United States      Office of Radiation Programs EPA 520/6-78-005
Environmental Protection   AW-459        June 1978
Agency         Wash DC 20460
Development and
Application of a
Risk Assessment Method
for Radioactive Waste
Volume I:
Generic Description

                           EPA REVIEW NOTICE                                ;

     This report has been reviewed by the  Office  of Radiation Programss U.S.    \
Environmental Protection Agency (EPA) and  approved  for  publication. Approval
does not signify that the contents necessarily reflect  the views and policies   !-
of the EPA.  Neither the United States nor the EPA  makes  any warranty, expressed
or implied, or assumes any legal liability or responsibility of any information,:
apparatus, product or process disclosed, or represents  that  its use would not
infringe privately owned rights.                         -  •

                                      EPA 520/6-78-005
               Final Contract Report
     Principal Investigators  Stanley E.  Logan
          Bureau of Engineering Research
           The -University of New Mexico
           Albuquerque,  New Mexico 87131
  Volume I:   Generic Description of AMRAW-A Model
             S.  E.  Logan,  M«  C.  Berbano

                     July  1978
                  Prepared  for
    0.  S.  Environmental  Protection Agency
         Under Contract  No. 68-01-3256
                 Project Officer
                  Bruce J, Mann
        Office of Radiation  Programs-LVF
                 P. O, Box 1502?
             Las Vegas, Nevada 89114

Page Intentionally Blank


    The EPA Office of Radiation Programs carries out a national program
to evaluate human exposures to radioactivity, and to promote the
development of controls to protect the environment and public health
from such radioactivity.  An important part of this program consists of
the development of environmental protection criteria and standards for
radioactive waste management and disposal.

    To sustain this effort, studies have been supported by EPA to
develop methods to evaluate the environmental adequacy of proposed
waste management alternatives, and this report describes one of the
first attempts to develop a comprehensive assessment model.  It has
been funded at a very modest level.  Much interest has been expressed
in this work, and through publication, EPA is making it available to
those involved with the development and use of models as decision-
making tools.

    In order for models to be useful as tools for decision-making
concerning radioactive waste management alternatives, their
capabilities and limitations must be fully understood.  It should be
noted that assessment models in themselves will not identify optimum
waste management choices.  However, they can be used to compare well
defined alternatives.  One of the necessary steps in any model
development and validation process is the comparison of results with
results obtained from the application of alternate models to test
cases.  It is hoped that as other comprehensive assessment models become
available, comparison studies can be performed,

    The methodology described herein has been applied, for model
illustration purposes, to a reference repository in a bedded salt
formation located in the southwestern United States.  Any results
published in this report should not be interpreted as implying
conclusions concerning the suitability of the reference site or any
site-specific method/repository combination for the preparation and
disposal of radioactive waste,

    Comments on this analysis as well as any new information would be
welcomed; they may be sent to the Director, Technology Assessment
Division (AW-459) Office of Radiation Programs, 0.S. Environmental
Protection Agency, Washington, D.C, 20460.
                                  tf. D. Rowe, Ph.D.
                           Deputy Assistant Administrator
                           for Radiation Programs (AW-459)

Page Intentionally Blank


     A Radioactive Waste Management Systems Model, developed and imple-
mented by The University of Mew Mexico under contract with the U. S.
Environmental Protection Agency, is presented.  The systems model and
associated computer code called AMRAW  (Assessment Method for Radioactive
Waste), has two parts.  The first part, &MRRW-R, consists of the Source
Term  (radioactive inventory versus time), the Release Model, and the
Environmental Model.  The Release Model considers various geologic and
man-caused events which are potential mechanisms for release of radio-
active material beyond the immediate environs of a repository or other-
location; the risk analysis mode uses events distributed probabilistically
over tine, and the consequence analysis mode "uses discrete events occur-
ring at specified times.  The Environmental Model includes:  1} the trans-
port to and accumulations at various receptors in the biosphere,
2) pathways from these environmental concentrations, and 3)  resulting
radiation dose to man,
     The second part of the systems model, &MRRW-B, is the Economic Model
which calculates health effects corresponding to the various organ dose
rates from AMRAW-&, collects these health effects in terms of economic
costs and attributes these costs to radionuclides, decay groups? and
elements initially in the waste inventory.  Implementation, with calcu-
lated results, of AMRAW for Terminal Storage in a Bedded Salt Reference
Repository are presented.  Preliminary demonstrations for the repository
operations phase of waste management and terminal storage in a shale
formation are described; possible applications to other radioactive and
nonradioactive hazardous materials are discussed,  AMRftW uniquely links
all steps together in a  continuous calculation sequence.


     Funding for this project was initially provided by the Energy/Environ-
ment Program, office of Research and Development, and subsequent funding
by the Office of Radiation Programs, EPA.
     Persons at the EPA, other federal agencies, national laboratories,
federal contractors, and foreign correspondents have provided helpful
suggestions during progress of the work or through review of draft reports.
These contributions are greatly appreciated though space does not permit
acknowledgement of each individual contribution.
     The work on this broad interdisciplinary program centered in- the
Chemical and Nuclear Engineering Department (Ch/NE) of the College of
Engineering at The University of New Mexico (UNM),  The principal investi-
gator, S. E. Logan,     assisted by M. C. Berbano and numerous graduate
students in Ch/NE.  A component of the-effort concerned the Economic
Model, handled by the UNM Economics Department.  Other departments at
UNM provided support in       of geologic descriptions and disruptive
events, environmental pathway analysis, and computer programming.  UNM
departments and personnel participating at various levels of activity and
at various times during the study are as follows:
     Chemical and Muclear
     Engineering Department
Faculty:  S. E, Logan
          M. C, Berbano
          K. K. Cox
Students:  W. P. Carroll
           R, L, Conarty
           D. L. Cox
           M. W. Davis
           R. D. Erickson
           H. S, Ng
           M. W. Young

      Economics Department
S. Ben-David
D. S. Brookshire
A. V. Krieese
W. D. Schulze
   Electrical Engineering
   and Computer Science Department
Students;  K, E, Patterson
           C. M. Vining

   Geology Department
Faculty:  D. G. Brookins
          A. M. Kudo
          L. A, Woodward
Students;  J, Iwerks
           P, A. Longmire
   Biology Department
Faculty;  J. R, GOSE

     Econoinics  Degartment                   Mathematics  Department
 Student:  J. M. Dye                     Student;   G. M. McKerney
     Physics Department
 Student:  C. C. Herrmann

     Other persons outside of UHM contributed  significantly to the com-
 pletion of the  study through their direct participation/ the furnishing
 of categories of data, or helping with  critical reviews  of draft versions
 of the report.  These individuals  are listed below under AMR&W sub-models.
 It should be noted that participation by these persons does not necessarily
 imply their endorsement of the AMRAW methodology  or any  of its components.
     Inventory_at^Risk  (Source Term) .   J. O. Blomeke of  QRNL (Oak Ridge
 National Laboratory) furnished ORIGEH computer output for radioactive
 waste projections.
     Release Model.  A. Sanford  {New Mexico Institute of Mining & Tech-
 nology)  conducted a seismic analysis for the model repository site; I. J.
 Winograd (U.S.  Geological Survey)  and H. Lambert  (consultant) provided
 critical reviews,
     Transport  to Environment.  T. E. Kelly (Geohydrology Associates)
 provided hydrologic study for the  model repository site; J. O. Duguid
 (ORNL, now at Eattelle Columbus Laboratories)  provided a description of
 the Duguid-Reeves ground water transport model; R. E. Moore (QRNL) pro-
 vided air dispersion computer output from the  AIRDOS code; T. H. Pigford
 (University of  California) and H.  C. Burkholder (Battelle Pacific North-
west Laboratories) provided critical review of ground water transport.
     Environment-to-Man Pathways.  J, P. Witherspoon (ORNL) provided food
 concentration versus ground deposition  computer output from the TERMOD
 terrestrial code; agricultural economists at the  Hew Mexico State Univer-
 sity provided livestock production data; T. W. Fowler and C. Nelson  (EPA)
 suggested the concept of integrated concentration in foods; S» V. Kaye
and C. C- Travis (ORNL) reviewed  the pathway analysis modeling and con-
 firmed suggested revisions; J. E.  Till  (consultant) reviewed revised
pathway analysis, provided suggestions  and helped in resolving dose con-
version factor questions.

     Economic Model.  W, H. Ellett  (EPA) provided additional insight into
 interpretation of the BEIR report,  and B. M. Bunger  (EPA) provided review
     Improvements in the mathematical representation, of the model were
suggested by D. E. Cabrilla  {EPA}.  J. M.           J. M. Briggs (EPA)
reviewed AMRAW programming and converted from IBM to a CDC system.  Other
persons at the EPA who helped with extensive review of draft reports
include S, T. Bard, C* Y. Hung, J. Neiheisel, and J. J, Swift,
     The EPA Project Officer during the first 1 1/2 years of the study
was S, M. Golberg (now DOE), followed in turn by R. F. Kauffmann and
B. J. Mann.  The guidance and suggestions provided by these persons is
     Prior to the start of the EPA contract, early development of the
AMRAW model, following the framework established as part of the Logan
Ph.D. dissertation, was supported by the Sandia University Research
Program {Sandia Laboratories) and the State of New Mexico Energy Research
and Development Program (now administered by the New Mexico Energy and
Minerals Department).
     The computer logistics and mountains of computer printout for the
final series of cases used in this report were handled by H. S. Ng/ the
many computer aided plots were made by C. C. Herrmann and editorial ser-
vices during preparation of this report were provided by R. L. Conarty.
     Appreciation is extended to the UNM Bureau of Engineering Research,
directed by G.  W.  Hay, for the patient typing, most of which     done
by Jo Williams, printing by M, A.  Arnot,  and contract administration help
by Joyce Meyer»
     Last but not least, the prinicpal investigator acknowledges the
tolerance of his wife,  Marjorie,  during more than two years of continuous
evening and weekends contributed to successful completion of the work.

                OF A  RISK
                      VOLUME  LISTING


             OF AMRAW-B MODEL


                           VOLUME I

                      TABLE OF CONTENTS
Forward	,	   ±ii
Abstract	,	,	_  ,     v
Acknowledgements	..,,.....,..,	.. [ *    vi
List of Volumes	    ix
List of Figures.	,	.-.....,.,...,,..,.,.,....,...   Xii
List of Tables,	  xiii
List of Abbreviations, Symbols
  and Nomenclature,	   x±v

CHAPTER  1,   INTRODUCTION  ,,,..,,..,,.,.,,,,,,,,,, r,..,    1
CHAPTER  2,   SUMMARY ....I,,,,,..,.,,,.,,*,,,.*,.,,,,,,    5
             AMRAW-A MODEL .,.....,.,.,.,,,.,,.,.,.,.,,   15
      A,   AMRAW-A MODEL  ,,,,,,,,,.,,,..,,,.,,,.,,,,,.,   20
      B,   SOURCE TERM  ,,,,.,.,..,.,,.,.,,.,,,.,.,,.,,,   25
      C,   RELEASE MODEL  .I.,,,..,,.,,,,,.,.,..,,.,.,,,   31
           1.  Release Scenarios ,,,,,,,,,,,,,,,	».,,,.   3^1
           2.  Release Barriers ,,,,,,,,,,.,,,.,,,,,.,,,,,,   i|l
           3.  Leaching in Ground Water  ,,,,,,,,,,,,,,,,,,,,   i|2
           4.  Model  Output ,,,,,,,,,,,,.,,,.,,,,,,,,	   51
      D,   ENVIRONMENTAL MODEL ,..,.,,,.,,,.,,.,,..,,,,•  52
           1.  Transport to Environment  ,,,,,,,».,,,,,,,,,,,   52
           2,  Environmental  Pathways  ,,,,.,,,,,,,,,,,,	   90
      E.   MATHEMATICAL          OF        .,,,,,...,.,., 103
           1,  Continuous Representation  ,,,,,,,,,,,,,,,,,,» 103
           2,  Discrete Representation ,,,,,,,,,,,,,,,,,,,,, 108

CHAPTER 6,  APPLICATION OF MODEL ..................... 119

          GROUND WATER TRANSPORT ..................... 121
          IN TERRESTRIAL FOODS ...... ...... ,,,,,, .....
bLOSSARY i i i i i i i i i i i < i i i < i i i i i i i i i < i i i i i i i i i i i i i i i i t i t
KEFERENCES  • i < ..... 9 i i > i t t i • i > > i i i i i i t i > i • i t i i ( < t • i t t i  JLHH

                              VOLURE  I

                           LIST  OF FISURES
4-1    Radioactive waste management systems model,...........	  ig
4-2    One branch of systems model.,	.........................  18
4-3    Releases from geosphere to preliminary
       environmental input receptors	,	  32
4-4    Fault tree symbolism	  35
4-5    Simple fault tree	  37
4-6    Conceptual dynamic repository simulation response............  40
4-7    Preliminary environmental input receptors	  53
4-8    Dispersion to a zone during a release
       time increment	  54
4-9    Adjustment for inter-receptor transfers	„..	  5?
4-10   Conversion of adjusted inventories to concentration	  59
4-11   Sequence for residual activities in time
       increments subsequent to release. »	  61
4-12   Movement of leachant from disposal horizon
       to upper aquifer	,,,......,»	  66
4-13   Transport to air     land surface environmental
       input receptors in Eone 2 following volcanic
       explosion release to air in 400 - 500 y time
       interval	, —	  88
4-14   Main environment-to-man pathways	  91
4-15   Basic pathway relationship.	  93
4-16   Response of concentration of Sr-90 in food
       to unit deposition	  96

A-l    Transverse distribution of concentration
       of peaks at distance of 10 km for plane
       and line sources	.,	 124
ft-2    Concentration distribution 10 km from
       the source for plane and line sources
       with instantaneous release	125
A-3    Concentration distributions in peak
       from line source, at distances
       of 10 and 20 km		... 12?
A-4    Effective plume dimensions	130

