANetwork: BITNETPurpose: Discussion group on various ground-water protection issues.Access: LISTSERV

Expert Systems

Name: Integrated Model Evaluation SystemSource: Environmental Protection Agency

Office of Solid Waste and Emergency ResponseVersar, Inc.Ecological Sciences and Analysis Division9200 Runsey RoadColumbia, Maryland 21045

System Requirements: MSDOSCost: Not yet determined

Name: GMSYSPurpose: Estimate leach rates from landfillsSource: ORD-BBSCost: Free

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APPENDIX C

SOLUTION METHODOLOGY

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APPENDIX C

Solution Methodology

Every ground-water model is based upon a set ofmathematical equations. Solution methodology refersto the strategy and techniques used to solve theseequations. In ground-water modeling, the equationsare normally solved for head (water elevations in thesubsurface) and/or contaminant concentrations.

Mathematical methods developed to solve the ground-water flow and transport equations can be broadlyclassified as either deterministic or stochastic.Deterministic methods assume that a system or processoperates such that the occurrence of a given set ofevents leads to a uniquely definable outcome, whilestochastic methods presuppose the outcome to beuncertain and are structured to account for thisuncertainty.

Most of the stochastic methods are not completelystochastic in that they often utilize a deterministicrepresentation of soil processes and derive theirstochastic nature from their representation of inputsand/or spatial variation of soil characteristics andresulting chemical movement. While the deterministicapproach results in a specific value of a soil variable(e.g., solute concentration) at pre-specified points inthe domain, the stochastic approach provides theprobability (within a level of confidence) of a specificvalue occurring at any point.

The development of stochastic methods for solvingground-water flow is a relatively recent endeavor thathas occurred as a result of the growing awareness ofthe importance of intrinsic variability of thehydrogeologic environment. Stochastic methods arestill primarily research tools; however, as computerspeeds continue to increase, stochastic methods will beable to move further away from the research- orientedcommunity and more into mainstream managementapplications. The more widespread use ofdeterministic methods suggests a more immediate needfor code-selection guidance. Therefore, this sectionfocuses primarily on deterministic methods.

Deterministic methods may be broadly classified aseither analytical or numerical. Analytical methods

usually involve approximate or exact solutions tosimplified forms of the differential equations for watermovement and solute transport. Simple analyticalmethods are based on the solution of applicabledifferential equations which make a simplifiedidealization of the field and give qualitative estimatesof the extent of contaminant transport. Such modelsare simpler to use than numerical models and cangenerally be solved with the aid of a calculator,although computers are also used. Analytical modelsare restricted to simplified representations of thephysical situations and generally require only limitedsite-specific input data. They are useful for screeningsites and scoping the problem to determine data needsor the applicability of more detailed numerical models.

Analytical models are used in ground-waterinvestigations to solve many different kinds ofproblems. For example, aquifer parameters areobtained from aquifer tests through the use ofanalytical models, and ground-water flow andcontaminant transport rates can also be estimated withthe use of analytical models. To avoid confusion, onlyanalytical models designed to estimate ground-waterflow and radionuclide transport rates are discussed inthis section.

Numerical models provide solutions to the differentialequations describing water movement and solutetransport using numerical methods such as finitedifferences and finite elements. Numerical methodscan account for complex geometry and heterogenousmedia, as well as dispersion, diffusion, and chemicalretardation processes (e.g., sorption, precipitation,radioactive decay, ion exchange, degradation). Thesemethods always require a digital computer, greaterquantities of data than analytical modeling, and anexperienced modeler-hydrogeologist.

The validity of the results from numerical modelsdepends strongly on the quality and quantity of theinput data. Numerical and analytical codes have theirrespective strengths and weaknesses which areinherent within their formulations. The fundamentalcharacteristics of both analytical and numericalmethods are presented below and are discussed in moredetail in the following sections:

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Analytical

! Provides a solution at any location and pointin time;

! Exact, closed-form solutions or well-documented, convergent solutions(approximate analytical);

! Requires regular geometry of the domain;

! Generally requires uniform materialproperties;

! 1-, 2-, or 3-D capability;

! Transient effects can be considered;

! Less prone to computational errors thannumerical methods;

! Usually requires that problems are linear;

! Low computer storage requirements;

! Data can be easily input.

