ML061000654

E-mail from J. White of USNRC to D. Leach of Entergy Regarding Ground Water ANSI Standard

ML061000654
Person / Time
Site:	Indian Point
Issue date:	12/23/2005
From:	Jason White Division of Reactor Safety I
To:	Leach D Entergy Nuclear Operations
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FOIA/PA-2006-0081
Download: ML061000654 (30)

Text

Johnp White? Ground water ANSI standard Paae 1 1

• - -R-I V a From: John White To: Dleach@entergy.com Date: 12/23/05 10:21AM

Subject:

Ground water ANSI standard Don, I am sure that you have this, but wanted to make sure...John John R. White Chief, Flant Support Branch 2 U.S. Nuclear Regulatory Commission, Region I 475 Allandale Road King of Prussia, PA 19406 Office: (310-337-5114 Fax: '310-337-6928 Cell: .484-919-2206 Email: jrwl@nrc.gov VOLSk

i i.

ANSI/ANS-2.17-1 980 evaluation of radionuclide transport

[OCT 3- m in ground water for nuclear power sites OANSI/ANS

7  ?

1 l ANSI/ANS-2.17-'1980 A,

American National Standard for Evaluation of Radionuclide Transport in Ground Water for Nuclear Power Sites Secretariat American Nuclear Society Prepared by the Ametican Nuclear Society Standards Committee Working Group ANS-2.17 Published by the American Nuclear Society 555 North Kensington Avenue La Grange Park, Illinois 60525 USA Approved April 9, 1980 by the American National Standards Institute, Inc.

i J i i l

American An American National Standard implies a consensus of those substantially con-National cerned with its scope and provisions. An American National Standard is intended I as a guide to aid the manufacturer, the consumer, and the general publi4c. The Standard existence of an American National Sandard does not in any respect preclude anyone, whether he has approved the standard or not, from manufacturing, marketing, purchasing, or using products, processes, or procedures not conforming to the standard. American National Standards are subject to periodic review and users are cautioned to obtain the latest editions.

CAUTION NOTICE: This American National Standard may be revised or with-drawn at any time. The procedures of the American National Standards Inmtitute require that action be taken to reaffirm, revise, or withdraw this standard no later than five years from the date of publication. Purchasers of this standard may receive current information, including interpretation, on all standards published by the American Nuclear Society by calling or writing to the Society.

Published by American Nuclear Society 555 North Kensington Avenue, La Grange Park, Illinois 605"25 USA Price: $28.00 Copyright e 1980 by American Nuclear Society.

Any part of ths standard may be quoted. Credit lines should read "Extracted from American National Standard ANSI/ANS-2.17-1980 with permission of the publisher, the American Nuclear Society." Reproduction prohibited under copyright convention unless written per-mission is granted by the American Nuclear Society.

Printed in the United States of America

Foreword (This Foreword is not a part of American National Standard for Evaluation of Radionuclide Tmisport' in Ground Water for Nuclear Power Sites, ANSI/ANS.2.17-1980.)

The purpose of this document is to specify standards for determining the con-centrations of radionuclides in the ground water resulting from both potential acciden-tal and routine releases from nuclear power plants. This standard was prepared by Working Group ANS-2.17 of ANS-2 Subcommittee, Site Evaluation, of the American Nuclear Society Standards Committee.

The initial meeting of the working group was held in October, 1974. At that meeting, the working group was designated as ANS-2.9, Standards for Evaluating Water Supply and Waterborne Radionuclide Transport for Nuclear Power Sites. This working Iroup was subdivided into surface water and ground water subgroups, and, the wo:king group was formally subdivided at the March, 1975 meeting of the ANS-2 subcommrittee into ANS-2.9, Standards for Evaluating Water Supply and Waterborne Radionuclide Transport for Power Reactor Sites: Ground Water, and ANS-2.13, Standards for Evaluating Water Supply and Waterborne Radionuclide Transport for Power Reactor Sites: Surface Water.

The draft standard, ANS-2.9, was balloted on May 31, 1977, by the ANS-2 Sub-committee with 12 approved, 10 approved with comments, 2 disapproved, 1 not voting, and 2 unreturned ballots. As a result of comments received during this balloting, the draft standard was further sub-divided into ANS-2.9, American National'Standaxd for Evaluation of Ground Water Supply for Nuclear Power Sites, and ANS-2.17, American National Standard for Evaluation of Radionuclide Transport in Ground Water for Nuclear Power Sites. These draft standards, dated January, 1978, were transmitted to the ANS-2 Subcommittee in June, 1978, for information and informal comments. The draft standards were revised to incorporate these informal comments. As a result of these revisions, the two disapproved ballots were changed to approved with comments.

This standard covers parts of the material that meet the requirements of Section 2.4, Hydrologic Engineering, and Section 11.2, Liquid Waste Management Systems, of the "Standard Format and Content of Safety Analysis Reports for Nuclear Power Plants,"

Regulatory Guide 1.70, issued by the Nuclear Regulatory Commission (NRC).

Before preparing the Safety Analysis Report (SAR) Sections 2.4 and 11.2, for the licensing of nuclear power plants, the applicant should be aware of hydrologic work which has been done by others in the area of interest. Almost invariably, much work can be saved by utilizing all or parts of studies of local, state, and federal agencies.

Such information as historical ground water levels, pumping tests, well logs, with-drawal and recharge rates, geologic data, hydraulic parameters of underlying for-mations, location and extent of aquifers, and water quality can be obtained from such sources.

Federal agencies which have useful data are the U.S. Geological Survey, Corps of Engineers, Bureau of Reclamation, Soil Conservation Service, Forest Service, Ten-nessee Valley Authority, Environmental Protection Agency, and the Nuclear Regula-tory Commission. Most states have one or more agencies which are concerned with various aspects of water resources. Various local and interstate agencies, including soil and water conservation districts, irrigation districts, and river basin commissions, can be sources of information. SAR's for other nuclear facilities in the region can provide data.

It is also profitable to discuss the specific site in detail with the hydrology staff cf the NRC prior to starting preparation of Section 2A. In such discussions the scope of work can often be reduced, and methodologies and procedures can be agreed upon, which will save many man-hours and dollars; both for the applicant and for the NRC Staff.

i A 1 Working Group 2.17 of the Standards Committee of the American Nuclear Society had the following membership:

David L Sielken, Chairman, Sargent & Lundy L Wendell Marine, .R J. DuPont de Nemovurs &

Y. C. Chan8 Stone & Webster Ey'gincing Cor. Company poration John A. McLaughlin, Pacific Gas and Electi Com.

Stanley R Davis, University of Arizona pany James 0. Duguid, Battelle Memorial Institute Willein M. McMaster, Tennessee Valley Authority Thomas Nicholson, Nuclear Regulatory Commission The chairman of the working group prior to the preparation of Draft 4, dated Decem-ber, 1978 was Patrick J. Ryan, Bechtel, Inc. Prior to his retirement, Donald L. Milliken represented the Nuclear Regulatory Commission.

Subcommittee ANS-2, Site Evaluation, of the American Nuclear Society Standards Committee had the following members at the time of its approval of this standard:

R. V. Bettinger, Chairman, PacificGas and Electric George Nicholas, Dames & Moore Company R Noble, Dames & Moore Iis E. Escalante, Los Angeles Department of T. Pickel, Oak Ridge National Laboratory Water and Power Craig Roberts, US NuclearRegulatoryCommission J. A. Fischer, Dames & Moore Patrick J. Ryan, Bechtel, I1c.

Walter W. Hays, U& Geoogicl Survey James A. Smith, General Electric Company G. E. Hein, Sargent & Lundy J. D. Stevenson, EDAC Inc.

G. F. Hoveke, Sargent & Lundy Sam Tucker, Florida Power and Light Company D. H. Johns, Southern CaliforniaEdison Company N. R. Wallace, Bechte4, Inc.