B-l    Compartment diagram of the terrestrial food
       pathways by which radioactivity can be
       transferred to man.,.,..	...............3-32
B-2    Linear plot of 1-129 concentrations in
       response to unit initial deposition of pCi/m	 139
B-3    Response of concentration  of 1-129 in food
       to unit initial deposition of yCi/tn^	„	141

                              VOLUME  I

                           LIST  OF TABLES

 TABLE                                                             PAGE

 4-1    Receptor and transfer Coefficient
       Sequence in &MRAW ........................... ....... .... .....   19
 4-2    Selected Significant Radionuelicles .............. ....... , .....   27
 4-3    Fraction of Total Hazard Represented by
       Groups of Selected Radionuclides f  Percent ....... .............   28
 4-4    Factors Comprising Environment-to-Man
       Coefficients ..... ........... ................ ........ . ....... .   94
 4-5    Sample Calculations, Environmental Pathways
       in Zone 2, Total Body Dose Rates from Sr-90
       Following Volcanic Explosion Release to
       Air in 400 - 500 y Time Interval. ...... ..... . ..... . ..... .....
 5-1    Directory of AMEAW-A Output Tables ........................ ...
B-l    Peak Concentrations in Food
       Following Unit Deposition of 1-129 ... ...... ..................  133







Section 4.A
Section 4.B
Section 4.C.I
 V A2

 V B2

 B S C
(Assessment Method for Radioactive Waste) Assessment
Model and associated computer  code

That portion of AMRAW which,  includes Source Terms, Release
Model, and Environmental Model

The economic part of AMRAW

Distribution coefficient used  in ground water transport

 Thermal  efficiency

 Thermal  energy produced

 Capacity factor

 Rated  electrical power capacity

 Duration of  time period
 Fault tree  "and"  gates

 Fraction of inventory transferred to a given input
 receptor if release occurs

 Transfer coefficient to given preliminary environmental
 input receptor

 Fault tree  "or" gates

 Constants used in illustrating forms of P(t)


                Annual probability of release occurrence

     »  etc.
              Time  at which  P(t)  commences  change  or when discrete
              event occurs in using  delta function
              Time  increment within  which t  lies  in using delta func-
              Probability factors
Section 4.C.2.  none
Section 4.C.3.
              Incremental  amount  leached  for n  leach period renewals
              Initial total radioactivity of species subject to  leaching
              Concentration of mobile  species at time t and space x
              Uniform initial concentration of  mobile species
              Effective diffusivity for the species
              Total exposed area  of specimen
              Radioactive  species material flux across interface
              Dissolution  rate constant
              Stokes-Einstein constant, 1.38 x  10   gem /see  molecules



Cumulative  amount of radioactive  isotope  leached  from
solidified waste  for a specified

I  a
**  n
Molecular weight  of diffusing species
Molecular weight  of solvent
Avogadro ' s  number
Radius  of diffusing particle  in cm
Absolute temperature, °K
Molecular volune  of the  solute at normal boiling point,
cm^/g mole


  TI(X, t)




Specimen volume

Spatial coordinate  in cartesian  space

Spatial coordinate  in cartesian  space

Spatial coordinate  in cartesian  space

Empirical constants in leach equation

Transformation variable used is  solution of diffusion

Solvent viscosity at absolute temperature, T °K

Fraction of initial amount leached

Density of diffusing species in  solid state

An association parameter for the solvent
Section 4.C.4   None
Section 4.D.I






  D, .


Modified coefficient of compressibility of the medium

Longitudinal dispersivity

Transverse dispersivity

Time transfer coefficient, incorporating radioactive and
environmental decay,  and transport retardation

Zone land surface area

Zone surface water area

Concentration of the dissolved species

Concentration of the dissolved species appearing as the
solution to the radio/melide mass transfer equation

Dispersion tensor

Component of dispersion  tensor D"

 (in AMRAW) Effective decay factor between two times

Deposition concentration  for land and ground  surface
 (Ci/cm2) due to air deposition













Deposition on  land  surface of  zone

Deposition on  water surface of  gone

 (in &MRAW) Dispersion parameter (land surface area or
water volume)

 (ADJl in &MRAW) Maximum fraction of inventory (or value
of G ) which can be transferred

Component along x axis of coefficient of dispersion
divided by retardation factor,  R,
Component along y axis of coefficient of dispersion
divided by retardation factor,  R.

Fraction of amount  of species  sorfoed on solid medium
per unit mass  of medium

Fraction of amount  of species  remaining in solution
per unit volume of  solution

{ADJ2 in BMRAW) Transfer rate constant

Storage constant

Gravitational  constant

(ADJ in AMRftW) Fraction of inventory transferred from one
receptor pool  to another pool per unit time

(in AMRAW) Non-accumulating matrix which retains inte-
grated deposition for current time increment for use
in calculating transfer to terrestrial food products

Pressure head

Total hydraulic head

Intrinsic permeability tensor

Hydraulic conductivity tensor

Scalar limit of K for homogeneous and isotropic medium

Distribution coefficient—a measure of retention of    '
species on porous medium

Amount of particular radionuclide released by leaching
during a release time interval, Ci

Ratio of amount leached, M, to the thickness of aquifer
in which leached, Ci/m

 Pressure at arbitrary datum z

 Pressure at elevation 2,




V, fi V.
 i    3



 Retardation factor

 Release increment to Preliminary Input Receptor

 Environment Input Receptor inventory by zone

 (in AMRAW)  Concentration components

 (in ftMRAW)   Accumulated net total concentration in yCi
 per em^ or  cm^ by zone and Environmental input Receptor

 (DELT1  in         Time interval over which environmental
 decay constant is applied?  also,  time increment for
 which transfer is calculated


 Pulse velocity

 Magnitude of Darcy flux

 Components  of  the  Darcy flux

 Velocity of fluid  relative  to  solid

 Pore  (or seepage)  velocity

 Velocity of solio"

Fluid velocity in the predominant flow direction (= e • v )

Coordinate  axis and distance in predominant flow direction

Repository  inventory for a particular nuclide at time—
 input to AMRAW

Transverse  distance from plume centerline

Effective width of plume

Transverse distance corresponding to average concentration

Elevation head

Aquifer thickness

Dispersion  allocation factor for air concentration

Dispersion  allocation factor for ground deposition

  6. .
   s n
 s    s



jtection 4 .D.2

Coefficient of consolidation of the medium

Fluid compressibility

Kronecker delta


Volumetric moisture content

Radioactive decay  constant

Environmental decay constant—input to M1RAW

L    ' cons t ant s

Fluid viscosity

Macroscopic strain tensor

Bulk density of porous medium

Fluid density

Fluid density at pressure p

Incremental pressure in fluid

Dilatation of medium

Saturation of porous media:  volume fraction of porosity
which is water-filled
Concentration or dilution to the consumed or exposed

Transfer coefficient which transforms environmental
concentration in a receptor to corresponding dose
commitment rate to a specified organ,

Subroutine in &MRAW-A for ground water transport

Same as  t in Section 4.D-l time increment for which
transfer is calculated

Dose rate conversion per unit of exposure or consumption
for the specified organ

Subroutine in AMRAW-A which handles the Eelease Model
and provides transfer coefficients used to accumulate
releases to four preliminary input receptors







Section 4.E.
A2, (t, T, r)

 DC(t, T}
Same as defined in 4.D.I.

Subprogram in FAULT which handles leaching into ground

Same as defined in 4,D.I.

Subroutine provides transfer coefficients for transport
from preliminary input receptors to the environmental
input receptors

Subroutine which evaluates transfer coefficients
between environmental concentrations and population
dose rates for various pathways

Amount of exposure or consumption per year
Transfer coefficient for transfer from repository to
receptor j by release mechanism i.

Expectation value for the transfer coefficient from all
release events at time t to receptor j

Time transfer coefficient accounting for radioactive
and environmental decay between release time t and
population dose time T; can account for transport pro-
cesses in receptor j

Local dose transfer coefficient

Nonspecific transfer coefficient

Radiodecay factor between times t (release time) and
T (population dose time)

Local dispersion factor which provides uniform concen-
tration values of a radionuclide deposited in a zone

Same as defined in Section D.I.
 Gm(t, T, r)

 H(t, T, r)

Total transfer term to receptor j from other receptors m

Subscript denoting a release event

Environmental receptor of current interest

In subscript refers to geographical zone

It. (t, T, r)    Transfer  term representing losses  from receptor j  to
  3             other receptors  m

ffi             Environmental receptor  other than  j

Ml{T, r)       Local man. dose rate

M2 (T)          Nonspecific sian  dose  rate

P., (t)         Probability of release  by  mechanism  i  to environmental
  ^            receptor  j during t - at to t

     "*"             .,.•*•
q(t, r)        Activity  in Ci at r from nuclide released at time  t

r              Space variable in rectangular coordinates Cx, y", g)

        -*•              '23              -*•
R(t, T, r)     Activity  in Ci/cm  or Ci/cm  at time T at r  due to release
               in  interval t -  dt to t
      •*•                                                r.        •+
RT(T, r)       Total activity for all  release times— £ K(t, T, r)

S£t, T, r)     Net total source term representing total activity  at r
               in  receptor j  at time T due to release in interval t -
               dt  to t

t              Release time  of  radionuclide from  waste site to Prelimi-
               nary Environmental Receptor

t  ,            Radioactive half-life
T              Time of interest for  population doses

X(o)           Amount of nuclide at  some  reference  time

X(t)           Amount of nuclide at  time  of release

Y(t)           Radioactivity in Ci at  time t for  radionuclide  of
  -+•                                                            ,   •*
Z(r)           Fraction  of released  nuclide deposited at position r

a              In  superscript to refer to release time

0              In  superscript to refer to population  dose time

6              (=  /dT) Period during which transfer calculation of  G
               is  calculated

X              Radioactive decay constant

T              Variable r time

w              Specific  activity in  Ci/g  of a particular nuclide  of


Appendix A




Appendix B







Width  of rectangular plane  source

Ratio  of amount  leached during  a release  time  interval
per  unit area of a plane  source, Ci/m2

See  Section 4.D.I
 Soil  surface  area  required  to furnish food  crops  for
 one man  (ID3™2}

 Concentration of radioactivity in beef (uCi/kg)

 Same  as defined in Section  3.D.2.

 Concentration of radioactivity in the milk
Dietary  factors that  correct the transfer  coefficients to
man from those for  "reference man" to  those  for  the
population under study  (dimensionless)

Radioactivity present in the soil below the  root depth
Radioactivity present on the above -surf ace food  per m
of surface on which the food crop is grown  (pCi/m2)

Fallout  source, which for this calculation was assumed
to be present only at time t = 0  (yCi/m2-d)

Ground deposition source  (yCi/m2)

Radioactivity present in the grass compartment  (pCi/m2)

Radioactive present in man
Radioactivity present in the subsurface pool  associated
with one man's food supply
Radioactivity present in the soil from the ground
surface to the root depth of the grass (pCi/m2)

Radioactivity present at the soil surface  (pCi/m2)

Fallout correction factor to account for different
depositions to the above-surface food (S ) , the soil
below this food (S ) , and the pasture (S,5 (dimension-
less)                                   3

Kronecker delta function '
                                  xxi i

 X              Turnover rate of the stable isotope of the nuclide in

                man  (d""-*-} except for Sr where X  was isotope-dependent

 X              Radioactive decay rate of the nuclide under study (d  )

 T,   ,.          Fraction of the beef herd slaughtered per day (0.00381
  beef          r3~l\

  mi He          Transfer rate of milk from the udder (2,0  )

T               Amount of meat eaten by a man each day (0,3 kg/d}

T   .            Amount of milk consumed by a man each day (1.0 i/d)

 e/m            Crop harvest rate, ra /d

T               Fractional transfer rate, crops to soil surface (0.0495

 e's            fl~l^

T  .             Transfer rate, grass to meat, m /kg-d

T               Transfer rate, grass to milk, m /£-d
                           ""              *   —                    ^ i

T               Fractional transfer rate, grass to soil, 0.0495 d

Tpfd            Fractional transfer rate, soil pool to soil sink, 1.096

                x 10~4 d~l

T  m            Fractional transfer rate, soil pool to man, d

Tr ,d            Fractional transfer rate, pasture soil to soil sink, 1.096 x

                KT4 d*1

Tr(g            Fractional root uptake rate, soil to grassr 2.74 x 10~5  d"1

Ts              Fractional transfer rate, soil surface to soil pool,

                0.0693, 0.006i3, and 0.000693 d*1 (each problem run three

                times once for each value of T    listed)