Numerical

! Provides a solution only at prespecifiedlocations and moments in time;

! Approximate solutions;

! Irregular domain and boundaries can besimulated;

! Nonuniform material properties can besimulated;

! Can simulate non-linear problems;

! 1-, 2-, or 3-D capability;

! Transient effects can be considered;

! Computational errors can be a problem;

! Can require large computer storage;

! Large amount of data input.

Analytical Methods

Analytical methods that solve ground-water flow andcontaminant transport in porous media arecomparatively easy to use. However, because thegoverning equations are relatively simple, analyticalsolutions are generally restricted to either radial flowproblems or to cases where velocity is uniform over thearea of interest. Except for some radial flow problems,almost all available analytical solutions belong tosystems having a uniform and steady flow. Thismeans that the magnitude and direction of the velocitythroughout the system are invariable with respect totime and space, which requires the system to behomogeneous and isotropic with respect to thehydraulic conductivity. The three most general typesof analytical methods include the following:

! Approximate analytical

! Exact analytical

! Semi-analytical

Typical analytical solutions, which are termedapproximate, are in the form of an infinite series ofalgebraic terms, or a double infinite series, or even aninfinite series of definite integrals. Because an infiniteseries of numbers cannot be solved for exact solutions,each one of these expressions must be approximated bytruncating the series after considering a predeterminednumber of terms. If, on the other hand, the analyticalsolution can be expressed by equations which take aclosed form (finite number of terms), the solution issaid to be exact. Even though the solution may containerrors due to rounding.

In general, exact analytical equations tend to requireinfinite domains and boundaries. These constraintstypically result in solutions that are more appropriatefor solving problems of well hydraulics than thoseassociated with ground-water flow and contaminanttransport.

An obvious problem with approximate analyticalequations is that they are of an open form and may notconverge if they are inherently unstable. Therefore, itis very important that care has been taken during thecode development process to ensure that the equationsused do converge properly and that the codedocumentation provides the methods by which theconvergence was examined. It is also important to

C-4

recognize that just because a code is written usinganalytical techniques it does not mean thatconvergence may not still be a problem even if theformulation is correct.

Semi-analytical methods are more complex thananalytical methods and more simplistic than mostnumerical methods. These techniques use the conceptsfrom fluid mechanics and velocity potentials which areextended using numerical tools to construct flow andcontaminant patterns. Advantages of semi-analyticalmethods include the following:

! Require only simple computer input data anddo not require the design of a mesh as withfully numerical methods;

! May be used where complex boundaries (e.g.,multiple pumping wells) do not allowanalytical equations to be written;

! Techniques can be used to easily estimatetravel times of a conservative, retarded, ordecaying contaminant to a downgradientreceptor;

! Can provide screening information to judgethe need for more sophisticated modeling.

Limitations of semi-analytical methods include thefollowing:

! Mass transport by dispersion and diffusion isgenerally not considered, which in manycases may lead to predictions of travel timesthat are longer than actual values and mayunderestimate the true impact of acontaminant source;

! Usually are formulated in two dimensions andthree-dimensional effects are ignored;

! Heterogeneous properties of the media cannotbe simulated although some semi-analyticalmethods do allow for anisotropy;

! Most semi-analytical formulations are forsteady-state problems; however, in some casesthey can be extended to handle transientproblems.

Numerical Methods

Unfortunately, the equations of flow and continuity inthe form of partial differential equations do not lendthemselves easily to rigorous analytical solutions whenboundaries are complex. Therefore, if a realisticexpression for hydraulic head or concentration as afunction of space cannot be written from the governingequations, boundary and initial conditions, thenanalytical methods are generally abandoned and moreapproximate numerical methods are used to solve theset of equations. The most common of these methodsinclude the following:

! Finite Difference

! Integrated Finite Difference

! Finite Element

! Method of Characteristics

Of particular importance to the following discussion isthe understanding that the flow and transportequations, which describe the movement of groundwater and contaminants, are composed of both spatialand temporal terms both of which requirediscretization within the model domain. These termssimply describe the concentration or head (i.e., waterelevations) in space and time. The numerical methodsmentioned above (i.e., finite element and finitedifference) are used as discretization methods for thespatial term, whereas the time-stepping methods,discussed later in this section, are used to discretize ordescribe the temporal term.