R. E Keever, Nuclear Technology, Inc. Donald A. Wesley, General Atomic Company E. J. Keith, EDS Nuclear Inc. Earl Ivan White, General Atomic Company C R McClure, Bechtel, Inc. Karl Wiedner, Bechtel Power Corporation S. Milioti, American Electric Power &rvice Cor-poration

4 4 The members of American Nuclear Society's Nuclear Power Plant Standards Com-mittee (NUPPSCO) at the time it balloted this standard in July 1979 were:

J. F. Mallay, Chairman M. D. Weber, Secretary Name of Representative Organizations G. A. Arlotto .. US Nuclear Regulatory Commission R. E Basso Inc.

a..Cloyti, R. G. Benham...........General Atomic Company (for the Insitiute of Electricaland Electronics Engineers)

RI V. Bettinger ........... Pacific Gas & Electric Company P. Bradbury .......... Westinghouse Advanced Reactor Dinision D. A. Campbell ................................................... Westinghouse Electric Corpor2tion C. 0. Coffer .......... Kaiser Engineers L. J. Cooper .......... Nebraska Public Power District W.H ILArdenne ........... General Electric Company F. X. Gavigan .......... US Department of Eitergy G. J. Gill ....... Bechtel Power Corpor2tion H. J. Green ........................

..................................... Tennessee Valley Authority A. R. Kasper .......... Combustion Engineering, Inc.

P. W. Keaten ......... GPU Service Corportion J. W. Lentsch ......... Portland General Electric Company D. M. Leppke ......... Fluor Power Services, Inc.

J. F. Mallay.......... Ba bcock & Wilcox Company (for the American Nuclear Soeiety)

A. T. Molin ......... United Engineers & Constnctors J. H. Noble ......... CT. Main, /nc.

E. P. O'Donnell .. Ebasco Services, Inc (for the Atomic Industrial Forum, TIn.)

T. J. Pashos ......... Nuclear Services Corporntion M. E. Remley .. R ockwell International J. W. Stacey ......... Yankee Atomic Electric Company S............

Stone & Webster Engineering Corpon2tion J. D. Stevenson ......... Woodward-Clyde Consultants (for the 4merican Society of Civil Engineers)

G. P. Wagner .... ...... Commonwealth Edison Company J. E. Ward.......... Sargent &Lundy C. L Wessman .......... General Atomic Company J. E. Windhorst .......... Southern Company Selvices (for the American Society of Mechanical Engineers)

E. R.Wiot .......... NUS Corponition

i J Contents Section Page

1. Scope and Purpose .. 1........................

1.1 Coverage .......................................... 1 1.2 Exclusions .......................................... 1

2. Definitions ................ I 1...

3. Evaluation Criteria .................. 2 3.1 Routine Releases ................ 2 3.2 Postulated Accidental Releases ................. ; 2

4. Description of Ground Water System ................ 3 4.1 Regional Hydrogeologic Systems ................ 3 4.2 Local Hydrogeologic Systems Near the Plant Site ................ 4 4.3 Ground Water-Surface Water Interrelationship ................ 5

5. Radionuclide Transport ................ 5 5.1 Ground Water Flow Paths ................ 6 5.2 Travel Time of Ground Water and Radionuclides ................ 6 5.3 Dispersion and Dilution ................ 6 5.4 Methods Used in Computations ................ 7 5.5 Potential Effects of Postulated Releases ................ 7

6. Monitoring Program ................ 7 6.1 Monitoring Objectives ................ 7 6.2 Monitoring Methods ................ 8 6.3 Methods of Reporting Results of Monitoring, Sampling, and Analyses ... 9

7. References .............................................. 9 Appendix Methods for Analysis of Radionuclide Transport in Ground Water.. 10

- a I Evaluation of Radionuclide Transport in Ground Water for Nuclear Power Sites

1. Scope and Purpose exchange capacity (ion exchange capacity).

The amount of exchangeable ions measures in This standard presents guidelinesior the deter- milligram equivalents per gram of solid material mination of the concentration of radionuclides at a given pH.

in the ground water resulting from both flux (specific discharge, darcy velocity) postulated accidental and routine releases from (LT-'). The volume of discharge from a given nuclear power plants] cross-sectional area per unit time divided by the area of the cross section.

L1 Coverage. This standard presents the heterogeneity. The properties or conditiors of methods to evaluate potential radionuclide isotropy or anisotropy vary from point to point transport in ground water for use in evaluation in the medium.

of nuclear power plant sites. This standard con- homogeneity. The properties or conditions of tains mandatory requirements as designated by isotropy or anisotropy are constant from point the use of the word "shall". to point in the medium.

hydraulic conductivity (LT-'). "A medium 1.2 Exclusions. This standard does not discuss has a hydraulic conductivity of unit length per the release of non-radioactive waste to ground unit time if it will transmit in unit time a unit water, nor the radioactive source terms for the volume of ground water at the prevailing ground water evaluation studies. viscosity through a cross section of unit area, measured at right angles to the direction of Slow,

2. Definitions under a hydraulic gradient of unit change in head through unit length of flow."[2J The term In general, ground water terms are used in ac- "hydraulic conductivity" has been called per-cordance with definitions as described by Loh- meability, coefficient of permeability, field coef-man and others.[l]l Definitions are given below ficient of permeability, and conductivity.

for terms which can have more than one hydrogeologic unit. Any soil or rock unit or meaning to ground water hydrologists. zone which by virtue of its porosity or per-anisotropic. The properties at any point within meability, or lack therof, has a distinct influence a medium are different in different directions. on the storage or movement of ground water.

dispersion coefficient (L21`) A measure of infiltration. The, process of downward the spreading of a flowing substance due to the movement of water from the surface into un-nature of the porous medium, with its in- derlying materials.

tercon nected channels distributed at random in intrinsic permeability (L2 ). The measure of all directions. the ability of a rock or soil to transmit fluid un-dispersivity (L). A geometric property of a der a fluid potential gradient (see definitionn of porous medium which determines the dispersion hydraulic conductivity).

characteristics of the medium by relating the isotropic. The properties at any point within a components of pore velocity to the dispersion medium are the same in all directions.

coefficient. pore velocity, seepage velocity (L7T). The distribution coefficient (M- 1L3). The quan- average rate of flow in the pores of a Eiven tity of the radionuclide sorbed by the solid per medium. This is approximated by dividing the unit weight of solid divided by the quantity of flux by the effective porosity.

radionuclide dissolved in the water per unit porosity. The property of containing interstices.

volume of water. Total porosity is expressed as the ratio of the volume of interstices to total volume. Effe-tive

'Numbers in brackets refer to corresponding numbers in porosity refers to the porosity through which Section 7, References. flow occurs[23 1

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• • American National Standard ANSI/ANS-2.17-1980 recharge. The process of water addition to the test, packer. A method of isolating a section of saturated zone or the volume of water added by a borehole by inserting one or more expandable this process. glands (packers) in order to measure hydraulic release, accidental. A release of radioactivity conductivity or water quality in the section.

that uis uncontrolled and unplanned. yield, specific. The ratio of the volume of release' routine. A release of radioactivity that water which the rock or soil, after being is either continuous, e.g., leakage from a cooling saturated, will yield by gravity to the volume of pond containing trace quantities of radioac- the rock or soil.

tivity, or a periodic controlled release of low-level radioactive liquids.

safety class. Applies to structures, systems, or 3. Evaluation Criteria components that have a safety function.

safety function. Any function that is necessary The purpose of this section is to set criteria for to assure the integrity of the reactor coolant evaluating routine and postulated accidental pressure boundary or primary coolant boundary, releases of liquid radioactive effluents to the the capability to shut down the reactor and ground water system. The definition of source maintain it in a safe shutdown condition, or the terms is not covered by this standard.

capability to prevent or mitigate the con-sequences of conditions of design which could 3.1 Routine Releases. During normal result in potential off-site exposures that are a operation of plants, routine releases of radioac-significant fraction of Title 10, Code of Federal tive materials potentially can be made to ground Regulations, Part 100, Reactor Site Criteria water systems. These routine releases are guideline exposures.[3] generally as low as reasonably achievable safety related. Of significance or importance (ALARA) and satisfy the limits of 10 CFR 20, because it applies to: Appendix B, Concentrations in Air and Water (1) Structures, systems, or components Above Natural Background, Table II, at the assigned to a safety class. discharge point.[4] For these reasons, the (2) Drawings, specifications, procedures, calculation of potential concentrations of analyses, and other documents used to deter- radionuclides from routine releases to ground mine or describe parameters affecting safety water systems need not be performed.

class structures, systems, or components.