                               CHAPTER 1
      One of  the major environmental concerns  associated with the .pro-
 jected increase in  nuclear power  generation is  the  handling and disposal
 of high-level  radioactive waste.   During operation  of  a nuclear reactor,
 fissioning fuel atoms result  in an accumulation of  fission products
 within each  fuel  element of the reactor  core.   These fission products
 are isotopes of lighter elements  and aiany of  these  isotopes are radio-
 active.   Significant  examples are Sr-90,  Tc-99,  1-129, Cs-135, and
 Cs-137.   In  addition, isotopes of actinide elements, primarily neptunium,
 plutonium, americiura  and curium,  are created  because .of neutron absop-
 tions which  do not  result in  fission.  Approximately one-third of the.
 energy-releasing  fissions, in  a light water reactor  (LWR) are of plutonium.
 which is created  during reactor operation.  Periodically, because of
 depletion of fuel atoms and accumulation  of neutron-absorbing fission
 products, a  portion of the core must be  removed and replaced with fresh
 fuel,   Reprocessing of spent  fuel recovers any  remaining uranium and
 plutonium for  subsequent recycling as fuel.   The fission products, small
 amounts  of uranium  and plutonium  that are not recovered, and the other
 actinides which are not recovered (neptunium, aroericium and curium),
 comprise the high-level radioactive waste.  If  spent fuel is not repro-
 cessed,  entire fuel elements,  including  all of  the  actinides contained,
 ultimately become high-level  radioactive  waste  [Ax77].  This waste,
 whether  from reprocessing or  in the  form  of spent fuel, includes radio-
 isotopes having very  long half-lives.  The waste must eventually be placed
 in  terminal  storage repositories which prevent entry into the"environment
 for up to tens of thousands of years.
      Management of  high-level radioactive waste  must insure that the
 risk  of  detrimental effects from  radioactive  contamination of the
 environment  is less than a level  considered acceptable by society in
 relation to  the various energy alternatives available.  The toxic resi-
duals and environmental disruption associated with use of the available
alternatives  to nuclear power also constitute a risk to society.   Placing

the risk of release of radioactivity associated with nuclear power into
perspective requires recognition of the corresponding risks from the
     Assessment of radioactive waste management may be divided into two
categories;  1} risk analysis, which considers both the probability of
occurrence of each of various radiation release scenarios and the conse-
quences of such releases, and 2} consequence analysis, which 'considers
only the consequences of various postulated low-probability potential
release events.  In either category, there are various waste management
options to consider and compare:  1) storage in alternate or other type
sitesi 2) alternate waste forms, 3) fuel reprocessing versus disposal
of spent  fuel,  4)  efficiency of U and Pu recovery in reprocessing, and
5} partitioning of waste into different components for beneficial uses,
transmutation of actinides to fission products in nuclear reactors [Bu?5,
CK.75, Cr77] and/or different terminal storage disposition.  Any flexible
assessment model must be applicable to any or all of these.
     A flexible assessment methodology is needed for the evaluation of
the various long-term waste disposal methods and management options
[ERDA76a].  State and Federal regulatory and R&D agencies must be in a
position to independently evaluate proposals for waste management acti-
vities in the course of carrying out their assigned functions including
the protection of public health and safety and protection of resources.
     In May, 1977, the International Atomic Energy Agency sponsored a
major international conference on Nuclear Power and its Fuel Cycle at
Salzburg, Austria [IAEA77],- which resulted in reaffirmed commitments to
nuclear power as an immediate substitute for fossil fuels and as a
mature solution towards meeting the increasing global energy needs.
The Salzburg conference also focused on the safe disposal of radioactive
wastes from nuclear power as one of the most important parts of the
nuclear fuel cycle that is yet to be fully established and demonstrated.
     Presently, most countries that have nuclear power programs are
studying the use of deep geologic formations for the safe emplacement
of radioactive wastes.  Only recently, two workshops were conducted to
help provide exchange of scientific information between investigators

•v-.'i'nvolved in assessment work.  A workshop on  "Geologic Data Requirements
:'.'-for Radioactive Waste Management Assessment Models"  [Lo761 sponsored by
\the Office of Waste Isolation for the D. S. Department of Energy  (DOE)
 /and arranged by The University of     Mexico, was held in June, 1976.
'. A followup international workshop:   "Risk Analysis and Geologic Modeling
 in Relation to the Disposal of Radioactive Wastes into Geologic Forma-
 tions," sponsored jointly by the QECD Nuclear Energy Agency and the
 Commission of the European Communities, was held in Ispra, Italy in May,
 1977  EOECD77],
      The United States, Canada, and  several countries in Europe have
 started modeling and risk analysis studies fOECD77].  in the U, S., as
 part of a recently-announced expanded national program in the manage-
 ment of commercial nuclear wastes, the National Waste Terminal Storage
 Program (NWTS) is underway by the DOE to provide federal repositories
 at multiple geographic locations with differing geologic formations in
 the continental United States for terminal storage of high-level radio-
 active waste [Mc76].  Formations being studied for possible location of
 terminal storage facilities include:  bedded salt in western and mid-
 western states; dome salts in gulf coast states; shales, which are
 widely distributed over the country, and a wide variety of granites and
 other crystalline rocks and volcanic formations.  The Los Medanos area
 in the Permian salt basin of southeastern New Mexico is under study for
 potential installation of a Waste Isolation Pilot Plant in bedcied salt
 [Wr77].  The proposed pilot plant is for DOE trans-uranium waste and
 experimental retrievable emplacement of some high-level wastes.  The
 Battelle Pacific Northwest Laboratories have started the Waste Isolation
 Safety Assessment Program (W1SAP) for DOE [Bu76a, Bu77, C£77];  the
 objective is to develop methods and generate data necessary to charac-
 terize the safety of generic geologic waste disposal concepts which are
 to be applied in the assessment of specific sites,  At the Sandia Labo- *
 ratories,  a study is underway for the Nuclear Regulatory Commission
 (NRC)  for application to repository  licensing [Lo76, Ti77]»
      The U.  S.  Environmental Protection Agency (EPA)  commissioned The
 University of New Mexico (UKM)  to continue development and application
 of  a  Radioactive  Waste  Management Systems  Model  initiated at     in

 1972  [Lo74a].  This model, implemented with a computer cede, M4RAW
 (Assessment Method for Radioactive Waste), evaluates long-term environ-
 mental impact attributable to each phase  of the waste management se-
 quence.  Emphasis in the study is placed  on the terminal storage (dis-
 posal) phase.  These various assessment programs including the UNM study
 for the EPA  [Lo76r Lo77, Go77] have varying approaches and points of
 emphasis.  This provides a complementary  approach to waste management
 assessment and affords greater confidence in final results than would a
 single centralized effort.  Related work  is study of the Oklo Phenomenon
 [IAEA75,Bo76]  which  concerns several natural reactors  which existed in a
 uranium deposit in Gabon, Africa 1.8 billion years ago.  This constitutes
 a very old natural repository for radioactive wastes.  Most'of the radio-
 nuclides were retained in the immediate vicinities of the reaction zones.
 As the studies progress, the Oklo data may serve to provide some vali-
 dation of the assessment models.
     This volume is one of four which report on the DMM radioactive waste
management assessment method and its application.  The purpose of this
 overall study for the EPA is to complete development of the model for
 technology assessment of radioactive waste management, including the
 AMRAW computer code,  and to demonstrate the model for one model reposi-
 tory site.  This demonstration includes sensitivity and consequence
 analyses for the terminal storage phase,  a preliminary demonstration for
 the repository operations phase and for terminal storage in another geo-
 logic setting.  The study also evaluates  the feasibility of applying the
model to other radioactive and nonradioactive hazardous materials.
     The scope of the study involved approximately 6.5 man-years of
effort.  This was interdisciplinary, with the central effort in the
Chemical and Nuclear Engineering Department of The University of New
Mexico and a major component effort in the Economics Department.  Support
was provided by the Departments of:  1} Geology,  2) Biology, and
 3) Electrical Engineering and Computer Science.  Additional supporting
effort was by the Department of Geoscience at the New Mexico Institute
of Mining and Technology and Geohydrology Associates,  Much helpful
 information was obtained front national laboratories (see the acknowledge-
ments section for details)  and individuals who reviewed earlier draft reports.

                               CHAPTER 2
     A Radioactive Waste Management Systems Model proposed by The
University of Hew Mexico has been developed and implemented under this
contract.  The  assessment model and associated computer code is called
MCRAW (Assessment Method for Radioactive Waste),  She full model includes
the several phases in the waste management sequence:  residuals treat-
ment  (interim surface storage and solidification) » waste transport,
repository operations, terminal storage, and any other intermediate
phases which may become applicable.  The effort during this study has
concentrated on terminal storage, but a preliminary application to repo-
sitory operations is included.
     AMRAW is divided into two parts which are run separately;
1) AMRAW-A consists of the Source Term   (Inventory at Risk), the Release
Model, and the Environmental Model, and 2) AMR&.W-B is the Economic Model.
AMRAW-&, described generically in this volume, uses externally-generated
values of input parameters for potential geologic and wan-caused release
events,  transport from points of release to the environment, environ-
mental pathways to man and calculation of radiation doses.
     The radiation dose rates determined by AMRAW-A are input to AMRAW-B,
described in Volume III.  The Economic Model in AMHAW-B determines inci-
dence rates of health effects corresponding to calculated dose rates,
determines the associated costs, and attributes these costs to radio-
nuclides, related groups of nuclidesf and to elements initially in the
waste inventory.  Initial inventory for the terminal storage phase of
waste management refers to the accumulated quantities at the end of the
repository operations phase.  Up until that time, risk reduction options
of  improved recovery and/or partitioning may be applied [C&75, Bu?5],
Cr77].  The allocated costs from the Economic Model provide a common
reference base for summing up the consequences of a number of health
effects  associated with many different radionuclides, with consideration
of the population affected, agricultural activities, and other factors.
In addition to comparisons between disposal options, feedback of these
calculated costs to the fuel reprocessing and residuals treatment phase

provides a basis for comparison of reprocessing and waste partitioning
options.  Due to uncertainties in data values and the difficulty in
assigning dollar costs to health effects, calculated results are not
represented as being a precise quantification of damage costs.  As use
of the model proceeds and improved input data becomes available, it may
become appropriate to apply the results more directly to cost/benefit
     In the model, released radioactive material is dispersed to environ-
mantal input receptors (air, ground surface, surface water, and ground
water) in each geographic zone in a study region around a repository.  The
input factors which define the dispersion are determined externally to
AMRAW.  Concentrations are accumulated in each environmental receptor
but adjusted during each time increment for transfers between receptors,
radiodecay and buildup and environmental removal processes.  In the
results reported in Vols. II and III, most of the cases use a conservative
environmental half-time of 30,000 years in lieu of data to support shorter
times.  The corresponding token value of environmental decay constants
is believed here to be unrealistically low and leads to overestimating
the persistance of released radionuclides and the resulting dose rates.
Sensitivity analysis cases reported in Vol. II investigate the effect
of lowering the environmental half-time.  Research is needed to deter-
mine nuclide-dependent environmental behavior to justify the use of more
realistic values for environmental half-times and to thereby obtain
improved calculations of estimated environmental concentrations as func-
tions of time.
     AMRAW-A calculates the radiation dose commitment rate via pathways
for direct exposure of the population in each zone and for food and
drink pathways.   A unique feature of the model divides the pathways and
resulting dose  rates into local dose (to the specific local population
groups)  and nonspecific dose.   The latter is from agricultural products
which are largely exported; the nonspecific population affected is out-
side of as well as within the study region.
     The remainder of this chapter applies primarily to the terminal
storage  phase.   As described in Section 4.C, AMRAW may be run for any
of several release scenarios.   When run for a discrete geologic event
(or combination  of events)  occurring at a specified time, the results

      . measure of consequences associated with -the event and, time of
/--•-occurrence.  Varying the events and-times of  occurrence comprises a
"----;consequence analysis.  In this mode of operation, the problems of
:.\--predictive geology are largely bypassed, but  a number of difficulties -
; do remain.  For example, if a volcano penetrates a repository, what
•-fraction of intercepted waste inventory is pushed aside or remains
./within magma in a buried..configuration and what fraction becomes ex-.
 palled by volcanic ejection?  Further, for the material ejected, what
 particle size and chemical form distributions may, be expected?  In
 cases reported in the other volumes of this report, it is assumed that
 one-half of intercepted inventory is ejected without reburial and that
 all material ejected into the atmosphere is of small particle size
 (effective deposition velocity 0.01 ia/s) , and is of a physical, arid chem-
 ical form which is immediately available to environmental processes.
 While it is believed here that these are overly conservative assumptions,
 research has not been done to provide better data.
      When AMRAW is run in a mode which distributes release events pro-
 babilistically over time, the results are a-measure of risk associated
 with the events and repository properties.  Risk is defined as the pro-
 duct of the  "Probability  of an Event" and the "Consequences of the
 Event."  Varying event scenarios, repository conditions, waste inven-
 tory, waste forms, or other factors comprise  .a risk analysis.  In this-
 mode, calculated values of environmental concentrations and dose rates
 tor in AMRAW-B, health effects and associated costs)  at the various times
 do not represent predicted values-  For example, a volcanic event with
 an estimated rate of occurrence of 2 x 10   /y distributed probabilist-
                                        -12          11
 ically spreads the event over l/(2 x 10   )  = 5 x 10  y»  Thus, while
 the probabilistic method assigns some annual probability of volcanic
 explosion and obtains associated radiation dose rates and resulting
 health effects to the population, it should be observed that the low
 probability means there is only one chance in 500,000 (5 x 10  /I x
 10  = 500,000)  that such a volcanic event would expel material at any
 time during a one million year storage period,-  The calculated results,
 using the probability of occurrence and consequences- of interest such as
 environmental concentrations,  applicable dose rates or health effects,
 give the risk and provide a basis for comparing, options with an objective

of minimizing risk.  Another mode in which AMRAW can be run. in the
future is to use data from dynamic repository simulation (see paragraph
4.C.l.d)  when results become available from persons developing the ana-
lysis concept,
     There are difficulties in predicting geologic events over long
periods of time into the future,  Gould  [G£65a,G*65b] discusses an out-
moded term:  the concept of "substantive uniformitarianisia" which
postulates uniformity of rates or material conditions.  This concept,
which assumes that changes which occurred in the past continue invari-
antly through the present into the future, is considered by Gould to be
incorrect in any strict formulation,  A concept which assumes spacial
and temporal invariance of natural laws has bee-n termed "methodologic
uniformitarianism."  This is a basic mode of inductive reasoning in
various fields of science.  Longwell  [G&65b3 suggests replacing this
term by "uniformity of process through time," and Gould [Gi65bl suggests
simply;  "inductive inference."  Workshops dealing with geologic data
for risk assessment [Lo76, OECD77], have considered both gradual pro-
cesses and sudden discontinuous events.  AMRftW input data for the pro-
babilistic mode does not depend upon any particular predictive concept
(see Section 4.C).  Demonstration of the model to date has depended
largely upon projection of processes of the recent past.  As advances in
predictive geology are made AMBAW is ready to accept the data.  It should
be recognized that uncertainty in the results increases as the length
of time into the future increases.  While absolute predictions of envi-
ronmental contamination and population dose rates are limited by the
geologic uncertainty, as well as other relevant future conditions,
results are particularly adapted to:  1) comparison of management options
for risk reduction purposes, and 2)  scoping of geologic event importance
by running the model for ranges of probability or dynamic scenarios.
Uncertainties in probabilities or omissions of events which are expected
to apply equally to two cases being compared tend-to cancel when making
relative comparisons.  Sensitivity analysis discussed in Vol. II demon-
strates these capabilities,
     Among the various geologic disruptive events is a leaching incident,
in which ground water gains access to a portion of the waste inventory.
The leach rates following the start of a leaching incident are calculated