Finite Difference

The basic idea of finite-difference methods is toreplace derivatives at a point by ratios of the changesin appropriate variables over small but finite intervals.Unlike analytical methods, where values can becalculated at any point in the problem domain,numerical methods (e.g., finite differences) makeapproximations at a predetermined finite number ofpoints and reduce a continuous boundary-valueproblem to a set of algebraic equations. Once thepartial differential equations have been converted intoa set of algebraic equations involving a number ofunknowns, the unknowns may be found by what aretermed matrix solvers.

In practice, the problem domain is divided into arectangular grid in which either the x and y

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Figure C.1 Finite Two-Dimensional Elements

intersections, called nodes, are designated as solutionpoints (i.e., mesh centered) or the solution points areat the center of the grid cell (i.e., block centered).Time step sizes are specified over the simulated timeof interest, and the mathematical expressions aresuccessively solved for each individual time step untilthe solution converges upon a value which satisfies thepredesignated convergence criteria (i.e., errortolerance).

The form of the system of equations is that the valuesof head at each nodal point are a function of x and ygrid coordinates, as well as the size of specified timesteps. The values of head are related to the values inthe surrounding nodal points and those at thebeginning and at the end of a time step. If the valuesat the beginning of a time step are known (which isusually the case), the values at the end of the time stepare the unknowns, and the resulting system ofequations is a system of N linear equations with Nunknowns. The value N indicates the total number ofmesh points. Thus, the mathematical problem to besolved is the solution of a linear system of equations.

The system of equations may turn out to be ratherlarge. For example, a grid with 50 mesh points in thex-direction and 50 mesh points in the y-direction willhave 2,500 unknowns as well as equations to besolved.

Relevant considerations related to the finite-differencemethod include:

! Uses a direct Taylor Series approximation ofthe derivative terms of the partial differentialequations at nodal points;

! Formulation is based on a rectangular (block-centered or mesh-centered) grid;

! Relatively simple to formulate as compared toother numerical methods;

! Conducive to efficient matrix solvingtechniques;

! May be sensitive to grid orientation effects insolving 2-D and 3-D flow and transportproblems;

! Use of rectangular grid necessitates staircase(or stepwise) approximation of irregularboundary and/or aquifer material zoning;

! May be prone to numerical dispersion oroscillation in solving transport problems.

A closely related alternative to the conventional finitedifference is the integrated finite-difference methodwhich uses integral approximations of the partialdifferential equations of nodal subdomains. Theprimary advantage of this method is that it willaccommodate non-rectangular grid elements, whichallow irregular boundaries to be efficiently modeled.The following, however, are the disadvantagesassociated with this method:

! Necessitates more complex grid generationscheme than the traditional finite-differencemethod;

! Subdomain boundaries surroundingindividual nodes must satisfy certainorthogonality constraints to ensure that massis conserved;

! Method leads to less efficient matrix solutiontechniques than the conventional finite-difference method.

Finite Element

While approximations to a continuous solution aredefined at isolated points by finite differences, withfinite elements, the approximate solution (i.e., heads or

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Figure C-2. Three-Dimensional Elements

concentration) is defined over the entire domain byinterpolation functions, although solutions to thefunctions are calculated only at the element nodes.This integral formulation for the governing ground-water flow or solute transport equation leads to asystem of algebraic equations that can be solved for theunknown(s) (i.e., hydraulic head, pressure head orsolute concentration) at each node in the mesh. Themethod of weighted residuals is the commonly usedgeneral approach that defines an approximate solutionto the boundary or initial value problem. When thisapproximate solution is substituted into the governingdifferential equation, an error or residual occurs ateach point (node) in the problem domain. Theweighted average of the residuals for each node in thefinite-element mesh is then forced to equal zero, thusminimizing the error between the approxi-matesolution and the actual solution. Relevantcharacteristics of the finite-element method ascompared with the finite-difference method include:

! Allows a much greater flexibility in handlingirregular domain geometry, materialheterogeneity, and/or anisotropy;

! Less prone to numerical dispersion; however,it is necessary to be more careful to limitpotential oscillation in solving the transportproblem;

! The elements do not have to be rectangular,but can also be other simple polygons(commonly triangles or quadrilaterals);

! Matrix solutions generally requiresubstantially greater computational effort andcomputer storage capability;

! Finite-element solutions are less sensitive togrid orientation.