(3) Services to design, purchase, fabricate, 3.2 Postulated Accidental Releases. The ef-handle, ship, store, clean, erect, install, test, fects of a postulated accidental release of operate, maintain, repair, refuel, and modify radionuclides in the site ground water systems safety class structures, systems, or components. shall be evaluated. In cases of postulated! ac-sball, should, may. The word "shall" is used to cidental releases to surface water bodies which denote a requirement; the word "should" to recharge ground water systems, potential con-denote a recommendation; and the word "may" centrations shall be calculated and these shall to denote permission, neither a requirement nor be used in the ground water analysis 2 .

a recommendation.

sorption. All mechanisms, including ion ex- Initial calculations may be made assuming in-change', that remove ions from the fluid phase stantaneous release to the ground water of' the and concentrate them on the solid phase of the entire source term under the maximum medium. hydraulic gradient in the direction of ground storage coefficient. The volume of water an water flow. These calculations may be made aquifer releases from or takes into storage per assuming the nearest potential user or discharge unit surface area of the aquifer per unit change in head.

2Guidance on performing this calculation for the Suirface test, aquifer. The effect of pumping a well as measured in the pumped well and in one or water body can be found in US. NRC Regulatory IGuide (R.G.) 1.113, Estimating Aquatic Dispersion of Emuents more observation wells, for the purpose of deter- from Accidental and Routine Reactor Releases for the Pur-mining aquifer properties. . pose of Implementing Appendix 1.

2

4  ; I l . I American National Standard ANSIIANS-2.1741980 area is l6cated at the site restricted area boun- nomenclature and lithologic descriptions.

I dary. Further, these calculations may be made using conservative values of the hydraulic con-Aquifers and less permeable. units shall be in-cluded.

ductivity and effective porosity. Conservative 4.1.2 Relationship Among Hydrogeologic values of hydraulic conductivity and effective Units. The distribution and interrelationship of porosity are those which lead to higher con- water-bearing, confining, and non-saturated centralions at the point of interest than would' units, shall be defined using maps, geologic cross be expected to occur. sections, and fence diagrams.

4.L3 Water-bearing Characteristics. The Alternatively, more realistic calculations may be water-bearing characteristics of each made of the rate of entry of the radioactive ef- hydrogeologic unit of regional importance Ehall fluent to the ground water. The more realistic be given. Information concerning total and ef.

calculations may take credit for the actual fective porosities, specific yields, storage coef-distances to the nearest user or discharge area, ficients, hydraulic conductivities, geophysical-the rate of release through the plant foun- log responses, thicknesses, drilling che rac-dations; plant features which may minimize the teristics, and water chemistry should be given.

release of radionuclides, and site characteristics Where possible, the expected variations of the which can reduce the concentrations of various critical parameters should be presented.

radionuclides, e.g., initial inflow into the 4.1.4 Recharge-discharge Relationships.

building. The recharge-discharge relationships of the aquifers shall be estimated. Information used in Only under rare conditions is it necessary to per- the estimation should be described and sum-form a detailed analysis of the postulated ac- marized in the form of graphs, tables, maps and cidental release. cross sections. This information includes:

(1) Representative existing water levels in,

4. De.scription of Ground Water System and head relationships between, individual aquifers shall be presented. The reliability of the

( The regional and local hydrologic systems of a data should be evaluated and limitations on the plant i3ite must be understood to assess possible reliability of the data should be noted. These pathways, travel times, dilutions and con- limitations are generally the result of utsing centrations of radionuclides in ground water. existing wells and historic data, and, the limitations consist of several types such as 4.1 Regional Hydrogeologic Systems. The where holes tap several aquifers of differing regional hydrogeologic system can encompass heads, where unreliable techniques such as leaky several thousand square kilometers and is air lines have been used to measure water levels, distinguished from the local system which or where water levels are measured only during generally encompasses a few hundred square or shortly after pumping of wells. If data are kilometers. The local system is a segment of the available, water-level change maps should be regional system. A complete understanding of presented which show the influence of natural or the local System, which is most vital to the ob- artificial variations of recharge and discharge. If jectives of the study, is usually impossible available, representative water-level data sb ould without regional information. Therefore, be presented in the form of well hydrographs.

regional information shall be included as a The seasonal variations of water levels and necessary prelude to the detailed study of the correlation of water levels with precipitation local system in order to identify those and river flows should be presented where ap-hydrof eologic systems which can be affected by plicable.

plant releases. For many regions, existing (2) Long-term changes in regional ground ground water studies will provide most of the water levels which can affect the transport of required information for this section. radionuclides shall be projected. This projeotion 4.1.] Major Hydrogeologic Units. Major should be for several periods over the plant life hydrogeologic units of the region shall be (e.g., at 10-year intervals) and for various con-defined with respect to accepted stratigraphic ditions of recharge and discharge of the aquifers.

tI 3

1. i I I .

American National Standard ANSI/ANS-2.1741980 4.1.1; Ground Water Flow Paths. -Paths of to determine the behavior of postulated ac-regional ground water flow shall be inferred for cidentally-released radioactive liquid in the each aquifer of regional importance. As a first aquifers. In addition, ground water quality data approximation, ground water flow directions can be used to identify modes of recharge to the may te taken as orthogonal to regional water aquifers, and to assess the interaction of ground level contours. However, some aquifers are water with geologic formations. Total ion-strongly anisotropic and flow directions can be exchange capacity of these hydrogeologic units almos' parallel to the regional water-level con- should be given.

tours. Such flow characteristics may be found in (5) Water-bearing characteristics of units.

carbonates, basalts, and other rocks with highly Effective and total porosity, specific yield, field developed secondary permeability. Aquifers capacity, hydraulic conductivity (both vertical having anisotropic flow conditions shall be and horizontal), leakance, transmissivity, characterized. storage coefficient, and dispersion coefficient should be given. Any significant development of 4.2 Lc'eal Hydrogeologic Systems Near the secondary permeability should be described Plant Site. This section deals with the (6) Well data. Available data should be hydrogeology of the plant site and its immediate tabulated and include aquifers penetrated, surrounding area. Data used to complete this location, elevation, use, owner, discharge rates, part of the study normally are obtained from static water levels, and drawdown. Data should studies and field work undertaken specifically also include details of well construction in-for site investigations. Although previously cluding grouting, screens, casing type, depth, published material and data from existing wells diameter, performation, and surface seals.

can be useful, information from other studies is (7) Well abandonment. Existing wells and sufficient only for a preliminary orientation and piezometers used for site investigations, which shall not be relied upon for all basic data. In- lie within construction areas, should be iden-formation from the regional study, however, tified and described and the method of a'aan-should be used to place the study of the local donment should be specified and documer.ted.

hydrogeologic system in its proper perspective.

For example, depths of test holes needed to 4.2.2 Documentation of Ground Water study aquifers which will be potentially affected Regimen. For all site hydrogeologic units that by site development or plant operation can be can be significantly affected by the postulated estimated from results of the regional study. release of radioactive effluents, the pre-

. 4.2.1 Description. Hydrogeologic units that construction ground water regimen shall be can be significantly affected by. the postulated documented. This documentation should in-release of radioactive effluents shall be clude:

described in detail. This description should in- (1) Contours of ground vater levels irt all clude information with the methods used to ob- pertinent water bearing units.

tain tihe information: (2) Direction of water flow, taking into con-(1) Lithologic description of the units. sideration aquifer anisotropy.

(2) Stratigraphic and structural relation- (3) Existing recharge and discharge areas ships of the units. Besides word descriptions, in- including ground water and surface water in-formation should be presented in maps, cross terrelationships.

sections, and fence diagrams. (4) Quantities and pore velocities of ground (3) Lateral extent and thickness of the water flow in and between the various units. This information may be combined with hydrogeologic units.

information on thickness and presented in the (5) Short-term changes of ground water form of maps with lines of equal unit thickness levels measured over a mimimum period of one (isopach maps). year and correlated with precipitation, liver (4) Hydrochemistry of the units. Sufficient flows, and soil-moisture data as appropriate in ground water quality data should be provided to order to help estimate the frequency and determine the physical, chemical, and bac- amount of recharge in local aquifers.

teriological characteristics of ground water, and (6) Historical long-term records of ground 4

American National Standard ANSI/ANS-2.17-1980 water :levels, if available. 4.3 Ground Water-Surface Water In-C. (7) Seasonal changes in quality and terrelationship. The ground water and surface radioactivity of the water in the aquifers that water regimens comprise one system that must may be significantly affected by postulated be considered as an interdependent unit. A con-releases of radioactive effluents, measured over stant interchange of water takes place between a minimum period of one year. the surface and subsurface. The nature and 4.2.3 Changes in Ground Water Regimen. amount of this interchange in the vicinity of the Changcs in the ground water regimen which are site should be documented to the level required anticipated from construction and operation of by the analysis used.

the plant and can affect the transport of radionuclides shall be presented. These can in- 5. Radionuclide Transport clude:

(1) Changes in hydraulic conductivity due In general the direction of ground water to ground water control or foundation im- movement and radionuclide transport is ap-provement activities such as installation of proximately orthogonal to water-level :on-slurry trenches and rock grouting. tours. 3 However, some aquifers are so strongly (2) Changes in direction of water flow. anisotropic that movement can be nearly (3) Changes in quantities of water flow. parallel to regional water-level contours. For (4) Changes in water levels within ail per- example, special attention should be given to tinent aquifers. sites underlain by carbonate rocks, basalts, and (5) Changes in water quality including in- various types of dense fractured rocks where trusion of saline water and movement of return- most analytical methods are invalid. In these irrigation water, domestic and municipal formations, water flux and radionuclide wastewater, and poor quality water within or movement may be estimated using tracer between aquifers. studies; however, even these methods are often 4.2.4 Methods. Methods of study will vary inadequate because tracer flow paths do not t widely according to geologic and hydrologic con- necessarily intersect observation wells. Never-ditions of the site. Data from regional studies theless, the general geometry of the aquifer and shall be used, therefore, to plan the detailed site hydraulic gradients will provide information studies which will utilize various combinations concerning the probable direction and total of the methods mentioned below. The following distance of travel.

list gives some of the more common methods presently used. Many of these methods are in- A conservative estimate of radionuclide trans-cluded in the investigation of site geology. port in a fractured rock formation may be ob-(1) Detailed geologic mapping of site. tained by assuming the movement to occur in a (2) Mapping of ground water levels for all single fracture in which dispersion and sorption pertinent aquifers are neglected. The fracture may be assumed to (3) Construction of hydrographs of ob- extend from the nearest point of critical concern servation wells. in a straight line, or the direction and the (4) Surface geophysical studies. dimensions of the fracture and the hydraulic (5) Remote sensing. Normally of limited gradient within the fracture may be estimated use, except in some regional applications. from data collected during the site investigation.

(6) Test drilling.

(7) Packer tests. Some fractured aquifers can be considered as (8) Percolation tests. quasi-isotropic, and described by analytical (9) Laboratory study of samples including methods, if fracture spacing is small as a)m-cores. pared to the distance between point under in-(10) Downhole logging. vestigation. 4 (11) Aquifer tests. 3 Where this relationship between movement and gracient (12) Tracers tests using more than one well, exists the analytical methods discussed in the Appendic can giving concentration as a function of time. be applied.

4References relevant to this section are listed in the Ap.

pendix.

5

- '1A American National Standard ANSIIANS-2.17-1980 5.1 Ground Water Flow Paths. With the ex- which is not sorbed in most cases. Travel tines ception of strongly anisotropic aquifers, the of other radionuclides can be longer than for direction of ground water movement from the tritium because of sorption by solids. In regions plant site can be determined using poten- of slow migration of ground water, as shovrn by tiometric surface maps for the site and vicinity. travel-time calculations, only the long-lived The flow path will be in the direction of the radionuclides such as 3H, 9 0 Sr, eTc, 137Cs, and hydraulic gradient, i.e., perpendicular to the the transuranic elements (if present) should be equipiotential lines. This method or tracer tests considered when the distance to the nearest. user can be used to determine the existing flow path is large. However, where rapid ground water from the site; however, future use of ground flow occurs, shorter-lived radionuclides should water by the plant or other users can alter the be considered, i.e., those with half-lives ap-existing flow path. Estimates of future with- proximately equal to or greater than the ground drawals of ground water may be used to ap- water travel time.

proximate future potentiometric surface maps, which in turn may be used to determine future In determinations of radionuclide transport by flow paths and hydraulic gradients. ground water, additional parameters may be required. These parameters consist of the 5.2 Travel Time of Ground Water and distribution coefficient, the decay rate, and the Radionuclides. The pore velocity of ground coefficient. of dispersion (or alternatively, disper-water can be determined by either experimental sivity).

or theoretical methods. The experimental methods consist of in-situ tracer studies using The distribution coefficient, Kd, is a function of tracers which have been demonstrated as not the particular radionuclide, the pH of both the being sorbed by the solid medium. Theoretical solids and the water, and the chemistry of both methods consist of solution of the governing the solids and the water. Therefore, if Ild is ground water flow equations using the ap- used, it shall be determined for radionuclides of propr'.ate boundary conditions and aquifer coef- consequence using solids and water samples ficienis. These determinations range from ap- taken from the aquifer in which the transport is plication of Darcy's law to obtain the ap- expect to occur. Sorption (retention) of proximately steady-state flux, to detailed radionuclides by the solids along the flow path modeling of the transient flow using increases the travel time of the radionuclides to sophisticated numerical models. In the sim- the point of use or discharge, or both. 'Thus, plifiecl approach, Darcy's law5 in one dimension when the distribution coefficient is zero, the is: radioactivity moves with the pore velocity of the water, and as the distribution coefficient in-Ve = -K dH creases, the travel time of the radioactivity becomes greater than the travel time 03' the where water. The retardation of movement by sorption Vx is the flux or specific discharge provides time in which radioactive decay reduces K is the hydraulic conductivity the concentration of radionuclides. The con-H is the total head centration of radionuclides is also reduced by dH is the hydraulic gradient in the direc- the sorption process in which the radioactive dx tion of flow. material is removed from the water and at-tached to solids. Sorption coefficients, however, The travel time of ground water between the can be lowered dramatically by formation of plant site and the nearest user can be calculated organic or inorganic complexes.

using the average pore velocity. If radioactive decay is neglected, this time will also be the 5.3 Dispersion and Dilution. The amount of travel time of the center of mass of the tritium dilution that occurs is a function of dispersion

$The application of more sophisticated models and the ap- within the aquifer. For calculation of proximations made by using Darcy's law we discussed in the radionuclide concentrations in the ground Appendix. water, the coefficient of dispersion is required.

6

A b American National Standard ANSIIANS-2.17-:.980 This coefficient can be approximated using em- rate and direction of ground water transport of C' pirical relationships, laboratory tests or tracer the radioactivity, the characteristics and the studies in the hydrogeologic unit.[5,6] The scale areal extent of the aquifer, the proximity of of the tests, the homogeneity of the medium, water users to the plant site, and the total and the concentration of the tracer can population of water users. Resulting con-significantly affect the results of the laboratory centrations of individual radionuclides at the and tracer tests. Well spacing for field point of nearest potential potable water supply measurements should be selected carefully, should not exceed the limits stated in otherwise the time involved and the cost can be 10 CFR 20, Appendix B, Table II, Column 2.[4]

excessive. Transverse dispersivity may be deter- Combinations of radionuclides should be within mined under natural flow conditions. These limits stated in 10 CFR 20, Appendix B, Note studies will provide both longitudinal and trans- 1.[4] Alternatively, resulting concentrations verse components of the dispersivity from which may exceed those stated in 10 CFR 20, Ap-the dispersion coefficient can be calculated. The pendix B, Table II, Column 2 for a short required travel time of the tracer between wells duration if they do not exceed those con-can be decreased by using a combination of in- centrations when averaged over a period of up to jection and pumping wells. Injection pressures one year.[4]

should be low enough so as not to affect significantly the hydrogeologic properties of the 6. Monitoring Program aquifer. [7]

6.1 Monitoring Objectives. The purpose of the 5.4 Models Used in Computations. The com- ground water monitoring program is to detect putations of radionuclide transport may begin the presence of any accidental release of radioac-by use of a simplified one-dimensional disper- tive liquid. The ground water monitoring sion equation or more rigorous niodels may be program may also be designed to encompass employed. 6 The movement of ground water and monitoring requirements for other purposes. The I radioactive constituents is described by a set of design of the monitoring program should be partial differential equations. These equations based on the analyses of the regional and local in their most general form can be solved only by ground water systems and radionuclide trrins-numerical methods. However, the equations can port. Most of the monitoring program should.be be simplified by assuming ideal physical proper- designed in accordance with the postulated ties of the aquifer, and the solution can be ob- ground water system, as described in previous tained using simplified boundary conditions. sections. The monitoring program should also be These simplifying assumptions must be well un- designed to include the varying needs of the pre-derstood if the investigator is to demonstrate construction, construction, operation, and post-that the results obtained from a given model are operation periods.

conservative, i.e., the model does not predict lower concentrations than will be expected to Monitoring for radionuclides in ground water is occur. Thus, the implementation of the most required for routine releases into aquifers sophisticated model is not required when a sim- providing drinking or irrigation water supplies.

plified conservative model predicts acceptable For routine releases into aquifers not providing concentrations at the nearest point of potential drinking or irrigation water supplies, monitoring ground water use or discharge. for radionuclides in ground water is not required since the routine releases are within acceptable 5.5 Potential Effects of Postulated Release. limits at the point of release.