• as  a function  of time within  AMRAW using radionuclide—dependent input
 parameters.    A method  for estimating the input effective  diffusivity
-is  presented.    Subsequent transport through.the geosphere in ground
 water is  calculated for appropriate time intervals  within  AMRAW for
 each radionuclide.   The paucity  of data for distribution  coefficients
 (K  )  for  specific sites and ground water qualities  introduces uncertainty
 into the  ground water transport calculations.   The  ingrowth of decay  pro-
 ducts during ground water  transport is presently handled by an approximate
 method.   One micliete at a  time is carried through the AMRAW calculations.
 When a particular radionuclide from a decay chain is  considered, leach-
 ing and ground water transport calculations are first made on the basis
 of  the average inventory of that  species present in the waste during  an
 increment of leach  time.  Then the quantity at a given  time and distance
 is  adjusted by a factor which accounts for net decay  or ingrowth of the
 species,  considering the total waste inventory.  If precursors have the
      leach rate and K   as  the species of interest,  these precursors
 appear in the  leachant  and move along with the species; the calculation
 of  ingrowth in this case is exact.   The  method becomes  approximate when
 precursor leach rates and  K  values are  different than  those for the
 decay product  of interest.
      The  AM5AW model and code calculates radiological environmental im-
 pact for  geological and man-caused disruptive scenarios ranging up to
 catastrophic events such as volcanic eruptions and  meteorite impact,
 Whether radiological effects  or damages  are important relative to the
 nonradiological  devastation has not been studied.   AMRAW calculates
 radiological effects from  the moment each disruption occurs,  assuming
 the population stays in place and is not affected by physical violence
 of  the event.  This  is,  of  course,  conservative and a more accurate evalu-
 ation would insert  a phase  lag before substantial reinstatement of local
population.  This is an area  of research which would be very  helpful  to
 risk  analysis  of natural disasters  as well as  nuclear risk analysis.
     Volume II presents  specific  discussions of input data  sources,
assumptions and limitations for:     1}  a base case for a repository in
bedded salt,    2} other  cases  demonstrating  sensitivity  and  consequence
analyses,   3)   a case demonstrating  application  to another  geologic

setting, and  4) application of the model to repository operations
and ground surface storage.  Volume III presents corresponding dis-
cussions for the Economic Model.  It should be noted that the work coveree
by this report is not represented as being complete in regard to potential
release mechanisms but is intended to demonstrate the degree of flexi-
bility.  There is a rapidly changing data base which can be repeatedly-
applied for updating the results.  AMRAW is a tool to aid management:
decisions, but it does not replace the need for extensive studies at
each proposed repository site.  The model can incorporate results of
such site studies for continuous refinement of results.

                               CHAPTER 3
                 CONCLUSIONS  AND
     The AMRAW model is interdisciplinary and successfully brings together
 results from several fields of study for technology assessment of each
 phase of radioactive waste management.  The model uniquely links each
 step from an inventory of radioactive waste through releases into the
 immediate environs, transport and dispersion to environmental receptors/
 pathway analysis for estimates of resulting dose-to-man, and calculation
 of corresponding health effects.  This sequence is handled as a contin-
 uous calculation with output of intermediate results providing released
 quantities, environmental concentrations, doses to population, and num-
 bers of health effects.  The AMRAW-A. part carries the calculation sequence
 through dose rates and the AMRAW-B part picks up from there and calcu-
 lates health effects.
     AMRAW does not replace but instead uses established models for
 various segments of the problem, such as air dispersion, geosphere and
 biosphere transport, environmental pathway analysis, and dosimetry.  The
 existing models or published results from their use, augmented by the
 judgements of experts in each discipline are externally used to prepare
 extensive input arrays and individual items of factors or coefficients
 used in AMRAW.  Individual calculation steps in AMR&W generally involve
 multiplication of sequences of related factors and adding to accumulate
parallel contributions, plus use of other simple functions for time-
 dependent adjustments,  While the individual steps are simple, the book-
 keeping is quite complex.  AMRAW provides a structural means for orderly
processing thousands of data items and keeping track of intermediate and
 final results for various forms of output display.  Two processes, leach-
 ing and ground water transport are handled analytically within AMRAW by
 subprograms (KLEACH and CRATIO, respectively).  These subprograms depend
upon input data from laboratory and field studies.  Other subprograms do
the bookkeeping to process input data for releases (FAULT), transport to
 the environment (TRINP) and pathway analysis (TRMAN).  Where preferred,
the leaching and ground water transport subprograms can be replaced by


 alternate subprograms which process  input data obtained by external use
 of more  rigorous  codes.  This alternate has not been done during this
 study but the modular structure of AMRAW provides flexibility to do so,
     Applications of AMRAW, presented in Vols. II and III, necessarily
 make use of data which has been available early in assessment efforts.
 Continuing studies of proposed repository sites in various geologic for-
 mations , measurements of site-specific sorption properties, and advances
 in predictive geology can provide updated input for AMRAW to refine and
 extend the applications.  The results obtained to date are not claimed
 to represent all disruptive or other release processes which potentially
 could occur.  However, the probabilistic or risk analysis mode, with
 consideration of the most disruptive events envisioned, obtains results
 which suggest that only a minor risk is associated with the model repo-
 sitory studied.  Consequence analysis results indicate that intersection
 of a repository by a volcano after 1000 y or later,  through  highly  unlikely/
 could result in population doses in areas close to the site  which exceed
 regmlartory limits but not at a lethal level.
     The AMRAW model, developed for applications to various phases of
 radioactive waste management, may also be applied to other nonradioactive
 hazardous wastes or various pollutant spills.   Application to seabed
 disposal by redefining environmental receptors and making other modifi-
 cations is a possibility through this has not been studied.
     It is recommended that improved and more comprehensive data be
 obtained in areas of:  1)  distribution coefficient (K )  and its dependence
 upon geologic media, pH, oxidation potential,  and other ground water
properties,  2}  environmental decay, which relates to removal and retention
mechanisms which reduce the environmental concentration of a nuclide with
time, independent of radiodecay, and 3)  resuspension from land surface
 into the air.  In addition, improved water usage and hydrologic informa-
 tion is needed.  New data and improved geologic disruptive event descript-
 ions should be input to AMRAW to update the earlier runs.
     Preparation of alternate subroutines for leaching and ground water
transport to process data externally generated by other codes is suggested.
     There are several types of AMRAW applications recommended for  further
work.   The model should be applied to various  proposed repositories in

different geologic media:  shale, basalt, granite, and dome salt.  Dif-
ferent emplacement methods such as drilled hole matrix: and conventional
mining may affect the results and should be investigated.  An application
which can help to place results obtained to data into perspective is the
calculation of risk associated with an undisturbed uranium ore body.
This is a naturally radioactive "repository" of low concentration but
having a large area.
     The increase in long term environmental risk if unreprocessed spent
fuel is disposed of as high-level waste, instead of disposing only repro-
cessing waste, should be assessed.  Partitioning and transmutation alter-
natives, and improved reprocessing separation should be assessed*
     Above all, it is recommended that important categories of .risk
assessment be completed promptly and decisions be made to resolve radio-
active waste management questions.

Page Intentionally Blank

                               CHAPTER 4
     The  Radioactive Waste Management Systems Model  (Pig. 4-1} has several
parallel  paths, each representing a phase  in the waste management se-
quence;   residuals treatment  {interim surface storage and solidification
at a reprocessing plant site)f waste transport, repository operations,
and terminal storage.  If other phases become applicable, such as interim
surface storage away from a reprocessing plant site, interim storage as
spent fuel, reprocessing of waste form, and other transportation steps,
each of these simply becomes  an additional parallel path in the model.
     Implementation of the model is by the MiR&W computer code.  The
code runs calculations separately for each branch of the model.  Input
data includes a flag {IW} which designates the model branch for which the
data applies.  This flag controls routing within the code to handle some
variations in calculations which depend upon the waste management phase
being studied.  Most of the current effort is applied to the terminal
storage (disposal) branch (see Part 1 of Vol. II).  A preliminary demon-
stration  of application to the repository operations branch is included
in Part 2 of Vol. II.
     The  model is basically a computer simulation or systems analysis
model; a  basic assumption is  that each system studied is linear,  AMRAW
does not  replace established models which are in use for various segments
of. the problem, such as air dispersion, geosphere and biosphere transport,
environmental pathway analysis, and dosimetry.  Instead, most of the
calculations within AMRAW make use of input arrays and matrices of factors
or coefficients obtained from the established models, augmented by the
judgements of experts in each discipline.  Simplified versions of leach^
ing and ground water transport models are used internally, but these as
well as the major model sections (Pig. 4-2} are each contained in sub-
programs, providing for replacement should this become desired.  Output
from AMRAW-A is provided at several stages through the model giving cal-
culated release quantities, environmental concentrations, and doses to




/ \

L '\
/ \
Figure 4-1.   Radioactive waste  management systems model,

      AMR&W-& interfaces the component models providing continuous cal-
•. isolations from the Source Term (Inventory at Risk}»  through the Release
"Model and the two parts of the Environmental Model (Transport to Environ-
 ment and Environment-to-Man Pathways), obtaining output doses to popu-
 lation.   This output is the major input to AMRAW-B which then calculates
 health effects and the corresponding damages in economic units.  The two
 parts of AMSAW can be linked together for a continous .run,  but it has
 been convenient to maintain them separately for development purposes and
 parametric studies.
     Further, AMR&W is a compartment model? a compartment model assumes
that the various components of the system can be lumped into compartments
and that all changes  and movements can be accounted for by transfer coeffi-
cients between compartments.  The component models shown in Fig. 4-2 deter-
mine the transfer coefficients which  link the various compartments and
receptors in sequence.  Table 4-1 summarizes the sequence of calculated
quantities and transfer coefficients.  In the model, the various compartments
and receptors are split into parallel sets:  1) the inventory divides into
a number of radionuclides, each varying with time, 2) environmental input
receptors are air, land surface, surface water and ground water, and 3)
dose commitment rates divide into local dose rates in each geographic zone
and a nonspecific category explained  later, and further divide into dose
rates to various body organs.  The are implied intermediate receptors which
are not specifically collected for output.  An example is a contaminant con-
centration in food.  This is lumped into the environment-to-man pathways
model component which includes a food intake factor and a dose conversion
factor in addition to a food concentration factor, for each pathway and
nuclide.  Operated in a risk analysis mode, it is assumed in AMRAW that risk
is defined as the product.- probability of occurrence of an event, multiplied
by the consequences should the event  occur,'  operated  in  a consequence
analysis mode, consequences are evaluated for discrete events  occurring
at specified times.   The mode of operation  is dictated by the  nature of
the Release Model input data.
     The following sections in this chapter  describe  the AMHAW-A part of
the model, and the component models in AMRAH-A in detail; Vol.  Ill





 Figure  4-2.   One branch  of  systems model,

               Table 4-1.  Receptor and Transfer Coefficient
                           Sequence in AMRAW
  Compartment or Receptor

Transfer Coefficient
  Inventory, grams
  Inventory, Curies
  Preliminary Environmental
  Input Receptors
  Environmental Input Receptors
  Dose Commitment Rates
                                                        Specific Activity
                                                        Release Probability and
                                                        Release Fraction
                                                        Transport to Environment
                                                        Environment-to-Man Pathways
  Health Effects
  Economic Valuation of Damages
                                                        Health Effect Incidence Rates
                                                        Health Effect Costs

describes &MRAW-B  (Economic Model).