Two typical problems that arise when solving thecontaminant transport equations are numericaldispersion and artificial oscillation. Numericaldispersion arises from grid size, time-step size, and thefact that computers have a limited accuracy, thus someof the round-off error will occur in computations. Thiserror results in the artificial spreading of contaminantdue to amplification of dispersivity. Hence, thecontaminant will disperse farther than it should witha given physical, or "real" dispersivity. This extradispersion will result in lower peak concentrations and

more spreading of the contaminant. Methods exist tocontrol numerical dispersion, but the methodsthemselves may introduce artificial oscillation.Artificial oscillation is the over or undershooting of thetrue solution by the model, and results in "waves" inthe solution. Usually numerical dispersion isassociated with the finite-difference method; however,numerical oscillation is associated with the finite-element method. Depending upon the methodemployed to solve the advection term, both methodscan exhibit both types of behavior. Special techniqueshave been developed to deal with these problems, oneof which is the Method of Characteristics (MOC).

This method has been widely used and can be appliedto finite differences as well as finite elements, in two orthree dimensions. The basic idea is to decouple theadvective part and the dispersive part of the transportequation and to solve them successively. However, allMOC methods are not strictly based on the principle ofmass conservation, hence large contaminant massbalance errors may arise. While it is recognized thatthese errors may be an artifact of the technique, thequality of the results of a numerical model are judged,in part, by the degree that mass is conserved.Furthermore, the MOC technique requires muchlonger run-times than finite-difference or finite-element techniques.

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Time Stepping

As mentioned previously, while finite-element andfinite-difference methods are used to approximate thespatial terms of the transient flow and transportequations, techniques are used to approximate thetemporal term. While there are several commonlyused variations of the finite-difference method, it isbeyond the scope of this discussion to elaborate on thespecifics for each of the techniques; what is important,however, is an introduction to the technical terms anda general understanding as to how the various methodsinfluence the model run-times as well as the results.Four of the most common time-stepping schemesinclude Explicit, Implicit, Mixed Explicit-Implicit, andAlternating Direction Implicit Procedure.Characteristics of each method are listed below.

Explicit:

! Numerical solution is conditionally stable.

! Often requires an excessive number of timesteps to simulate a practical problem.

! Due to numerical inefficiencies, method isunsuitable for simulation of field problemswith a high degree of heterogeneity and/ornonlinear flow conditions.

Implicit:

! Usually produces unconditionally stablenumerical solution for flow and transport.

! Much more flexible and robust than theexplicit time-stepping scheme.

! Matrix formulation and solution requiresubstantial computational effort (i.e.,relatively long computer times are necessaryto model practical field problems).

Mixed Explicit-Implicit:

! Based on combined use of explicit andimplicit temporal approximations.

! Usually produces unconditionally stablenumerical solution for flow and transport.

! More robust than the explicit time-steppingscheme, and generally more efficient than theimplicit scheme for ground-water flow andtransport solutions.

! Time-stepping scheme can be weighted infavor of either method (i.e., explicit orimplicit) using a factor that ranges from 0 to1. Weighting factors of 0, .5, and 1 result inexplicit, Crank-Nicholson, and fully implicitformulations, respectively.

Alternating Direction Implicit Procedure:

! Usually produces unconditionally stablenumerical solution for flow and transport.

! Much more flexible and robust than theexplicit time-stepping scheme.

! May be prone to mass balance problems whenapplied to field problems with high degree ofheterogeneity and/or nonlinear flowconditions.

! Unsuitable for variably saturated flowsimulations.

! Limited to rectangular finite-difference grids.

The end result of applying the time-stepping schemesdescribed above is that the flow and transport problemis broken into multiple equations with multipleunknowns for each pre-specified point in the modeldomain (i.e., nodes). These multiple equa-tions will,in turn, be solved through matrix algebra methodswhich are discussed in a later section.

Linearization of Flow and Transport Equations

In earlier sections, several situations were presented inwhich the equations describing ground-water flow andcontaminant transport are nonlinear. For transportproblems, the equations are nonlinear when changes inconcentration, pressure, and temperature causechanges in viscosity, effective porosity, or density (e.g.,multiphase fluid conditions). Nonlinear flow problemsinvolve those where the transmissivity is a function ofsaturated thickness (i.e., water-table aquifers) orhydraulic conductivity is a function of moisture content(i.e., unsaturated zone).