The potential effects of a postulated radioactive release to ground water are a function of the Monitoring may not be required for postulated concentration, volume, and chemical and accidental releases if it is demonstrated that physical form of radioactive liquids released, the such monitoring is unnecessary because of mechanism of transport to the ground water, the specific design and site characteristics. However, 6

Examples of simple calculations and discussion of more monitoring is required when local ground writer complex models are given in the Appendix. sources used for drinking or irrigation can be 7

J . - a4 American National Standard ANSI/ANS-2.17.1980 significantly affected by postulated accidental (1) Monitoring water levels and pumpage.

releases. Water levels shall be monitored to indicate trends in the ground water regimen for the pur-6.2 Monitoring Methods. pose of predicting the migration of potential radionuclide releases. Water level, purnpage, 6.2.1 Well Construction. Ground water and precipitation records during operation will systems are ordinarily monitored by test holes provide demonstration of the long-term per-and wells, although in some circumstances formance of the aquifer system. At least one! con-springs, ditches or drains are used. The wells tinuous water level recorder should be installed should be designed to last longer than the rest of for those major aquifers under the site that can the plant equipment in the event that be significantly affected by the postulated ac-monitoring is required for post-operation cidental release of radioactive effluents. A periods. In this manner, there will be no changes variety of water-level recording devices is in the data base due to changing data points or available for monitoring purposes. Whatever disturbance of the aquifer by drilling activities. system is selected, it shall provide data that can Wells should be designed and constructed to be plotted on a long-term well hydrograph. The avoid contamination from the surface and con- frequency of measurement should assure that tamination moving from one aquifer to another changes in the water level in excess of a few cen-through the well bore. This is especially critical timeters are observed. The ground water system where the well intersects two or more aquifers should be so understood that the cause cam be which are under different heads. identified for any long-term trend in water levels.

A single well should be designed to monitor no (2) Monitoring for radionuclide content of more than one hydrogeologic unit. If more than ground water.[8,9,10,11] The well system for one hydrogeologic unit is to be monitored at a monitoring potential radionuclides in ground specific point, the monitoring system should water generally requires a greater concentration consist of a cluster of wells, one to each unit. of wells in a smaller area than that for Water levels for more than one hydrogeologic monitoring water levels or water quality, unit may be measured within one borehole only because the system is designed to detect a sub-if an effective seal between units has been stance that is not aquifer wide it. its demonstrated. Vertical movement within one distribution. The design of this system shall hydrogeologic unit can be monitored by placing focus on locations where radionuclides can enter piezometers at different depths in the same unit. the ground water systems.

In general, monitoring wells should be The frequency of sampling shall be determined downgradient of the facilities with potential for on the basis of careful study of the hydrogeclogic accidental release to the ground water. This may system and the calculated travel time of not b.- in the same lateral direction for all radionuclide releases. Monitoring should begin hydrogeologic units that are monitored. Areal at least one year prior to fuel loading. The most and vertical spacing of monitoring wells should mobile radionuclide in ground water systemns is be consistent with the geohydrologic charac- tritium; more frequent analysis should be made teristics of the area. More homogeneous for- for this radionuclide than for others. Analysis mations would generally require fewer wells for tritium requires that water samples be than heterogeneous formations. collected. Ground water should be analyzed for tritium at least quarterly, and for other Observation wells should be periodically tested radionuclides of consequence as appropriate, but to ensure their proper functioning. Routine at least on an annual basis to establish maintenance is recommended to prevent background concentrations. If the tritium con-clogging. centration in any of the monitoring wells is 6.2.21 Types of Monitoring Data. Types of found to undergo a statistically significant monitoring data that shall be collected at the change with respect to the established site include the following: background level, or if a trend of increasing 8

• p *, 1 American National Standard ANSI/ANS.2.17-1980 tritivum level is apparent, analyses for other [3] Title 10 Code of Federal Regulations, Part k,. radionuclides shall be more frequent and the 100, "Reactor Site Criteria," Goverjunent cause of the increased tritium values shall be Printing Office, Washington, DC.

determined. [4] Title 10, Code of Federal Regulations, Part 20, Appendix B, "Concentrations in Air 6.3 Methods of Reporting Results of and Water Above Natural Background,"

Monitoring, Sampling, and Analyses. For Government Printing Office, Washington, those sites which have a ground water DC.

monitoring program, the results of the ground [5] GASPAR, E., and ONCESAU, M., 1972 water monitoring program should be maintained Developments in Hydrology I-Radioaictive by the owner and a yearly summary should be Tracers in Hydrology: Elsevier Publishing available for review by the NRC. This summary Company, New York, 342 p.

should provide a simplified description of the [6] WEBSTER, D.S., PROCTOR, J.F. AND hydrogeologic system being monitored, a map MARINE, I.W., 1970, Two-Well Tracer showing the locations of the monitor wells in Test in Fractured Crystalline Rock, U.S.

relation to plant facilities, and a table giving Geological Survey, Water-Supply Paper coordinates, ground elevations, drilled depths, 1544-I, pp I I-26.

intake depths and elevations, diameters, and [7] U. S. Army Engineers Waterways Ex-specific capacities of the monitor wells. These periment Station, 1976, Determination of items will remain the same from year to year Rock Mass Permeability,Technical Report unless new wells are installed or new un- S-76-2, 88 p.

derstanding of the hydrogeologic system is ob- [8] KRIEGER, H.L., 1976 Interim tained. If new monitoring wells are installed, Radiochemical Methodology for Drinking details of the construction should be provided. Water, Environmental Monitoring and The owner should maintain the current Support Laboratory, EP-500/4-75-008, U.S.

monitoring information and its relation to the EPA, Cincinnati, Ohio.

historical data from the monitoring program in [9] THATCHER et al., 1977, Method.; for both tabular and graphic form. The presentation Determination of Radioactive Substances should consist of a graph of monitoring values in Water and Fluvial Sediments: U.S.

versus time from the beginning of the Geological Survey, Techniques of Water-monitoring program to .the current year. Resources Investigations, Book 5, Chapter Sepazate graphs should be prepared for water A5, 95 p.

levels, chemical quality, and radionuclide con- [10) American Public Health Association, :L976, tent. If anomalous values or an adverse tem- StandardMethods for the Examination of poral trend are indicated, the NRC shall be Water and Waste Water, 14th Edition, notified immediately and an explanation shall 1193 p.

be provided as soon as possible. [11] Office of Water Data Coordination, '!977, National Handbook of Recommended Methods for Water-Data Acquisition,

7. References Chapter 5, Chemical and Physical Quality of Water and Sediment, U.S. Geological

[1] LOHMAN, S.W. and others, 1972, Survey, Reston, Virginia.

Definitions of Selected Ground Water Terms: U.S. Geological Survey, Water- When the preceding American National Stan-Supply Paper 1988, 21 p. dards referred to in this document are saper-

[2] IOHMAN, S.W., 1972 Ground Water seded by a revision approved by the American Hydraulics: U.S. Geological Survey, Prof. National Standards Institute, Inc., the revision Paper 708, 70 p. shall apply.

9

i - a;4 American National Standard ANSIIANS-2.17-1980 Appendix (This Appendix is not a part of the American National Standard for Evaluation of Radionuclide Transport in Ground Water for Nuclear Power Sites, ANSI/ANS-2.17-1980, but is included for information purposes only.)

Methods for Analysis of Radionuclide Transport in Ground Water A. Introduction Methods of data collection and reduction are presented in the Appendix of American National Stan-dard for Evaluation of Ground Water Supply for Nuclear Power Sites, ANSI/ANS-2.9-1980.

The movement of radionuclides in ground water can be described by two equations: one for the movement of the carrier fluid (water) and one for the transport of the dissolved constituents (radionuclides). In using these equations, the movement of the carrier in the region under con-sideration must be known before the transport equation can be solved.