     The AMBAW-A part of the AMRA.W computer code may be iron for one or
more branches of the model, depending upon the number of sets of input
data provided.  As stated earlier, each data set includes a flag (IW)
which designates the model branch for which the data applies.  The dis-
cussion which follows in this volume is based upon the terminal storage
branch, in that the frame of reference refers to the inventory emplaced
in a repository.  However, the calculation flow of the model and code
also applies to the other branches.  When applications are made to other
branches,      programming changes may be needed such as addition of
alternate calculation routing or additional subprograms.
     The total period of time to be studied is divided into time incre-
ments each of which is identified by the time (in years} at the end of
the  increment.   Various time-dependent parameters are averaged in each
time increment as the calculations proceed.  The AMRAW code runs one
nuclide at a time, considers one time increment, at a time for calculation
of releases, and follows the migration of each such release increment
through all subsequent time increments "in the environment."  Then, for
each time increment, net concentrations are accumulated for all prior
(or coincident)  release increments.  The number of times and their values,
specified by input data, must be a compromise between calculation resolu-
tion (small time increments)  and computer storage, output bulk and running
time limitations {large time increments),  Present applications divide
one million years into 50 times with 5 y increments at the beginning,
increasing in steps to 100,000 y increments after 100,000 y,
     Each branch of the model (Fig. 4~2) is entered with the mass of
each significant radionuclide in the inventory at risk at each time
(see Section 4.B).  This is converted to Curies in the inventory by an
activity transfer coefficient (specific activity).  It is assumed that
most of the risk associated with a given inventory of radioactive waste
can be represented by a fraction of the total number of nuclides present,
This is based on the finding that fewer than 25 nuclides represent most
of the total of a hazard measure evaluated for the total inventory.  The


handling of the nuclide inventory by SMR&W assumes that the total inven-
tory versus time is not affected by movement of portions of the inventory.
That is, as postulated migration proceeds/ the total inventory of. each
nuclide at any time is equal to the inventory if no migration occurs.
This is a valid assumption in itself but it leads to some errors in
estimates of distributions when precursors and daughters do not migrate
     The Release Model calculates the probability for release by each of
numerous potential release mechanisms, and the fraction of the inventory
released by each such occurrence, during each increment of time.  Ss
described in Section 4.C, &MRJW may be run for any of several release
scenarios:  1} probabilistic distribution of events over time, 2} discrete
event at specified time, 3) several events each at mean time of first
occurrence, 4} dynamic repository simulation, or 5} combinations of these.
Release calculations are totally dependent upon input parameters; MfRAW
does not possess predictve  capability for geologic events.  Modeling
done externally to AMRAW, plus professional judgement of experts
in fields of geology and hydrology are needed to define the data input
for this part of the AMRRW model.  Each event or combination of events
must be defined by the product of one or more time-dependent factors.
During each release time increment, AMR&W determines the fraction of
inventory of a given nuolide released by each event, and superimposes
and accumulates for all events as defined by the input data.  This pro-
cess is repeated in turn for each of the environmental receptors;  air,
land surface, surface water, and ground water.  Uncertainty in prediction
of geologic events appears to be the greatest limitation of assessment
models.  Leaching, following contact of waste by ground water, is calcu-
lated within AMRAW by a subprogram.  This subprogram indicates relatively-
high leach rates initially, decreasing to a lower constant rate after
some time.  Input parameters are based upon short-term leaching experi^-
wents,  resulting in error for long-term projections.
     Releases as determined by the Release Model are not necessarily
directly to the environment.  This is particularly true for deep releases
to ground water.  The first portion of the Environmental Model (see
Section 4.D.I) is therefore the "Transport to Environment" section.   This
adjusts each release increment, obtaining the contribution-to-

concentrations in environmental input receptors at -various times follow-
ing release.  These receptors are:  air, ground surface, surface water,
and ground water.  It is assumed that the environment can. be represented
by these 4 receptors.  Increased complexity could divide land surface
into surface and subsurface categories, for examples.  The adjustment
provides for dispersion into each of the four receptors in each of the
several geographical zones comprising the study region, and then converts
accumulated activities to concentrations by accounting for dispersion
areas or volumes in each zone.  The dispersion to receptors in each zone
uses factors furnished as input data.  Mr dispersion factors can be
based upon runs with an air transport code or a simplified analytic
method.  A basic limitation here is the predictability of long-term
meteorological conditions.  Dispersion associated with direct releases
to land surface is not well modeled at this time; input for current appli-
cations     used a simple exponential distribution.  The adjustment also
accounts for decay from the time of release to the time being evaluated,
transfer between receptors {such as deposition from air onto ground),
retardation in ground water flow, and other environmental removal or
fixation processes.  Ground water transport is calculated within M1R&W
by a subprogram which uses a simplified one-dimensional flow model with
two-dimensional dispersion.  This assumes equilibrium conditions for all
related physical processes.  Required data includes aquifer porosity,
longitudinal and transverse dispersion coefficients, ground water seepage
velocity, and the distribution coefficient K  for each nuciide.  Chain
decay for nuclides in decay series is handled by an approximate technique,
If a more rigorous treatment becomes necessary, an external code should
be used to prepare input data for AMRAW.  In this case, an alternate
subprogram in AMRAW would be required to process data such as by simple
     The last portion of the Environmental Model {see Section 4.D.2)
covers the pathways from environmental input concentrations to radiation
dose to the population, with dose rate calculations for several organs
of concern.  This part of the model considers each environmental receptor
in turn and each of two main pathways for each:  1)  air:  immersion and
inhalation, 2)  land surface:   direct surface exposure and ingestion of
terrestrial food, 3)  surface water:  submersion and ingestion of drinking


water and aquatic foods, and  4} ground water-,  ingestion of drinking
water.  In addition, each main pathway is divided into  an appropriate
number of subpaths reflecting, for example, various categories of. foods.
Calculations accumulate over  the several subpaths under each receptor
and results are not output for each main pathway or subpath.  Dose rate
results for paths which affect residents in a particular zone are accrued
as "local dose rates."  Examples are from air immersion and inhalation,
direct surface exposure, and  ingestion of drinking water.  Dose rates
associated with exported agricultural products are accrued under "non-
specific dose rates."  Evaluation of each pathway obtains the transfer
coefficient between an environmental concentration and  dose-to-man by
considering:  1) a biofactor  where appropriate to account for concentra-
tions in food relative to an  environmental concentration, 2} a factor
expressing consumption, exposure time fraction, or food production rate,
and 3) the appropriate dose conversion factor.  Assumption of a linear
system permits superposition  of effects such as environmental concentra-
tions and dose rates from several pathways.
     The AMRAW code is structured with sequences of compartments linked
by transfer coefficients (Table 4-1}.  The receptors represent the pro-
gress of releases, environmental concentrations, concentrations in food
and drink, radiation doses, health effects and associated economic
damages.  The transfer coefficients are evaluated in subroutines using
externally-determined input data.  The subroutines can  be modified or
replaced, providing a modular arrangement.  The philosophy is to keep
AMEAW as simple and straightforward as possible to avoid "black box"
mystery.  Factors for dispersion, biological accumulation, dose, etc.,
used in the transfer coefficients, are evaluated externally by various
existing transport and dose codes.  Calculation of leach rates and coeffi-
cients expressing ground water transport are both performed analytically
in subprograms in AMRAW,  Each of these can be replaced by alternate
subprograms if that need develops.  One example of this is the use of a
more sophisticated code for ground water  transport.   Such  a  code would be
prohibitive as a subprogram in AMRAW due to excessive computer time when
called thousands of times during a run, but a simple polynomial or other
scheme can be utilized in an  alternate AMRAW subprogram to process input
parameters generated externally by the more sophisticated  code.  The AMRAW


code serves SB a vehicle for bringing together data from several disci-
plines in an organized manner.
     The calculation sequence used in &MRAW is to consider one nuelide
at a time, carrying each through all of ths calculations discussed above
for the release and transport to environment parts of the model, leading
to net environmental concentrations in each receptor in each sons at each
time evaluated.  This is repeated for each nuclide, generating the com-
plete environmental concentration array before proceeding to the
environment-to-raan calculations.  For the pathway analysis, each nuclide
is again considered one at a time, at each time o\?er the time period
studied, developing the dose rate arrays,
     The following sections of this chapter provide details of each of
the sequential steps in the AMRAW-A part of the code.  Section 4.E gives
a mathematical summary of the model.

      Assessment of potential releases from a radioactive waste reposi-
 tory and the consequences of releases requires a definition of the
 quantity of waste present, the quantity of each significant radionuclide»
 and the variation with time due to radiodecay.  The quantity of material
 at  risk is the  "source term."  This is indicated in Fig. 4-2 as
 "Inventory at Risk,"   It should be noted that the "source term" as used
 in  this study represents the total inventory of each radionuclide con-
 sidered, at the various times of interest, whether totally confined
 within the repository or whether portions are in transit through the
 geosphere and/or biosphere.  In some other studies the source term refers
 only to quantities released to the geosphere and/or biosphere.
      If all of  the radionuclides of interest were in simple one-step
 decay,  initial  quantities  as input data would be  adequate,  with
 subsequent quantities calculated within the code.   However,  the actinides
 and their daughters,  here referred to as "heavy metals/" are in complex
 decay chains.   The quantities of some isotopes in decay chains increase
 over time,  reach a maximum and then display a net decrease through
 decay as precursors decay.  Instead of performing the complex calcula-
 tions within AMRAW, they are handled externally by any specialized code
 developed for the purpose, and the quantities of each miclide at selected
 times are input to AMRAW.   In this study, data calculated by ORIGEN,  the
 Oak Ridge isotope generation and depletion code [Bi73]  is used.  Currently,
 fifty times are used  between the start of repository operations and one
 million years,  with shorter time intervals at the beginning and increas-
 ing time intervals later.   The times used are specified as input parameters
 and may have any desired values, in years.  The number of times are
 limited only by computer storage, running time, and output cost consi-
 derations .
     In general, sources of nuclide quantity data do not correspond to
the desired times for AMRAW input.  Codes  such  as ORIGEN calculate gram
quantities at specified times but available output from other studies
usually has different times than  those selected for an &«RAW application
and/or have insufficient intermediate values.  Adjustment of these times

and addition of intermediate values may be accomplished with any adequate
curve-fitting method.  Cubic spline functions are a recent mathematical
development and provide an excellent method for curve-fitting.  Basically,
the technique involves interpolation by cubic splines such that a cubic
polynomial function is formulated between each pair of data points.
Coefficients are chosen so that the second derivative is continuous
across adjacent points.  A cubic spline curve-fitting computer program
developed by Holer (The University of New Mexico Mathematics Department)
and Malcolm [Fr77] was obtained and slightly modified for time adjustment
of nuclide concentration data for this study.  The auxiliary program for
the purpose is called "POLYEPA."
     The inventory of radioactive waste from spent nuclear fuel initially
includes up to several hundred radioactive isotopes.  Many of these are
present in small quantities or have short half lives and do not      a
significant contribution to the total hazard,  a screening method [Lo74b]
is applied to select the most significant radionuclides over the time
range of interest, to reduce the calculations by AMRAW to a itiore manageable
level.  The screening method uses a hazard measure defined as the activity
in Curies of a given radionuclide in a quantity of waste (such as from one
metric ton of fuel) divided by the corresponding Radiation Concentration
Guide {RCG} value  [CFR20].   Ingestion hazard uses     values for water and
inhalation hazard uses RCG values for air.  The ORIGEK code outputs
tables of these hazard measures.  Briefly, the screening method consi-
ders numerous times over the full time range of interest.  The three
fission product elements and three heavy metal elements with the highest
hazard measure are selected at each time considered.  Then the isotopes
are selected which collectively comprise over 99% of the hazard for
each selected element.  This method provides representation from the
two major categories of elements in the waste and representation over
the entire period of time studied.   During initial work on this study,
a waste blend 80% from enriched uranium fuel and 20% from self-sustaining
Plutonium recycle fuel was  assumed.  The screening method applied over
a time range of 10 years to one million years selected 7 fission product
isotopes of 6 elements and 16 heavy metal (actinides and daughters)
isotopes of 7 elements.   Because of special environmental interest in

C-14 and 1-129, these were added for the repository assessment, making
a total of 25 radionuclides for assessment, listed in Table 4-2.
                Table 4-2,   Selected Significant Radionuclides  '

      Fission Products
           C~14a      Sr-90     Zr-93     Tc-99     1-129     Cs-135
                       Y-9Q     Nb-93m                        Cs-137
      Heavy Metals
Cm- 2 44



       The activation product C-14 is included with fission products.
        Table 4-3 summarizes the percentages of total ingestion and inha-
 lation hazard measures  represented by the two major groups  of the 25
 selected nuelides and their total.  It may be noted that the selected
 nuclides represent 96%  or more of the total hazard for the  fission pro-
 ducts group,  the  heavy  metals group and the total of all miclides over
 a range of waste  age  up to one million years.   This tine range includes
 the  peak buildup  quantities and the start of net decay for  the most
 persistent of the selected nuclidesf including Ra-225 which peaks at
 between 600,000 and 700,000 years.  The small balance from  all of the*
 nuclides not  selected represents less than a few percent of the total
 hazard.   Values of 100% indicate a contribution from all other nuclides
 of less than  0.05%.   &MR&W may be applied over any appropriate time-
 range i  the one-million-year range used in this study does not necessarily
 indicate a required isolation period for stored radioactive wastes but
 was  arbitrarily chosen  as a starting basis for calculations.


           Table 4-3,   Fraction of Total Hazard  Represented by
                       Groups of Selected' Radionuclides, Percent
Ingested Hazard
Fission Products 100.00
Heavy Metals 99.5
Total 100.0
Inhalation Hazard
Fission Products 98.2
Heavy Metals 99.8
Total 99 . 7




Waste Age, Years
3 -4 *5
10 10 10



100.0 100.0
96,7 96,1
96.7 96.2

100.0 100.0
97.7 98.8
97.7 98.8




        The  activation product C-14 is included with fission products.
     Next,      discussion of the relationships between the nuclear
power generation scenario and the corresponding waste accumulation is
necessary.  Some variation of constituent nuclides in spent fuel occurs
with variations of irradiation history and with the type of fuel. Light
water reactors  (LWR) are fueled with enriched uranium in which the
fissile isotope is U-235.  However, about one-third of the fissions in
LWR's are plutonium fission, primarily fission of Pu-239 formed by con-
version of U-238 by neutron capture during the fuel lifetime in the
reaction.  Recycle of plutonium recovered by reprocessing of spent fuel
results in an increased fraction of fissions of plutonium in an LWR.
A high temperature gas-cooled reactor (HTGR) is initially fueled with
0-235 and utilizes conversion of thorium"into fissile U-233.  Slight
differences in the fission yield spectrum for the several fissile species
results in a minor effect on the fission product accumulation as com-
pared to the LWR case.  The main result from fuel cycles involving in-
creased plutonium utilization, as in Pu recycle in LWR's or the liquid
metal cooled fast breeder reactor (1MFBR), is an increase in the amount
of heavier actinides such as americium and curium produced by non~
fissioning neutron absorption.  If there is no reprocessing of spent fuel,