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Under nonlinear flow and transport conditions eachnode in the model domain has associated multiplenonlinear equations. Prior to solving for the unknownsof these equations through matrix algebra, anintermediate step is required in which the equationsare linearized. Two of the most common proceduresused to perform this linearization are the Picard andNewton-Raphson methods.

The Picard method:

! Is relatively simple to formulate as comparedto the Newton-Raphson procedure.

! Generally produces a symmetric matrix forthe flow problem and thus requiresconsiderably less computer effort for thematrix solution than the Newton-Raphsonmethod.

! May be prone to convergence difficulties forhighly nonlinear cases.

Qualities of the Newton-Raphson method include:

! Suitable for handling highly nonlinear cases.

! Generally requires substantially greatercomputational effort for matrix formulationand solution.

! Convergence of the procedure may depend oncontinuity or smoothness of the nonlinearfunctions.

As far as model selection is concerned, if it is expectedthat the problem will be highly nonlinear, the codeselected should be able to apply the Newton-Raphsonmethod. It should also be recognized that in thissituation the calculations will take a relatively longtime for the computer to solve. Flow and transportthrough the unsaturated zone become more nonlinearas the contrast between ambient moisture content andvolume of recharge (e.g., rainfall) becomes morepronounced. Therefore, the regional climate canprovide an indication as to whether unsaturated zoneflow and transport are likely to be nonlinear or highlynonlinear. For example, high-intensity rainfall eventsin the arid southwest would create very sharp contrastsbetween the ambient moisture content and theinfiltrating pulse. Under these conditions, the codewould most likely need the Newton-Raphson

formulation. However, in areas of the humidnortheast, the ambient moisture contents are generallyhigh enough that the wetting front saturations are notsignificantly different from the ambient moisturecontent and therefore the nonlinear equations could beadequately solved with the Picard method.

Matrix Solvers

As stated previously, following the spatial andtemporal discretization of the flow and transportequations and in the case of nonlinear problems, thelinearization of the equations, it then becomesnecessary to solve the systems of multiple equationswith multiple unknowns. The most efficient means ofaccomplishing this task is through matrix algebra.Matrix equations can be solved by several means.Some of the more common ones include:

! Direct Matrix Solution Techniques

! Iterative Alternating Direction ImplicitProcedure (IADIP)

! Successive Over-Relaxation Techniques

! Strong Implicit Procedure (SIP)

! Preconditioned Conjugate Gradient(PCG)/Orthomin Techniques

It is important to recognize that matrix solvingtechniques will rarely be the deciding factor in thecode selection process. However, some familiaritywith the capabilities of the matrix solvers will not onlyprovide a general recognition of the technical termsbut will also give some indication as to potentialhardware requirements. Therefore, the followingprovides a superficial description of the various matrixsolvers listed above.

The following qualities are inherent in the DirectMatrix Solution techniques:

! Produces highly accurate solution of thematrix equation with minimal round-offerrors.

! Generally applicable to both finite-differenceand finite-element schemes.

C-9

! Performs well for 2-D problems with up to2,000 nodal unknowns; unsuitable for largeproblems with many thousands of nodes.

Qualities of the Iterative Alternating Direction ImplicitProcedure (IADIP) include:

! Accommodates large 2-D and 3-D problemswith many thousands of nodal unknowns.

! Applicability limited to rectangular grids.

! Convergence rate is usually sensitive to gridspacings and material heterogeneity andanisotropy.

! Prone to asymptotic convergence behaviorand may require several hundreds orthousands of iterations to reach satisfactoryconvergence for a steady-state analysis.

Qualities inherent in Successive Over-RelaxationTechniques (i.e., Point Successive Over-Relaxation(PSOR), Line Successive Over-Relaxation (LSOR),and Slice Successive Over-Relaxation (SSOR))include:

! Accommodates large 2-D and 3-D problemswith many thousand nodal unknowns.

! Applicable to finite-difference and finite-element approximation schemes.

! Convergence rate is dependent on the choiceof relaxation factors and is usually sensitiveto grid spacings and material heterogeneitiesand anisotropies.

! Prone to asymptotic convergence behaviorand may require several hundreds orthousands of iterations to reach satisfactoryconvergence for a steady-state analysis.