In the following sections the equations for water movement and mass transport are discussed. In each section the discussion will begin with the most general equation and proceed to the simplest x-pressiorti. When applying these equations it is best to begin with the simplest form of the equation or solution, and if necessary, progress to more complex forms. However, when using the simplified (cx-pressiort, the assumptions that were made in their formulation must be considered (i.e., these cx-pressions are valid under the assumptions made in their formulation, and use of them for calculations where the assumptions do not apply will lead to erroneous results). Note that none of the models is valid for aquifers having widely spaced fractures or solution channels. Here the bulk of the flow occurs in the fractures or channels and cannot be averaged over the medium. Thus, the requirement of con-tinuous media assumed in the formulation of the equation has been violated. In fractured or cavernous aquifer, tracer studies can be used to obtain travel time and fluid flux. Also, none of the models is valid for conditions of varying ground water densities or aquifer thickness, such as those encountered in coastal areas at the fresh-water salt-water interface.

A.1 Ground Water Flow At any plant site the assumption of instantaneous release of radioactive liquids from tank storage is generally accepted as the most severe input of radionuclides to ground water. However, more realistic releases may be assumed. This more realistic type of release will usually bring the radioactive liquid into contact with soil moisture moving as unsaturated flow above the water table. However, the release can also be directly into the zone of saturation. The predominant direction of the unsaturated flow is downward until the flow reaches the zone of saturation. Within the zone of saturation the flow is predominantly lateral.

The governing equations in the unsaturated zone consist of a set of coupled equations for the movement of gas and water. To date, only computer codes of limited applicability are available for the solution of these coupled gas-water equations. When the assumptions are made that the water moves as a single phase and that no trapped air pockets exist, a single governing equation for saturated-unsaturated flow is obtained.(l)7 7Numbers in parentheses refer to corresponding numbers in Section A.5 References.

10

American National Standard ANSI/ANS-2.17-1980 dO 4 .1 tn. it' + OA' + A]JA= V*[K (h) *(Vh + Vz)] (Eq. 1)

'. where 8 is the moisture content n' is total porosity

.C' is the modified coefficient of compressibility of the medium Y is the modified coefficient of compressibility of water h is the pressure head t is the time K is the hydraulic conductivity tensor z is the elevation head V is the Del operator Equation (1) is nonlinear because for unsaturated flow both conductivity and moisture content are functions of pressure head. These relationships should be determined under existing field conditions to avoid the effects of disturbance of the medium. They are difficult to obtain from field measurements and must be obtained for each soil layer. Because of this difficulty, a reasonable empirical relationship or a known relationship from a similar soil type may be selected. Because of the large computez core requirement, the solution of Equation (1) in three dimensions is impractical. Equation (1) can be solved in two dimensions.(1) For saturated-unsaturated flow, the vertical dimension must be con-sidered along with one horizontal dimension, resulting in a vertical plane. From the solution of Equation (1) the pressure heads are known and can be used in Darcy's law to obtain the components of flux.

V = -K(h)* (Vh + Vz) (Eq. 2) where V is the flux.

Thus, Equation (2) can be solved to obtain the necessary flux data for the solution of the transport equation. In doing this operation numerically the components of the flux are not continuous. These discontinuities can cause difficulty in the solution of the transport equation and can be eliminated by solving the coupled set of equations in which the flux appears as a variable.

[-a'7 + OA3' + ~~~dh]

4r- t = -VV V (Eq. 3)

Equations (2) and (3) are adequate to eliminate the discontinuities in the flux; however, the amount of computer core required for their solution has been increased because of the increased number of variables.

The solution of the saturated-unsaturated flow equation will give the most realistic results because the unsaturated region has been considered in the movement of fluid from the point of release through the unsaturated zone to the water table. Depending on the nature of the problem, analytical or numerical methods like the ones described in References (1, 2, and 3) can be used to analyze saturated-unsaturated flow. When the unsaturated zone is neglected or all of the flow is considered to be in the saturated zone, Equations (2) and (3) become (a' -1 n' A') 'ah = V V (Eqq: 4)

V = -K * (Vh + vz) 11

S :

American National Standard ANSIIANS.2.17-1980 where the moisture content has reached total porosity and the hydraulic conductivity has reached its saturated value which is no longer a function of pressure head.

The hydraulic conductivity is a tensor which accounts for directional properties (anisotropy) that arise in formation such as layered sediments (i.e., hydraulic conductivity is different in different directions).

If the coordinate system is oriented parallel to the principal components of hydraulic conductivity, only the principal components of the tensor are required. If the medium is further assumed to be homogeneous and isotropic, hydraulic conductivity becomes a scalar and equation (4) becomes (at + :a'I3')- = -V V V=-K=- (Vh + Vz) (Eq. 5)

The terms a' and A' are defined as a' = ,aga

/' = p'g/ (Eq. 6) where p is the water density g is the acceleration of gravity

a. is the coefficient of compressibility of the medium

/3 is the coefficient of compressibility of water.

The specific storage coefficient is defined as Ss = pg (a + n' ,B) (Eq. 7)

Elimination of the flux terms from Equation (5) and substitution of Equations (6) and (7) into the results yield V2H K -aH (Eq. 8) where H is the total head.

This ecluation is valid for saturated flow in confined aquifers.

For a confined aquifer of thickness b, the storage coefficient and transmissivity are defined as S = S b T =K b (Eq. 9) and Equation (8) becomes V2 H = ST E (Eq. 10)

T 't(E.I0 12

A.nezi=an National Standard ANSIIANS-2.17-1980 In simulations using Equation (10) the boundary conditions of leakage should be used when ap-propfiate. For problems involving leaky aquifers, methods like those described in References (2, 4, 5 and 6) can be used.

For unconfined aquifers where compressibility of the medium and the water is relatively unimportant compared to the vertical movement of the free surface (water table), the continuity equation can be written as:

2)(b'Dig) + 'a (b'H) = SY (Eq. 10A)

Introducing Dupuit's approximation, Equation (1OA) can be simplified as follows:

V2 H2 _ (Eq. lOB) where

,y is the specific yield of the aquifer W' is the saturated thickness of the aquifer For steady flow in either confined or unconfined aquifers, Equations (10) and (lOB) reduce respectively to the following equations:

V2 H = 0 (Eq. 11A) 2 2 V H = 0 (Eq. lIB)

For simplified cases, analytical solutions of Equations (10), (1OB), (11A), and (1iB) like those given in References (3, 4, 5, 7, and 8) can be used. For more complex situations, numerical solutions like those described in References (6 and 9) should be used.

An approximation of the flux in the major flow direction can be obtained using Darcy's law.

V. = -K dHllLKAH! (Eq. 12) where AH/Ax is the hydraulic gradient in the direction of flow. This approximation is crude but in many cases it is acceptable because of the inability to accurately measure spatial variations in the hydraulic conductivity. Use of this equation assumes a homogeneous isotropic medium in which the gradient is constant over the increment Ax. The pore velocity (seepage velocity) may be approximated by dividing the flux, Vx, by the effective porosity. In many cases, use of this equation is inadequate and the analyst should use judgement to select a model that adequately considers variable hydraulic conductivity and transient conditions.

A.2 Mass Transport. The most general form of the mass transport equation is for transport in saturated-unsaturated media. If local equilibrium of mass transfer and first order chemical reactions are aisumed, sorption can be represented as a linear relationship and the general mass traniport equation can be written(l0) as 13

-American National Standard ANSI/ANS.2.17-1980 Rd OaC - V (oD. Vc) + V- (Vc) + (Rd 3 + XA Rd)c 0 (Eq. 13) where Rd is the retardation factor c is the concentration of dissolved constituent V is the dispersion tensor V is the flux A is the radioactive decay constant The radioactive decay constant, A, is calculated from handbook values of the half-lives of different isotopes in appropriate units of time by the following relationship:

- 1in 2 (Eq. 13A)

A life of the isotope Equation (13) can be solved numerically.(10) The retardation factor is defined as Rd=1+PbKd (Eq. 14) and the distribution coefficient (11) is Kd - radioactiiy/mass of solids (Eq. 15) radioactivity/volume of water where Pb is the dry bulk density of the medium ld is the equilibrium value of the distribution coefficient.

The distribution coefficient is unique for each chemically different radionuclide.

The dispersion tensor for isotropic media is Dii= aT V ij + (aOL-aT) Vi VjJV 6i 1 i= j, aij =0 i p j (Eq. 16) where 5jj is the Kronecker delta aT is the transverse dispersivity aL is the longitudinal dispersivity V is the magnitude of the flux ViVj are the components of the flux In general, the dispersivity is a fourth-rank tensor which contains 81 components; however, if isotropy is assuamed, it can be related to two constants, i.e., longitudinal and transverse.(7)

The transverse and longitudinal components of dispersivity may be obtained from tracer studies con-ducted in the aquifer. This can be done using the tracer data and an appropriate transport model.