-:-the spent fuel itself becomes  radioactive waste [Ax7711  increasing the
•'•'amount of 0 and Pu to be  disposed of by a factor of approximately 200
-:over the 0.5% assumed for reprocessing waste;  reprocessing is  generally
•assumed to recover 99.5%  of 0  and Pu.   The amount of waste from nuclear
'••power generation is,  of course,  proportional to the thermal energy pro-
duced, which     be expressed  as
                 P  = rated electrical power capacity
                  t = duration of time period
                  F — capacity factor  (average operating fraction of
                      rated capacity during period)
                e,_  = thermal efficiency.
 -.Any consistent set of units may be used.  Fuel burnup is expressed in
 terms of thermal energy produced per metric ton of heavy metal in the
 fuel loading,  A typical  design value  used  for LWR's  is  33,000 Mw-d/MT.
 -For more detailed discussions of the relations between fuel cycles and
 corresponding waste accumulations, the reader is referred to projections
 of waste generation by Blomeke, et al. [Bk74, KeC76].
      The source term for AMR&W input is preferably based upon a scenario
 which details installed capacity of each reactor type versus time,
 reprocessing status, interim storage periods, and other factors which
 determine the quantities of significant constituent radionuclides [S£77j
 placed in a repository to be assessed.  The projected quantities versus
 time accumulated in the repository are required for assessment of the
 "repository operations" phase.  The total accumulation is required for
 assessment of the "terminal storage" phase.  Results calculated for the
 repository can then be normalized and presented in terms of damage
 (environmental concentrations, dose rates, or other calculated results)
 per unit of energy production, per unit of fuel, per reactor year, or
 per unit of waste emplaced.  It should be noted that estimation of pro-
 babilities for disruption of events depends upon the respository size
 or area involved for storage of waste.  This dependence upon repository


size makes it difficult to rim AMRAM for, say, waste from one metric
ton of a particular fuel type.  Comparisons between different reactor types,
fuel cycles, reprocessing conditions or other consiaerations can be
accommodated in AMRAW by assuming a modal repository is filled, in
turn, by waste from each system to be compared.
    In summary, the source term for AMRAW is a matrix of grams of each
significant radionuclide over a sequence of specified times.  This
matrix is prepared externally to AMRAW in accordance with, any nuclear
power scenario to be assessed and furnished to AMRAW as input data.
If this matrix includes the times during which waste is being placed
in a repository, AMRAW may be operated for the "repository operations"
phase as -well as for the "terminal storage" phase.  Conversion to Curies
of activity is accomplished within AMRAW by multiplying an item in the
source term by the corresponding specific activity (activity transfer
coefficient in Figure 4-2 }  which is input to the code for each nuclidie

          first step in the assessment calculations  is  to determine the
         phenomena and man- caused events which are potential  mechanisms
    : 'release of radioactive materials from the repository.  One radian tie lide
•:.:&t-.-a:time is routed through AMRAW-A.,  The Release  Model (see  Figure 4-2)
•jajjpvieles transfer coefficients which denote the  fraction of  the reposi-
'.'i.'tpEy inventory which is released during each time increment; tills be-
.:'. comes input to the Environmental Model.  Environmental pathway analysis
vin: -the Environmental Model, described in the next section, uses input
---concentrations in four "receptors";  air, land surface,  surface water,
.'•••.arid; ground water.  It is convenient for calculation purposes to con-
.::.s.'idar the releases from the geologic formation during  an interval of time
';-to-:;four corresponding "preliminary environmental input receptors,"
••;. (figure 4-3} .   Release to air represents the initial ejection  into an
'-.:-:air, suspension.  Release to land surface and surface water is  the
^."initial commitment to these areas, and release to ground water is the
^-transfer by leaching into ground water at the point of ground water
.•-'-contact.  The "OR" gate symbol  in Figure 4-3  indicates  that any one or
.'•-'.any combination  of inputs constitutes a release  from the repository.
;.':Mpre specifically then the Release Model provides values for transfer
^.coefficients to  each of the four preliminary environmental input recep-
• -'to'rs.  These preliminary receptors should be visualized as being in the
{ :elose vicinity of the repository as a step toward subsequent calcula-
:-'tion of dispersion to the various geographic zones  in  the study region.
-.'•''-.    Careful siting of a waste  repository initially provides isolation
.'.-from circulating ground water and chooses a region  with predicted long-
;'-.t.enn stability to avoid disruptive changes.  There  are geologic proces-
•;-;s.es which can occur to disrupt  a repository and  lead to transport of
-waste inventories, denuding of deposits, or exposure of  deposits to ground
-'_-water»  Gera and Jacobs [Ge72]  considered the following categories:
. -I) catastrophic  events, including meteorite impact  and volcanism,
 2} slow geologic processes, including faulting,  erosion, glaciation and
.leaching  (followed by ground water transport), and  3)  plastic deforma-
 tion of the disposal formation by salt or shale  diapirism,  Man-induced
 processes include accidental or deliberate penetration by drill holes

                                       PRELIMINARY EWIFWOTAL
                                                      RELEASE TO
         Figure  4-3,     Releases  from  geosphere to preliminary environmental input receptors,

::which provide  ground water access ,  failure of shaft seals left after
'.repository  operations r  and thermal  response to waste emplacement.
      The  transfer coefficient as a  function of time to a given prelimi-
.nary environmental input receptor for a given release mechanism and
 radionuclide may be defined as
                              - PCt)  ftl(t), y~ .                   (4-2}
.Multiplication  of  this  coefficient by the length of a time increment
considered gives the  fraction of radionucli.de inventory which is trans-
-f erred during the  time  increment.   As explained in subsequent paragraphs,
there is  a flexible interpretation of the two factors in Eg,  4-2,
•depending upon  the release  scenario.   Al (t)  generally is the  fraction
of  inventory transferred if a release occurs,   This is the sudden trans-
fer by a  rapid  event  (specified by input  data)  or the accumulated
-transfer  during the time increment of interest by a slow event such as
leaching  into ground  water  (calculated within AMRAW} ,  P(t) is the
.annual probability of occurrence of release  and is expressed  as
                    P(t) = P.(t)P0(t)  -•«  P (t).                  {4-3)
                             1     f.          n
To provide flexibility, each component factor  of  P(t),  treated as being
.statistically independent, may  be any  of five  functions:

         1}  Constant;  p {t) = C.  Most presently available  data on pre-
             diction of geologic  events are accommodated by this  simple
             repre sentat ion.
         2)  Step Function:  P  (t) = C  if t < t
                              n                P
                             P  {t) = C + B if t  2L t  ,
                              n                    p
             where t  is the time of change by amount B-  This  function
             applies, for example, to  initiation  of continuous  leaching
             following a discrete offset faulting event.
         3)  Ramp Functions  P  (t) = C  if t < t
                              n                p
                             P  (t) = C + B(t - t  )  if  t >  t
                              n                p       -  p

              where  t   is  the  time  of start of change  and B for this
              function  is  the  slope.   This function or the exponential
              function  (described next)  is useful for  a gradual process
              such as erosion  which has  a most probable rate and there-
              fore a most  probable  time  until exposure (and hence release
              via weathering)  but also     decreasing  probability of
              exposure  earlier by higher rates of erosion.
          4}   Exponential  Function;  P (t)  = C  if t < t
                                      n                  p
                                     P (t)  ~ C + exp[B(t - t )]   if t  2-t
                                      n                      p           p
              where  t   is  the  time  of start of change  with exponential
              constant  B,
          5)   Delta  Function;   P  {t}  = O  for t < t
                               n                  p
                                          and t > t
                               P  (t)  = I/At   for t =  t
                               ii                      P
              where  t   is  the  time  of occurrence of a  discrete  event and
              At  is  the time increment within which t   lies.  Subsequent
              multiplication by At  then  generates a unity probability
              during the increment.  This function applies to discrete
     Input data used by the Release Model  in AMRAW consists  of  the fol-
lowing for each of  the  four receptors:   1)  the  number of  release  events
or event  combinations  (currently dimensioned  for up to nine  events),
2} the number of  factors  P (t) comprising  P(t),  specified for each event
{currently dimensioned  for up  to four factors),  3)  specification  of the
function  type and corresponding values  of  parameters  C, B,  and  t   for
each factor and 4)  release fraction Al(t)  for each event.   For  release
by leaching into  ground water, an  input value  for Al{t) is  overridden
by a time- and nuclide-dependent value  calculated by  an AMRAW function
subprogram (DUEACH},
     1.   Release  Scenarios.  The structure  of the  Release Model provides
for making AMRAW  computer runs for several  release scenarios;   1} proba-
bilistic  distribution of events over time,  21 discrete event at specified

 /time, 3) several events each at mean time of first occurrence* or
 ;4-)' dynamic repository simulation.  In addition,, combinations of these can
 'be accommodated.  Available geologic data at the present time provides
 /for only the first two of these scenarios.
          (a)  Probabilistic Distribution.  Running AMRAW in a mode with
 potential release events spread out over time by probability density
 -functions provides a measure of long-term risk, where risk is defined
               n• v _ / Probability of 1     / Consequences of
                      I  Occurrence    I     I   Occurrence
'.•This mode accrues components of risk from a variety of events during
'.each time increment over the range of time considered.  Low probability
 events,  though not likely to occur within a study period such as 10
/years, are given weighted consideration in evaluation of risk and pro-
• vide for relative comparisons of various waste management alternatives.
      Systematic analysis of geologic and man-caused events which may
 combine  in various ways to result in release of radioactive material
 from a waste repository is necessary.  Fault tree analysis provides a
'.systematic method for organizing M1BAW input data, through any technique
..which combines events into sets may be used.  Symbolism used in fault
 trees is shown in Figure  4-4.  A simple fault tree, illustrating how
•probabilities combine at AND gates and OR gates is shown in Figure 4-5
.Each path through a fault tree which leads to a release represents a
'. set of conditions existing at a given time which together can permit a
"'.release  to occur.   Each such path comprises a "cut set,"  All of the
 cut sets in a simple fault tree can be identified by inspection.  Each
'•cut set  can be represented by a series of probability factors.  For
..example, one cut set in Figure 4-5 consists of the right hand input
.'to gate  B  and, say, the middle input to gate 8 ,  resulting in outputs
'/Of the OR gates B,  and B , satisfying the AND gate A  causing output
                  ii.       £,                           JU
 of the top event.   The overall probability for the cut set can be ex-
pressed  by X1 • X2  • X3»  or if preferred &2 • X3-
      Fault tree analysis usually considers a constant probability for
•each gate input.  In this study, the method has been extended with a
 capability to represent each factor in a cut set as a function of time.


System component or basic fault event.
               OR GATE         gate Is In the failed state if
                         at  least one of its Inputs is in
                         the failed state.
               AND  GATE   This  gate is in the failed state
                         only  If  all, of its Inputs are
                         simultaneously In their failed
               EVENT  DESCRIPTOR.  The rectangle is used to
                         describe the event represented by
                         a gate.
               TRANSFER  SYMBOLS.  These symbols are used
                         to transfer  an entire part of
                         the  tree to  other locations on
                         the  tree.
               INHIBIT  CASE,  This represents an event
                        which occurs with      fixed
                        probability of occurrence.  The
                        inhibit gate is in the failed
                        state only if its inputs are in
                        the  failed state and the inhibit
                        condition has occurred.  It is a
                        special type of AND gate.
           Figure 4-4.    Fault tree symbolism.

Figure 4-5.  Simple fault tree,

 The overall probability of each cut set is P{t) with component factors
 P  (t), previously described.  Fault trees prepared for a demonstration
 application of AMRAW are presented in detail in Volume II of this re-
 port and were presented at a geologic modeling workshop at Ispra, Italy
 in May, 1977 [Lo77].  The present status of available geologic data
 results in large uncertainties ia estimates of probabilities which
 affects the calculated risk, but doesn't preclude relative evaluation
 of various management options.
     Complex fault trees can involve up to hundreds of cut sets; the
 number of cut sets increases rapidly with the use of OR gates.  MOCOS
 is a computer code [Pu?4] which may be used to obtain the cut sets for
 fault trees if they are of sufficient complexity to require computer
 selection of cut sets.   It possesses the capability of determining the
 cut sets for up to twenty gates in the fault tree per run.  These cut
 sets are grouped in the output according to the top gate specified in
• the input and the number of input components which comprise the cat
 set.  This type of code reduces the possibility of errors and the time
 consumed in the determination of cut sets.  The output is also easier
 to interpret for anyone who is not familiar with fault tree analysis.
 The cut sets and failure probability for each input event of the cut
 sets may be punched out on cards.  This capability of MOOTS allows the
 overall failure probability of each cut set to be subsequently deter-
 mined and ranked by the use of an additional computer program.  This
 procedure may provide the ability to consider only those cut sets with
 overall failure probabilities above a specified cut-off value.  In this
 study,  fault  trees  are  simple enough  to reduce  by visual inspection
 and the use of MOCUS  is not required,
          (b)  Discrete  Events.   Running AMRAW in a mode with discrete re-
 lease events forced to occur at specific times provides for analysis
 of event consequences.    Calculated results must subsequently be
 weighted by judgment which considers the probability of each such event
 actually occurring.  This mode does not  require estimates of proba-
 bilities, but fault trees serve as a convenient display of event rela-
 tionships and assist in  selecting events or combinations of events to
 be considered in consequence analysis.  The probability function input


^provisions in AMR&W provide for specifying discrete events.   A rapid
'•.•'e'^ent occurring at a specific time  is  simply input as a delta function
v:'.jpius the corresponding release fraction Al.   Repeated occurrences are
•'ih'ajidled by additional pseudo cut sets, each with the appropriate 'delta
'-/-•function,  to offset faulting event which initiates exposure to ground
:•' : ' '                                          /
.•falter and results in leaching is input as the appropriate step func-
,-tion, assuming that once initiated  the leach incident continues until
•'a.'given radionuclide is depleted by decay and/or leaching removal,
/:X-f rock mechanics studies indicate  that a fracture should be considered
-.-.as- closing up or healing after SOUK time  elapses,  this is handled by
//another factor with reverse step function to "turn off" the  leach inci-
 dent at the appropriate time.
:/:. ;•'••''•      (o)  Statistical Mean-Time OaauTrenee,   A possible  mode of opera-
/-'•tion of AMR&W is to estimate the mean  time to first occurrence for each
•postulated event by statistical analysis  and then input each of these
-:/as  discrete events at appropriate times.   No work has been done on
•••this approach during this study? it is expected  that more geological
-.-research is first needed,
'•/.:'•'•        (d)  Dynamic Repository Simulation.   This involves  geologic mod-
/--.e/ling of tectonic movements, rock mechanics and  waste/rock interactions,
/.'to.- represent the gradual geologic processes and  thermal effects of
••':waste emplacement.  Work  on such modeling is beyond the scope of this
••.Study but was started recently at Bat-belle Pacific-Northwest Labora-
-;.;-tories arid at Sandia Laboratories.  Preliminary  concepts were presented
yby  Burkholder (Battelle)  and Tierney  {Sandia)  at the Ispra,  Italy geo-
"/.logic modeling workshop in May, 1977  [OECD77,  Bu77].
•:':• ;. It may take another year before results from dynamic modeling are
•:ready for input to assessment models,  but the flexibility of the AMRAW
-.;.Eslease Model provides for dynamic  input  now.  It is visualized
•'•.here that the results of a large effort in dynamic simulation will     ,
^.-produce a graph of release rate, perhaps  in Ci/y,  versus time.  There
/pan-, be such a graph for release to  each environmental receptor, and
-,for.-different radionuclides.  The graph can be restated as fraction of
-instantaneous  repository inventory released per year.  Figure 4-6
^arbitrarily illustrates a possible  graph  in which  no release is expected
-;until some future time when small releases occur followed by increas-
ingly disruptive events.   This can  be  input to ABRAW as one  "cut set"