Qualities inherent in the Strong Implicit Procedure(SIP) include:

! Accommodates large 2-D and 3-D problemswith many thousand nodal unknowns.

! Much more robust than IADIP andPSOR/LSOR/SSOR techniques.

! Convergence rate is sensitive to iterationparameter and grid spacings.

! Applicable to finite-difference approximationand flow problems only.

Qualities inherent in the Preconditioned ConjugateGradient (PCG)/Orthomin Techniques include:

! Accommodates large 2-D and 3-D problemswith many thousands of nodal unknowns.

! No relaxation factor or iteration parametersare required and convergence rate is usuallyinsensitive to grid spacings and materialanisotropy and/or heterogeneity.

! Much more robust than other alternativeiteration techniques.

! Applicable to both finite-difference andfinite-element approximation schemes butrequires substantially less storage andcomputer (CPU) time with finite-differenceapproximation, particularly for 3-D problems.

D-1

APPENDIX D

CODE ATTRIBUTE TABLES

Site-Related Features of Ground Water Flow and Transport Codes

COMPUTER CODE BOUNDARY/SOURCECHARACTERISTICS

AQUIFER SYSTEMCHARACTERISTICS

SOIL/ROCK CHARACTERISTICS REFERENCECITATION

POIN

T S

OU

RC

E

LIN

E S

OU

RC

E

AR

EA

LL

Y D

IST

RIB

UT

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SPE

CIF

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SPE

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SO

UR

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RA

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TIM

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EPE

ND

EN

T

MU

LT

IPL

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RC

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D A

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RS

AQ

UIT

AR

DS

WA

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R-T

AB

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CO

NV

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S

MU

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IPL

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RS

HO

MO

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S

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GE

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S

ISO

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AN

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TR

OPI

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FRA

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MA

CR

OPO

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S

LA

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D S

OIL

S

COMPUTERCODE

TRANSPORT & FATE PROCESSES MULTIPHASEFLUID CONDITIONS

FLOWCONDITIONS

TIMEDEPENDENCE

DIS

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MA

TR

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RIA

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/

STE

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TA

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TR

AN

SIE

NT

Code-Related Features of Ground Water Flow and Transport Codes

COMPUTER CODE SOLUTION METHODOLOGY GEOMETRY

Analytical Numerical

Spatial Discretization TemporalDiscretization

Matrix Solvers

APP

RO

X. A

NA

LY

TIC

AL

EX

AC

T A

NA

LY

TIC

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SEM

I-A

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2-D

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2-D

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3-D

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3-D

COMPUTER CODE OTHER RELEVANT FACTORS

Source CodeAvailability

Code Testing andProcessing

Output

PRO

PRIE

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NO

N-P

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E

E-1

APPENDIX E

INDEX

E-2

INDEX

A

Adsorption S-12, 3-3, 4-35, 4-37, 4-51, A-2, A-6Advection S-9, S-12, S-13, S-16, 4-20, 4-25, 4-35, 4-37, 4-38, 4-39, 4-40, 4-45, 5-4, 5-20, A-2, C-6, D-3Alluvial flood plane 4-15Analytical model 4-7, A-2Anion exclusion 4-17, 4-41, A-2Anisotropic S-7, S-9, S-10, S-11, 4-2, 4-9, 4-25, 4-28, 4-32, 5-7, A-2, D-3Aquifer S-5, S-8, S-9, S-10, S-11, S-12, S-16, 1-3, 1-4, 3-5, 4-4, 4-9, 4-10, 4-12, 4-13, 4-16, 4-18, 4-22, 4-24, 4-25, 4-27, 4-28, 4-29, 4-30, 4-35, 4-36, 4-37, 4-38, 4-39, 4-45, 4-46, 4-47, 4-49, 5-4, 5-8, 5-16, 5-20, 5-22, A-2, A-3, A-4, A-5, A-6, B-4, C-2, C-5, D-1Aquitards S-10, S-11, S-16, 4-10, 4-22, 4-28, 4-30, 4-37, 4-45, 4-46, 5-4, 5-20, 5-22, D-2Artesian well A-2

B

Basalt 3-4, A-2Bedrock 4-15, A-2Benchmark S-15, 5-1, 5-2Biofixation 4-17, 4-18, 4-41, A-2Bulk density A-2