Equation (13) may be used in conjunction with Equations (1) and (2) or Equations (2) and (3) for simulation of radionuclide transport. In using Equations (1) and (2) the problem of discontinuous flux 14

j1 American National Standard ANSI/ANS-2.11-1980 can arise in the numerical scheme whenever the advective-transport term in equation (13) is com-parable to or greater than the dispersion term. Thus, in fine-grained sediments where the coefficient of dispersion is small, Equations (2) and (3) must be used.

The assumptions of local equilibrium and first-order chemical reactions result in sorption bei:2g a linear relationship. These assumptions are incorporated in Equation (13).

When. the medium is assumed to be fully saturated, Equation (13) becomes Rdn' -V (B3Vc) EV +X Rd c = 0 (Eq. 17) and n Dij = aT V 'jj + (aL - aT) ViVj/V (Eq. 18)

The various forms of the transport equations, presented previously, have been solved by numerical in-tegration. The numerical methods used for solution of these equations in a general flow field are discus:;ed in References (9, 10, 12, 13, 14, and 15).

When the fluid flux is assumed to be uniform and steady, Equation (17) becomes Rdk_.+/-- V. (D.Vc) + V- Vc + XRd c = 0 (Eq. 19)

If the dispersion tensor is assumed to be homogeneous and anisotropic and the flux is assumed to be parallel to the x-axis, Equation (19) can be written as Pede Rdac:-D, DX 22C .DVYDi2C2 2 -D WC + VX De

- DZZ-+~-.+ ~c + A Rd C- =E0(Eq. 20 20).

where the components of the coefficient of dispersion are given from Equation (18) as I)D, = aLV. D -y

=D aTVnx (Eq. 21)

Equation (20) can be rewritten in the form 2 V- -E 2 + Ia +t i7xZ

+ c =0 (Eq. 22) where E:; = (Eq. 23) where U is the approximate rate of movement of the radionuclide and may be used to estimate the travel time.

The simplified form of the transport equation, Equation (22), can be solved analytically in an infinite region with simple boundary conditions.

15

. Americam National Standard ANSI/ANS.2.17-1980 The longitudinal and transverse dispersivities used in the calculation of the components of the disler-sion coefficient, Equation (21), should be obtained from tracer studies in the aquifer under con-sideration. Extrapolated, calculated, or laboratory-derived values of dispersivities should seldom be applied to full-scale field problems. The above equations are strictly valid only for isotropic media, :but may bB applied to slightly anisotropic formations when the dispersivities are obtained from field studies.

A.3 Solutions to the Mass Transport Equation. (15, 17, 18, 19, 20) The equation of mass transport used inL this section was formulated under several assumptions which will be reviewed before discussing its solution. The molecular diffusion was assumed to be many orders of magnitude smaller than the mechanical dispersion, and was neglected. The medium was assumed to be homogeneous and isotropic.

The fluid flow was assumed to be uniform steady flow parallel to the x-axis. The sorption of the radionuclide was assumed to be linear. Chemical reactions were assumed to be rapid such that equilibrium exists between the dissolved and sorbed radionuclides. The radioactive liquid was assumed to have the same density as the ground water. These assumptions yield Equation (22). For the solution of this equation, it is further assumed that the region is infinite and that the concentration in lihe region is zero at time equals zero. For the case of an aquifer of finite thickness, the appropriate models are referenced in Appel and Bredehoeft.(19)

A.3.1 Instantaneous Line Source. For the instantaneous release from a line source passing through the point (xl, Yi) and parallel to the z-axis, the solution of Equation (22) is

- 1{ exp [(x - x1 ) -Ut]2 + (y - Y) 2 +

dn(ExEy) /2 4Ext 4Et (Eq. 24) where m is the instantaneous mass per unit length in the z direction.

In using Equation (24) for calculation of radionuclide transport, m is calculated by dividing the tot al activity of a particular tadionuclide contained in the release by the assumed length of the line source.

A.3.2 Instantaneous Rectangular Plane Source. For the instantaneous release from a rect-angular plane source of width f, parallel to the y-z plane and centered at the origin, the solution of Equation (22) is Mt exp - (X- Ut)2 +Xt'lrerf Y +f/2 -e~rf~ Yf/2 4Rdn (TExt):F 1 2 { 4Ext J 2 (EAt)2 2 (Et)1I2J (Eq. 25) where m' is the mass per unit area of the plane source.

Thus, for calculations using Equation (25), m' is calculated by dividing the total activity of a particular radionuclide contained in the release by the source width times the assumed thickness.

A.3.; Continuous Line Source. For continuous release from a line source passing through the origin and parallel to the z-axis, the transient solution of Equation (22) is t qrYT .2.r)]

C=Jr q exp _ (t )]2 + + X(t-r) dr (Eq. 26) 0 47TRdn(ExEy)I2(t r (4Ex(t- r) 4Ey(t- s) }

where q is the time rate of release per unit length in the z direction.

16

i r - O American National Standard ANSI/ANS.2.1'1-1980 Equation (26) can be integrated numerically using Legendre-Gauss quadrature. However, as the time C becomes large, Gauss-Laguerre quadrature may be required for the integration. Computer programs; for performing this integration are available in most subroutine packages.

The steady-state solution of Equation (26) is obtained by letting time approach infinity. This yields a solution in terms of Bessel functions which may be approximated to give the steady-state solution C q exp - L -u (Eq. 27) 4Rdn(7TExEyL) 2EX }

where gEyx 2 + EXy 2) (U2 Ey + 4 ExEy))] I 4EXEy A.3.4 Continuous Rectangular Plane Source. For continuous release from a plane source of width f, parallel to the y-z plane and centered at the origin, the transient solution of Equation (22) is C q' ip _4E(t_ )2 +M f y + f/2 -y-f12 t ZNd(_rEx)_/2_(t-

_)/2 p (-4Ex(t-r )] + (tr)[erf 2[Ey(t-7)11 2 erf 2 [Ey(t-T)]l.dr (Eq. 28)

When using the solution for a rectangular plane source, it should be noted that as the distance from the source becomes large as compared to the source width, the results approach those given by a line

( Therefore, the solution for a rectangular source can be used near a waste tank, and the solution

.source.

for a line source can be applied farther from the tank. When using any of the solutions given in this section, the effort involved in calculation of concentrations can be minimized by computer evaluation of the. solution.

A.3.5 Example Problems. Example problems 1 through 4 are based on the following data and dif-ferent assumptions have been made regarding dispersion, sorption, decay, and the nature of the release.

The basic assumptions are listed separately under each example.

A tank, 1.0 meter in diameter, containing 20.0 curies of 90Sr ruptures, and the radioactive liquid enters an unconsolidated sand aquifer which has an average saturated thickness of 10.0 m. The aquifer has the following properties:

Vx =1.2 m/day n  :=0.35 n' =0.35 K 17.3 m/day aL =20.0 m (see. Reference 9) aT ==4.0 m (see Reference. 9).

Pb ==1.8 gm/cm3 Ed ==80 cm 3 /gm (for 9OSr in this aquifer)

The problem is to calculate the. change in the concentration at the point x = 120 Mn,y =0.

Example 1. Assume that the radioactive liquid is distributed uniformly across the entire saturated thickness of the aquifer and that no dispersion, sorption, or decay occurs. Under these assumptions the 17

, ? r 0

. .American National Standard ANSI/ANS-2.17-1980 radionuclide moves as a slug at a rate equal to the pore velocity in the aquifer. The concentration, pore velocity, and travel time are as follows:

C= 2OCi 20 x 0euCi 6 = 7*

n(Vol. of Aquifer) .36 x 10 xi x X1x0 CM3 mf Pore Velocity = Vx/n = 1.2/.35 = 3.4m/day Trave2 time = distance/pore velocity = 120/3.4 = 35.3 days Thus the slug would arrive at the point under consideration after 35.3 days with no reduction of the initial concentration. In this time period there will be no appreciable decay of the 28-year half-life 9Sr. 'rhe distribution of the 90Sr across the entire saturated thickness of the aquifer is not realistic; however, the example is useful for comparison with the following example calculation.

Example 2. This example differs from Example 1 only in that longitudinal dispersion is considered.