               Figure 4-6
TIME (years)
          Conceptual dynamic repository
          simulation response.
with a sequence of step,  ramp,  and exponential  factors represented by
factors P (t)  described earlier.   An alternate  is to break the curve
into two or more additive components.   Each  of  these components can then
become a separate cut set with  appropriate defining factors.
         (e)  Example of Release  Model  Calculations,  As an example of
the calculation through the  Release Model, consider data from the proba-
bilistic mode  presented in Volume II and release of Sr-90 to air as a
result of a volcanic explosion  sometime during  the time interval 400 -
500 years (after start of repository operations).  AMRAW calculates the
average inventory during a time increment as the arithmetic average at
the beginning and end of the increment  as illustrated by the example.
This is considered to be more valid than using  inventories at the ends
of the time increments.  The average inventory  of Sr-90 at risk comes
from the source term for times  of 400 and 500 years;   (7.82 x 10  + 7,85
    23                                              2
x 10 )/2 = 4.30 x 10 g,  Multiplying by specific activity, 1.42 x 10
Ci/g obtains 6.11 x 10  Ci.   The  Release Model  obtains from data input
for the volcanic explosion cut  set:  one factor, a constant, for P{t) =
2.4 x 10   , and the expected value of  release  fraction Al(t) = 0.075.

             transfer coefficient becomes
                                             _i y
                     = P£t)al{t) =  (2.4 x 10   ) (0.075)
                     =  1.8 J£  1Q~13,
     .the release going to the  air preliminary environmental input

          (6.11 x 105Ci>£1.8 x ItT^/yXlOQy)  = 1.1 x 10~5Ci -
    " 2.  Release Barriers.  A multi-barrier concept is applied in a
•••gesologie  isolation repository to prevent  or impede release to and
•••transport through the geosphere to the biosphere.   Each of these is
          briefly in the following paragraphs.
;••: !';.-•'; '      (a)  Geologic S-bz*uatw?&.  A  site  for  geologic isolation of ra-
•:;eti.oaetive waste is chosen to provide  a stable  geologic formation with
      rock free of circulating ground  waters.   In AMEAW, potential dis-
          are considered which could change the initial conditions and
        waste material or allow ground water to reach the repository
:•::;.'•. : '      (b)  Container,  Most of the waste  emplacement methods under
'/••'.consideration utilize a sealed metal canister  to contain a solidified
yfojm of the waste.  For rock-melting concepts,  the  canister is sacri-
/.ficial and is only a temporary barrier.  For non-melting concepts, the
.•;caiiister provides a barrier for up to tens of  years.   In &MRAW, this
vCpntainer is neglected for terminal storage  analysis  for which a geo-
;iogical time frame is involved.
:';•/. '••[.:•-.      (o)  Leaah Resistance.  A major barrier to release of ncclides
•-into the geosphere is the use of a leach  resistant  solidified form of
:;wa,sts , such as glass.  Leaching occurs only  if events occur which per-
:-.irti'-t::f round water to come into contact with     laced waste.   The next
•.•section of this chapter describes the calculation of  leach rates in an
••MiflAW subroutine.
•••."•'.       fd)  Nualide Retention by Sorption.   If release to the geosphere
,• by.; leaching occurs, entry to environmental input receptors requires
;. transport via ground water movement to the biosphere.   During the

migration, sorption processes such as:  adsorption, ion exchange, col-
loid filtration,  reversible precipitation, and irreversible minerali-
zation occur, retarding nuclide movement.  The ground water transport
model is in the Transport-to-Environment portion of the Environmental
Model, described later in this chapter  (Section D.I.).
     3, Leaching in Ground Water.  Leaching of a waste deposit followed
by transport in aqueous solution is an important process that occurs
prominently in the Release Model and subsequent Environmental Model
particularly for an underground repository storage.  The calculation of
leach rates in an AMRAW subroutine applies the leaching model presented
in following paragraphs .
     Many  studies on  the incorporation  of  the radioactive waste in
solid media  [Br74, Gd69, Me73, Me?2, Ra72, Sm69] have included the effect
of time on leaching.  The time law expression fA£61, Lu70, We67]
                             L = at f   + Bt                       {4-4}

which was  developed from studies on the leaehability of commercial
glasses by aqueous solutions  [Gv66» Me73]  has been used to character-
ize the  cumulative amount, L» of the radioactive  isotope leached from
the solidified waste  for a specified leach period.  Here, it is assumed
that the glass matrix does not undergo devitrification.  In Bq, 4-4
a and 0 are empirical constants and t is time.
     Equation 4-4 shows that the amount leached follows a parabolic
relationship with time at short times and  approaches linear kinetics at
longer times.  Differentiation of Eq. 4-4  with respect to time yields
which shows that the rate of leaching varies with the reciprocal of the
square-root of time at short times and becomes constant at long times .
     It must be pointed out that an accurate evaluation of Eq. 4-4
will require experimental leaching tests to determine the constants a
and P {Gci74, We67, A£61, Lu70] .  However, experimental tests may not be
available in measuring a and (J for a specific leach process, in which
case an approximation for L may be employed.  For example, various

          investigations have made use of Fick's laws of diffusion
      , Br74, Gd69, Gd74, Gf74, Me73,  Ra72,  Rt73a, Sro69] as a means of
            JJ.  Consequently, the  diffusional transport model by Gpdbee
         [Gd74| , which considers Fickian diffusion with a concentration-
 Dependent dissolution rate  for sparingly-soluble species , has been em-
 ployed in this analysis to  describe the amount of radioactive species
 •'leaving the solid waste matrix.
 •v':/''--   The governing equation and the accompanying limiting conditions
 ;':'a|S': -.'developed by Godbee and  Joy  [Am72, Gd74]  for the diffusion of radio-
 •'•'activity from the semi -infinite solid waste  are given by
                                             - c)                     (4-6)
                          € = C         t=0rx>0                (4-6a)

                          C=0         t >  0,  x = 0                {4-6b}

                          C=Cs        t >  0,  x = »                (4-6c)

;.yvhere C is the concentration of  the  mobile species at any time t and
-::-space x, V  is the effective diffusivity for  the species, k is a disso-
'.:•..••;••.•.'       e
:;'."fut.ion rate constant, and C  is  the  uniform initial concentration of
-.mobile species.  The initial concentration of mobile forms of a species
yrt-C-}  may be assumed to be at saturation for these forms in the matrix,
•/jnX'addition, the rate of transformation of less mobile forms of the
ysp.ecri.es to more mobile forms can be  taken  as  linearly related to the
•{•concentration driving force  {C - C)  which  is  the difference between the
ysaturation concentration  and the  average  concentration of mobile
-visj3ecd.es at any time.  The rate referred to is the second term on the
Bright .side of Eq. 4-6.   The dissolution  rate of the waste matrix
-•-itself is also assumed to be low compared  to  the migration rate of
.-'.species to the matrix surface, so  that essentially there is no moving
'.';.-";••'•:•  Equation  4-6 does not consider radioactive decay which takes
..place in competition with the diffusion process and also occurs in the

leachant.  Leaching during an  increment of time is determined on a basis
of the average inventory of a  particular radionuclide as listed in the
source term.  Following leaching,  a  decay factor is applied to account
for radioactive decay.  Evaluation of  the factor (DECFAC)  and its appli-
cation are described in Section D.I. of this  chapter.
     A method of solution  [Da70, Gd74]  of Eq. 4-6  involves the intro-
duction o£ a transformation variable
                          n{x,t) = c   - c(x,t)
into Eqs, 4-6 to  4- 6c to yield the  following  corresponding expres-

                           n = o
t = 0, x > 0
                           n = c
t > 0, x = 0
                           n = o
t > 0, x = m .
     Equations 4  -  8 to  4 - 8c may be solved  analytically  [Da?0],
        n =
          + exp
    + (kt)
where erfc y = 1 - erf y
                        erf y = — I e    dz.

     The error function (erf) is a monotone increasing  function  ranging
from 0 to 1.  Properties and tabulated values of the error  function  and

 complementary function (erfc)  can be found in texts  and handbooks  of
 ' mathematics  [Sb70, Kr67 ].
          (a)  Pv&dictov Equation for Leashing,  Direct substitution of
 -Sg..' '4 - 9  into lq. 4  ~ 7  gives the concentration of  the mobile  species
 :':'':iii':':the medium as a function of time and space, which is
c- Cs ll~ -exp
k \1/2~
iT~ i

sx*f c


2 CO t)I
fraction, £, of the initial amount leached, L  in Eq.  4-13 is divided
by AQ, i.e.
          o    s
                        1/2 -kt
     Equation 4  - 13 is thus the predictor equation for the amount of
radioactive species leached from the solidified waste for a specified
leach period (L in Eq. 4 ~4 ) .  It should, again be pointed out that
radioactive decay is applied subsequently by use of a decay factor.
Godbee and Joy [Gd74] interpret the application of Eq. 4-13  to that
of a "stable isotope."
     It is important to examine Eq. 4 -13 to determine whether its be-
havior is consistent with that predicted by Eq. 4 - 4 .  At short times,
Eq. 4 -  13 becomes  [Da70, Gd74]
which, for small kt, follows a parabolic relationship as in Eq. 4-4.
For very long times, erf  (kt)    approaches unity and Eq. 4-13 becomes
 [Da70, Gd74]
                      L  * -2- A CO k)
                       P   V   o  e
for the amount leached.  As was observed in Eq. 4 - 4  the above equa-
tion (4- 165 also follows a linear relationship with time.  Much of
the available results from work on the leaching of glasses  [Rt73b,  SmG9] ,
especially silicates, reveal that the total amount leached varies with
the square-root of time at short times and approaches a linear relation
at longer times.  This is the behavior predicted by Eq, 4-13.
     Differentiation of Eq. 4-15  with respect to time when kt is very
small yields
V   o
and the differentiation of Eq. 4- 16 with time  correspondingly yields

                          <3L    F
                          T^ s ~ A   (t? k)1/Z                    W-18)
                           dt   V   o    e

           tiroes Eq.  4-1? predicts the leach rate as a function of the
            of the square-root of  time;  Eg. 4 ~ 18   predicts a constant
            at long times.  Both cases are consistent with the predic-
          Eq. 4 - 4.
          use of the effective diffusivity "P   as  it is applied in
  g.:/.;4:-- 6  is appropriate since it is implicitly assumed that the dif-
        of the species from the solidified waste  can be characterized by
       "concentration changes  on the diffusing species, in which case
        . diffusion is the controlling mechanism,  and P  can henceforth
            to be independent of time, position,  and concentration.
         this analysis t?  is  estimated using  Eq. 4  -  23,  discussed in
        l owing section.  Subsequently the estimated t?  is utilized in
             the dissolution rate constant  k  by iteration via a. curve-
         procedure.  The value of k is  adjusted until the theoretically
           profile (e.g., L  vs. t plot  of Eq. .4 - 13)  adequately coin-
       with experimentally measured leach data  [Gd?4] ,  Leach data from
          -glass by Mendel and MeElroy  [Gd74, Me72J  is used in this iter-
       -procedure.  Comparison plots of  the  experimental amounts of Cs-137
         and those predicted by Eq. 4 - 13  from a phosphate -glass product
     .'';;av. cement-sludge matrix are presented  by Godbee and Joy [Gd74] ,-
           is very good,
               Estimation of Diffusivity.  The  kinetic theory of liquids
vis..-;iipt.-as developed as for gases, where  the  kinetic theory of gases is
:^i^Jtnown [Da70, Pe63, Pr58] .  It is not surprising, therefore, that
::;.fJ|isi5re-:-are no satisfactory methods of predicting  diffusivities in liquid
v^SteiBsyfrom first principles.  Diffusivity  coefficients in liquids are
:vabo'Qt;>:fou-r orders of magnitude smaller than  in gases and are more diffi-
        : -measure [Pe63] .
y::;:;;j::y:y;--Estiination of the diffusivity coefficients  is  done with the use of
••th^.'/;:St:okes-Einstein relation  [Bi60] , given by

                                                           	1 /"     2
where K is the Stokes-Einstein constant equal  to  1.38 x  10  g  cm /
sec  molecule °K; |J is the solvent viscosity  at absolute  temperature
               — ^
f °K (2,35 x 10~   g/cm sec at 523°K for water); and it  is  the radius of
the diffusing particle in can,  Eq. 4-19 considers the  diffusing par-
ticle to be spherical in shape and also assumes that the solvent, here
taken as water, appears to the diffusing species  as a continuum [Bi60].
Using an average temperature of 250°C  (523°K), Eq. 4 - 19  simplifies
                    ft    1.88S x 10"17     cm2  .
                    ^e ~      I~           ~d~                   (4-20)

     The radius FL  of the diffusing species  is approximated  using the
Loschmidt method.  Present [Pr58] adequately describes this  method,
which assumes that the molar volume in the solid  state  (M/p) is of the
order of magnitude of N (2R. } , i.e.