C

Calibration 4-12, 4-16, 4-31, 4-32, 4-40, 4-47, A-2Capture zone S-13, 4-40, 4-43, A-2Chain decay S-17, 5-5, A-3Channeling 4-37Chemisorption S-13, 4-41Clay S-13, 4-16, 4-17, 4-49, A-3, A-4, A-6Complexation 3-3, 4-16, 4-17, 4-50, A-5Concentration gradient S-13, 4-40Conceptual model S-1, S-5, S-6, S-8, S-12, 1-3, 1-4, 1-5, 3-1, 3-2, 3-3, 3-5, 4-1, 4-3, 4-6, 4-7, 4-10, 4-11, 4-12, 4-14, 4-21, 4-24, 4-31, 4-32, 4-39, 4-47, 5-8, 5-15, 5-16Convergence 4-15, 4-34, C-4, C-5, C-8, C-9Curvilinear elements 4-37, A-3

D

Darcy's Law 4-30, 4-49, A-2, A-3Deterministic model 4-47, 5-15, A-3Dip 4-31, 4-36, A-3Discharge 3-4, 3-5, 4-13, 4-31, 4-32, 4-43, 4-49, A-3Dispersion S-6, S-9, S-10, S-12, S-13, S-16, 1-2, 3-5, 4-13, 4-17, 4-20, 4-25, 4-27, 4-28, 4-32, 4-35, 4-37, 4-38, 4-39, 4-40, 4-45, 5-4, 5-16, 5-20, A-3, A-4, A-5, C-2, C-4, C-5, C-6, D-3Distribution coefficient S-13, S-14, 2-2, 4-9, 4-15, 4-41, 4-42, 4-50, 5-8, A-3Downgradient S-2, S-3, 1-3, 2-1, 2-4, 3-5, 4-5, 4-11, 4-12, 4-13, 4-19, 4-27, 4-43, 4-45, 5-20, C-4

E

Effective dose equivalent 2-6Effective porosity 4-4, 4-30, A-3, C-7Equilibrium isotherm S-17, 5-5Exposure scenarios S-4, S-5, S-6, 2-4

F

Facilitative transport 4-5, 4-15, 4-48, 4-49, A-3Fault 4-50, A-3Finite difference 4-26, A-3, A-5, C-4, C-5, D-5Finite element 4-26, A-3, A-5, C-4, C-6, D-5Flocculation 4-16, A-3Fractured lithology A-3Freundlich isotherm A-3

G

Geochemical facies 4-15, A-4

E-3

H

Hydraulic gradient S-13, 4-4, 4-17, 4-40, 4-49, A-4Hydrodynamic dispersion S-12, S-13, 4-35, 4-37, 4-39, A-4Hydrofracturing 4-17, A-4Hydrogeologic unit 4-50Hydrostatigraphic unit A-4Hysteresis 4-44, A-4

I

Immiscible S-14, 4-42, A-4, A-5In-situ coating 4-16In-situ freezing 4-16Institutional control S-4, 2-4Integrated finite difference A-5, C-4Intrinsic permeability S-11, 4-32, A-4Inverse model A-4Ion exchange S-13, 4-18, 4-41, 4-49, 5-16, A-4, C-2Ionic or molecular constituents S-13, 4-40, A-5

J

Joint sets 4-36

K

Kinetic activity 4-40, A-5

L

Langmuir isotherm A-4Layered lithology A-4Leach 1-3, 4-20, A-5, B-4Leachate S-2, S-10, 1-4, 2-1, 2-2, 4-28, 4-43, A-5Limestone 3-4, 4-36, 4-49, A-5Lithography 3-2, 4-7Littoral A-5Loading rates 4-43, A-5Low permeability barriers S-12, 4-38, A-5