Assume that the radioactive liquid moves in the aquifer with no sorption, decay or transverse disper-sion. Note that Ed = 0 and the solution for an instantaneous line source, Eq. (24) is undefined because Ey = 0. However, the solution for an instantaneous plane source, Eq. (25), for y = 0, f = 1, By = 0 becomnes me exp - J((XUt) 2 +x

2Rdn( 7rExt)1 2 4E+t M

From Equations (14), (21), and (23) the following coefficients are calculated:

Re! =1.0 DM: = 68.6 m2 /day E] = 68.6 m 2 /day

° = 3.4 m/day The remaining coefficients are in' = 2.0 Ci/M2 and X = 0. Substitution of the coefficients into the above solution for various times yields:

TIME CONCENTRATION (days) (u1Ci/m1) 0 0 16 1.8 x 102 32 3.4 x 10-2 40 3.0 x 10-2 Note that the concentration at the point under consideration increases to a maximum value and then decreases as the radionuclide front passes the point. Also note that the arrival time of the maximum concentration is approximately the same as the previous example, but the maximum concentration is diminished.

Example 3. In this example the effect of sorption is added. Assume that the radioactive liquid moves in the aquifer with no decay or transverse dispersion. The solution ised in Example 2 applies. From Equat~ions (14), (21), and (23) the following coefficients are calculated:

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American National Standard ANSIIANS-2.1,'71980 R.1 = 412.4 k Dxxy = 68.6 m2 /day E  : 0.17 m 2/day UJ = 0.01 m/day Substitution of these coefficients, in', and X into the solution for various times yields:

TIME CONCENTRATION (days) (gCi/ml) 0 0 5,000 3.2 x 105 10,000 9.0 x 10<

15,000 7.0-x 10-Example 4. In this example the effects of transverse dispersion and decay are added. Assume that.the tank rupture produces an instantaneous line source, and locate the origin of the coordinate system at the tank. Thus, in Equation (24), xl =0, y1 =-. From Equations (14), (21), and (23) the following coef-ficients are calculated.

R( 412.4 68.6 m2 lday 13.7 m2 /day 4 0.16 m2 /day 0.03 m2 /day 1 0.01 m/day The half-life of 9 0 Sr is 28 years, and the release per unit area. of aquifer is 2.0 Ci/m2 . Using the half-life, X is calculated to be 6.66 x 10-5 (day T). Substitution of the coefficients into Eq. (25) for various times yields::

TIME CONCENTRATION (days) 46Ci/ml) 0 0 5,000 5.3 x 107 10,000 7.5 x 107 15,000 3.4 x 107 Note that the arrival time of the maximum concentration remains approximately the same as in Example 3 and that the maximum concentration has been reduced.

Table 1 summarizes examples 1 through 4 and demonstrates the effect of considering more realistic assumptions.

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0 Table 1 Example Summary 0

Approximate maximum concentration Example Longitudinal Transverse Radioactive Arrival Time Concentration Problem Dispersion Dispersion Sorption Decay (days) (aCi/ml) 9; z

1 no no no no 35.3 7.3 I-.

(slug flow) 2 yes no no no 32 3.4 x 102 3 yes no yes no 10,000 9.0 x 10o 4 yes yes yes yes 10,000 7.5 x 107

.~j

, American National Standard ANSI/ANS.2.17.31980 AAA Notation aL Longitudinal dispersivity (L) aT Transverse dispersivity (L) b Thickness of a confined aquifer (L) b' Thickness of saturated aquifer (unconfined) (L) c Concentration of dissolved constituent (M/L 3 )

A, Dij (L2 Dispersion tensor WT) d Mean grain diameter (L)

Ei Coefficient defined by Equation (23) (L2 IT) f Source width (L) g Acceleration of gravity (LIT 2 )

H Total head (L) h Pressure head (L)

K Hydraulic conductivity (LIT)

K Saturated conductivity tensor (LIT)

K(h) Conductivity tensor (LIT)

Kd Distribution Coefficient (L3 IM) m Instantaneous release per unit length (MIL)

• m' Instantaneous release per unit area (M/L2 )

n Effective porosity n' Total porosity q Time rate of release per unit length (MILT) q' Time rate of release per unit area (MIL 2 T)

Rd Retardation -factor S Storage coefficient Ss Specific storage coefficient (1/L)

Sy Specific yield T (L2 Transmissivity WT) t Time (T)

U Coefficient defined by Equation (23) (LIT)

V Magnitude of the flux (LIT)

V, Vi Flux (L/T) z Elevation head (L) a Coefficient of compressibility of the medium (LT 2 /M) a' Modified coefficient of compressibility of the medium (i/L)

, Coefficient of compressibility of water (LT2 /M)

)3' Modified coefficient of compressibility of water (i/L)

Bij Kronecker delta p Moisture content X Radioactive decay constant (l/T) p Density of water (M/L 3 )

Pb, Bulk density of the medium (MIL 3 )

7 Dummy variable (T)

V Del operator (1/L) 21

• . r - American National Standard ANSI/ANS-2.17-1980 A.5 References

[1] REEVES, M. and DUGUID, J.O., Water Movement Through SaturatedPorous Media: A Finite.

Ellement Galerkin Model, Oak Ridge National Laboratory Report, ORNL-4927, 1975.

2 NEUMAN, S.P., "Saturated-Unsaturated-Seepage by Finite-Elements," Proc. ASCE, JourndI of Hydraulics Division, Vol. 99, No. HY 12, December 1973.

[3] WALTON, W.C., Ground Water Resource Evaluation, McGraw-Hill Book Co., New York, 1970.

[4] cLOVER, R.E., Transient Ground Water Hydraulics, Water Resources Publications, Fort Collins, Colorado, 1976.

[5] I)AVIS, S.N. and DeWIEST, R.J.M., Hydrogeology, Wiley, New York, 1965.

[6] TRESCOTT , P.C., PINDER, G.F., and LARSON, S.P., Finite-Difference Model for Aqruifer Simulation in Two Dimensions with Results of NumericalExperiments, U.S. Geological Survey, Techniques of Water Resources Investigations, Book 7, Chapter C1, 1976.

[7] BEAR, J., Dynamics of Fluids in Porous Media, Elsevier Publishing Co.,; Inc., New York, 1c'72.

[8] DEWIEST, R.J.M., Geohydrology, John Wiley-& Sons, Inc., New York, 1965.

[9] E'INDER, G.F, "A Galerkin Finite-Element Simulation of Groundwater Contamination on Long Ifland, New York," Water Resources Research Vol. 9, No. 6, December 1973.

[10] DUGUID, J.O. and REEVES, M., Material Transport Through Porous Media A Finite-Elentent GJalerkin Model, Oak Ridge National Laboratory Report, ORNL-4928, 1976.

[il] ETHERINGTON, H., Nuclear EngineeringHandbook, First Edition, McGraw-Hill, New York, 1958.

[12] FANG, C.S., WANG, S.M., and HARRISON, W., "Groundwater Flow in Sandy Tidal Beach -

'wo Dimensional Finite-Element Analysis," Water Resources Research, Vol. 8, No. 1, 1'l72.

[13] HERBERT, R. and ZYTYNSKI, M., "A New Technique for Time Variant Groundwater Flow Analysis," Journal of Hydrology, Vol. 16, 1972.

[14] NEUMAN, S.P. and WITHERSPOON, P.A., "Analysis of Nonsteady Flow with a Free Suriace Using the Finite-Element Method," Water Resources Research, Vol. 7, No. 3, 1971.

[15] SZABO, B.A. and McCRAIG, I.W., "A Mathematical Model for Transient Free Surface Flow in Non-Homogeneous or Anisotropic Porous Media," Water Resources Research, Vol. 4, No. 3, 1968.

[16] CARSLAW, H. and JAEGER, J., Conduction of Heat in Solids, Oxford University Press, London, 1959.

[17] BIRD, R., STEWART, W., and LIGHTFOOT, E., Transport Phenomena, John Wiley & Sons, Inc., New York, 1960.

[183. I9LARLEMAN, D., Transport Processes in Water Quality Control, Department of Civil Engineering, Massachusetts Institute of Technology, Boston, Massachusetts, -1970.

[19] APPEL, CA. and BREDEHOEFT, J.D., Status of Ground-Water Modeling in the U.S.

Geological Survey, U.S. Geological Survey, Circular 737, 1976.

[20] CODELL, R.B. and SCHREIBER, D.L., "NRC Models for Evaluating the Transport of Radionuclides in Ground Water," Proceeding of Symposium on Management of Low-Level l'adioactive Wastes, Georgia Institute of Technology, May, 1977.

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