M

Macropores S-9, S-10, S-11, S-16, 4-5, 4-9, 4-15, 4-22, 4-25, 4-28, 4-32, 4-33, 4-34, 4-35, 4-44, 5-4, A-5, D-3Matrix diffusion S-9, S-12, S-13, 4-14, 4-15, 4-18, 4-20, 4-22, 4-25, 4-38, 4-39, 4-40, A-5, D-3Mechanical dispersion S-13, 4-39Metamorphic rock 4-36, A-5Model S-1, S-2, S-5, S-6, S-7, S-8, S-10, S-11, S-12, S-13, S-14, S-15, S-16, S-18, S-19, S-20, 1-2, 1-3, 1-4, 1-5, 2-7, 2-8, 3-1, 3-2, 3-3, 3-5, 4-1, 4-3, 4-4, 4-5, 4-6, 4-7, 4-9, 4-10, 4-11, 4-12, 4-13, 4-14, 4-15, 4-16, 4-20, 4-21, 4-22, 4-23, 4-24, 4-26, 4-27, 4-28, 4-30, 4-31, 4-32, 4-37, 4-38, 4-39, 4-40, 4-42, 4-43, 4-44, 4-45, 4-47, 4-48, 4-50, 4-51, 5-1, 5-2, 5-4, 5-5, 5-7, 5-8, 5-10, 5-13, 5-14, 5-15, 5-16, 5-20, A-2, A-3, A-4, A-5, B-2, B-4, C-2, C-4, C-6, C-7, C-8Molecular diffusion S-13, 4-35, 4-39, A-5Monitor wells S-4Multiple aquifers S-9, S-10, S-11, S-16, 4-16, 4-22, 4-25, 4-28, 4-30, 5-4, D-2

N

Numerical model 4-9, 4-11, 4-47, A-5, C-6Numerical oscillations S-12, 4-39

O

Off-centerline dispersion modeling 3-5One-dimensional S-8, 3-4, 4-2, 4-5, 4-6, 4-27, 4-45, 5-20Organic Complexation 4-17, A-5Oxidation-reduction potential 4-16

P

Particle track A-5Partition factors S-2, 2-2Perched water 4-32, A-5Porous media S-12, 3-5, 4-4, 4-9, 4-14, 4-35, 4-36, 4-39, 4-44, 5-7, A-3, A-5, A-6, C-3Pyrophoric 4-31

E-4

R

Radial flow 4-9, A-6, C-3Radioactive decay S-11, S-12, S-14, S-17, 3-3, 4-12, 4-28, 4-37, 4-38, 4-41, 4-42, 5-5, 5-16, A-3, A-6, C-2Receptors S-5, S-6, 1-4, 2-6, 3-2, 3-5, 4-4, 4-5, 4-11, 4-12, 4-19, 4-27Recharge 3-4, 3-5, 4-4, 4-5, 4-9, 4-13, 4-18, 4-19, 4-20, 4-28, 4-29, 4-30, 4-31, 4-33, 4-34, 4-35, 5-7, 5-22, A-6, C-8Regional scale 3-4, 3-5Remediation S-1, S-2, S-4, S-7, S-12, S-13, S-16, 1-2, 1-3, 1-5, 2-1, 2-3, 2-6, 2-7, 3-1, 3-2, 4-1, 4-2, 4-3, 4-7, 4-11, 4-21, 4-29, 4-30, 4-32, 4-38, 4-40, 4-43, 5-4, 5-7Retardation factor/coefficient A-6

S

Sandstone S-11, 4-9, 4-36, 4-37, A-6Saturated zone S-11, 3-4, 4-5, 4-6, 4-7, 4-10, 4-12, 4-13, 4-19, 4-30, 4-31, 4-34, 4-35, 4-43, 4-44, 4-48, 5-8, 5-20, A-6Secondary mineralization 4-16Sedimentary environment A-6Shale 3-4, A-6Silt A-6Solute S-12, S-13, 4-33, 4-37, 4-38, 4-39, 4-41, 4-42, 4-47, 4-48, 5-8, 5-16, 5-20, A-2, A-3, A-4, C-2, C-6Solution features 4-15, A-6Source term S-5, S-10, 3-2, 3-3, 4-12, 4-18, 4-24, 4-27, 4-28, 4-43, 4-44, 4-45, 4-48, 4-50, 5-20, A-6Speciation S-9, S-17, 4-17, 4-25, 4-41, 4-49, 5-5, A-6, D-4

T

Three-dimensional S-8, 4-1, 4-7, 4-12, 4-13, 4-15, 4-19, 4-27, 4-45, 4-46, 5-20, 5-22, C-4, C-6Two-dimensional 4-2, 4-5, 4-6, 4-12, 4-13, 4-19, 4-45, 4-46, 4-48, 5-16, 5-20, 5-22, C-5