                                     * I                          (4-21)

where N  is Avogadro's number (6,025 x 10    	-	 ) j M is the mole-
cular weight of the diffusing species; and p is the mass density  in the
solid state in g/cm .  Eq. 4-21 simplifies to
                                    -9  3nr
                      Rk = 5,92 x 10    f -    cm                {4_22)
which is combined with Eq. 4 -  20 to yield

                    Pe ~ 3.18 x 10"9  ^*|~"    ZSL.'              (4-23)

    It should be pointed out that Eq, 4-23 provides merely a rough
approximation for the diffusivity coefficient.  The Wi lice -Chang semi-
empirical equation  [Sk74] , given by
                                       M }       2
                  f)    f Tn   irt™-"      s      era
                  £e = 6.39 x 10      ^6     -j-                 (4-24)
                                    u v
is a better relation to use where the solvent is water.  Here, T and p
are defined as before  (except that \i will have units of centipoise) ,


    '-is the molecular weight of the solvent, V  is  the  molecular volume of
    :                        i _              3
     solute at the normal boiling point  in cm  /g  mole,  and x is an
.^''association" parameter.  The association parameter  x  refers to the sol-
:xysnt and is 2.6 for water  [Da?0|.  However, there  is apparent rigor in
0-enploying Bej, 4 - 24,  particularly where it  is  applied beyond simple
•-Vspbstanees.  For example, in estimating V, the contributions of the
Sterns in the molecule are added up in the case of complex substances» and
:'varie subtracted in the case of ring-compounds  [Ba?Q],   Specific details
••':bf waste form and chemical composition  are beyond  the  scope of this
"•.study, necessitating use of the StoJces-Einstein  approximation for deter-
;...mining effective diffusivity D  instead of the more  accurate Wilke-
:-Chang equation,
'••.• •        (G)  Example of Leashing Calculations.  An  offset fault which
;:-results in ground water coming in contact with a portion of the canis-
::ters in the repository inventory constitutes  a leach incident,   1MRAW
"•calculates the amount leached during a  given  release time increment and
.'Obtains the corresponding release fraction Al(t).  An  example is pre-
sented here to illustrate the steps.  Consider a leach incident during
.the/ 'time increment 900 - 1000 years  (after beginning of repository
operations), and consider release of C-14 by  leaching.   The average
V'Wiwentpry of C-14 corresponding to these times,  obtained from the source
/term, is {3,64 x 1Q4 + 3.59 x lQ4}/2 =  3.62 x 10 g.  This is multiplied
•.:.by;.:.its specific activity, 4.45 Ci/g, to yield the  radioactivity, i.e.

                   (3,62 x 104)(4.45) =  1.61 x 105  Ci.

 If this-activity is evenly distributed  in a total  canister inventory of
62,500 canisters but only one row of 250 canisters is  subject to leach-
ing at a time (both values are input to AMRAW),  then the C-14 exposed
to leaching, A , is 1.61 x 10 (250/62,500) -  6,44  x  102 Ci.   Section
6.B, Vol.. II, describes the canister dimensions, where  the total surface
                                            4   2
area per canister exposed, F , is 4.38  x 10   cm   (this  value assumes
that the;-canister disintegrates into ten parts)  and  the specimen volume
                               ET   *2
per canister, V , is 2,22 x 10  cm   (both values are input to AMRAW).
      Proctor [Pc66]  describes a typical composition  of  radioactive
wastes from the reprocessing of spent reactor fuel.  If, for example,


C-14 Is present In the solidified waste matrix  as  carbonate,  for cal-
cium carbonate M = 100 and p = 2.71 g/crn   [Pe&3] can be  substituted in
Eq. 4-23  to approximate D .  *Chus, from Eq, 4-23

            V  = 3.18 x 10"9   V1PF  =  9.S5X1Q"10  2L_-
             e                 I  100                       d

This estimated I?  is used to determine the dissolution rate constant k
                e                                         _3
as described in Section 4.C.3, and is found to be 4.96 x  10  /d.  This
determination of $  and k is done externally to AMSAW and the values
are furnished as input data.  Finally, use of Eq,  4-16 yields  the
predicted activity of C-14 leached during the time Interval,  t = 100 x
365 dayst
         2.22 x 10
                  4               I'" ...... '    '      """ ....... ' •••'  •• '  -•'
              * 10   (6.44 x 102)   {9,55 x 10~10)  {4.96 x 10~3)
                100 x 365 + ~
                            2 4.96 x 10~3
=• 10.1 Ci,
This is the activity leached into the ground water preliminary input
receptor during the time increment of interest.
     As performed within AMRAW, the calculation sequence is rearranged
for programming convenience as follows;
     1)  Calculate mass leach rate, gm/cm -d, in a subprogram  (RLEACH),
     2)  Multiply by the areas exposed to leaching, P  , and, by the
         time interval, t = 100 x 365 d, obtaining grains leached during
     3)  Divide by average inventory during interval  (grams), obtaining
         dimensionless release fraction, Al{t).  This value, calculated
         as grams released per gram inventory, also represents Ci re-
         leased per Ci inventory.
     4)  Multiply by annual probability of leach incident, P(t), obtain-
         ing the transfer coefficient, A(t).
     5)  Multiply A(t)  by average inventory (1.61 x 10  Ci) and by time

           increment, t,  (100 y), obtaining  the  release to the ground
           water receptor.
:/;--:-'.    The calculation may consider either a  discrete  leaching event com-
•'•:Kiencing at a specified time or may be distributed probabilistically.  For
':_•;& 'given time increment, t, an input probability of 1/t when multiplied by
'^duration t generates a unity probability for occurrence,   therefore,
•'•'if  the probability is 1/t, a leach incident occurs  (or continues)  and
::.the amount released becomes the 10.1 Ci calculated above.   In a
".'probabilistic mode where P(t) is the probability of  offset faulting
>'-'(5t»ch as 1.4 x 10   y~ ) , the release on a  probabilistic basis is cor-
.':respondingly less.
'/.•;•. •   More specifically, the calculation in  AMRAW divides a given re-
-'.--lease time increment into 10 sub-intervals  (5 if increment is 100 years
;::Q'r- less) , and calculates the average of leach rates  obtained for each
-','-.;.'-;   4,  Model Output.  In suaroary, the Release Model in AMRAW provides
•:.values of transfer coefficients used by AMHAW,  for each radionuclide in
vturn, to generate a matrix (denoted by the  computer  variable R1J)  of
^releases in Curies to each of the four preliminary environmental input
'.-•receptors (air, land surface, surface water, and ground water) , during
':-.each of the time increments considered.  Subsequent  transport to envi-
•','rpBHiental receptors in each geographic gone, adjustments for decay pro-
-ioasses and accumulations for all release increments  is handled by the
';:'finvirontnental Model.

     The Environmental Model is divided into two parts:  1) Transport to
Environment, and 2) Environment to Man Pathways.  The first part uses
releases to the four preliminary environmental input receptors from the
Release Model output matrix and calculates the corresponding concentra-
tions in the environmental input receptors for each of the geographic
zones.  The second part of the Environmental Model performs the pathway
analysis and calculates dose to man.
     1.  Transport to Environment.  The Release Model calculates quanti-
ties of each radionuclide, in Curies, released during each time interval
{by probabilistic, discrete event, or other modes},  The releases are
initially collected in Preliminary Environmental Input Receptors {Pig.
4  -  7 ) representing four categories of environmental input:  air, land
surface, surface water, and ground water.  Several steps are required to
calculate environmental receptor net concentrations for the subsequent
pathway analysis.  These steps are summarized as follows and then dis-
cussed in detail:
         1}  Calculate dispersion of the release increment to the several
             geographic zones,
         2)  Adjust for transfers from each receptor to the other three
         3)  Calculate average concentrations for the activity remaining
             in each receptor.
         4)  Calculate residual activity during each time increment sub-
             sequent to release.
         5)  Accumulate concentrations in each time increment from all
             current or prior releases,

         (a)  Dispersion to Zones,   The first step in obtaining environ-
mental concentrations is to allocate the initial releases to each geo-
graphic zone.   The relationships for one zone during the time increment
coincident with the release time increment are illustrated in Fig,  4-8.
AMRAW terminology, with subscripts omitted, is shown as labels where this
can be helpful in relating this discussion with other material describing

Figure  4-7,
Preliminary environmental
input receptors.



IN ZONE, Cly/cm3
 IN 20H6, Ci
   Figure  4-8.    Dispersion to a  zone during  a release time  increment.

 the  code.  The  first  factor, A2,  accounts  for  retardation,,  radiodecay, and
.environmental decay effects.  Data statements  in the program set these
 values equal to unity for the first  three  receptors  (air, land  surface, and
 surface water)  for the environmental time  increment which is coincident
 with the release time increment.  For ground water, A2  is evaluated by a
 ground water transport subroutine  (CRATIO), described later.
       The  dispersion allocation factors, ZQNALQ,  are not calculated
 within AMSAW but  are determined by application of existing dispersion
 models or  codes,  considering the effective surface areas of land and
 iwater  in each zone,  and  are furnished to AMRAW as input data.   First,
 consider the receptor for  air.   Any of several codes calculate air
 concentrations and  ground  deposition as a function of distance and
 direction  from a  release point.   For a continuous uniform release rate
 {in  Ci/y},  air concentrations,  (Ci/cm }/(Ci/y),  and ground deposition
 rates,  (Ci/cm -y)/(Ci/y) can be obtained.   The ground deposition rate
 is approximately  equal to  air concentration multiplied by an effective
 deposition  velocity but  the effects of wet deposition cause some vari-
 ation  from  this relationship.   If an acute release occurs at some time
 within a given release time increment and  involves activity equal to
 the  integrated chronic release  for  the release time increment,  inte-
 grated  concentrations result which  are numerically equal to the chronic
 case.   Integrated air concentration, (Ci-y/cm  )/Ci,  and integrated ground
 deposition,  (Ci/cm  )/Ci  can therefore also be  obtained.  Acute  releases
 are  assumed  in Fig.  4-8  and in AMRAW programming, but it should be
 pointed out  that the  corresponding  integrated  dose during a time incre-
 ment is numerically  the  same whether a release is treated as chronic or
 acute.  The  air concentration factor, ZONALO,  and ground deposition
 factor,...ZONDEP, in Fig.  4-8,  are  simply  the  area weighted average
 values for each zone  obtained by an  air dispersion code, e.g.  [Mo75].
      Time increments in AMRAW  are  generally set  to be  at least several
 years.  Therefore, air deposition is relatively instantaneous  following
 -a  release.   This is  shown  in Fig. 4  - 8  as  a deposition  concentration,
 DEP, in:units  of Ci/cm .  The corresponding deposition  on land  surface
 area in; the  zone, AREAG, is ground deposition  DEPGND,  in Curies.   The
 deposition on  surface water area, AREAW, is DEPWTR,  also in Curies.

deposition on surface water area, &KE&W, is DEPWTR, also in Curies.
     Bext consider the receptors for land surface and surface water.
In addition to air deposition, the fault tree model includes direct
release to land surface and water surface.  Mechanisms include ballis-
tic trajectory dispersion from violent events, lava flow, etc.  Again,
the allocation factors, ZQNALO, are determined by external modeling
furnished to       as input data.  Models for this purpose are not well
developed and approximations are necessarily used for current AMRAW
     The allocation factor, 3QN&LQ, for the ground water receptor is
used as a flag to denote whether or not there is discharge or well water
withdrawal in the      with flow front the repository area,  a value of
0.0 indicates a direction of the zone relative to the repository such
that contaminated water cannot enter the zone or that other factors
preclude such water from entering the biosphere in the zone,  ft value
of 1.0 indicates discharge or use in the zone.  In this case, the factor
A2 is the ground water transport factor, calculated by a subroutine
(CR&TIO) for the distance from the repository to the average discharge
point in the zone and for the accumulated transport time for the release
increment.  The ground water transport model is described later in this
     The initial values of releases after allocation to the zones are
represented by p-2 in Fig. 4-8.   At this stags, the inventories are
retained in Curies because further adjustments are required before
conversion to environmental concentrations.
         (b)  Intev'TQoepto'f Adjustment,   Simultaneously with the dis-
persion to the four receptors in each zone, transfers between receptors
occur.  For example, surface deposits can be partially resuspended into
the air, or washed off into surface water, ground water can discharge
to surface water,  and ground and surface water can be deposited on land
surface by irrigation.  These and other transfer processes for a given
zone are shown in  Fig. 4  - 9.    Resuspension from surface water and
ground water is included in Pig. 4  - 9 as dashed lines; AMRAW checks
for input data related to these transfers but they are expected to be
noncontributors.   Air deposition to surfaces is included in the



         C i  y/cnr
                                                          	, J
                            Figure  4-9.    Adjustments  for inter-receptor transfers.

dispersion  calculations previously  discussed  and does  not  require  fur-
ther treatment in the adjustment  sequence.  Each transfer  process  is
visualized  as transferring  a  fraction  of  one  receptor  pool, with cal-
culated radionuclicte content, per unit time to another receptor pool?
the  untransferred balance  then becomes more  diluted.   The fraction of
inventory transferred from  one pool to another (ADJ in AMRRW) is there-
fore represented by the exponential expression
                     G  = E
                      ra    m
1 - expf-Q.5F  At)
where E   (designated ADJ1 in MffiAW) is input data representing the maxi-
mum fraction which can be transferred  (<_ 1.0), F   {ADJ2 in AMRAW} is a
transfer rate constant, and the average  time for transfer of portions of
the inventory  (average of transfer to the beginning and to the end of
the time increment considered) is one-half of the time increment At
(DELTE in M4RAW).  If the rate constant  is large, a step transfer
G  = E  is used.  Resuspension into air  uses a modified expression
(G  is multiplied by land surface inventory and At and divided by land
area} to obtain  integrated air concentration, consistent with the units
for that receptor.  In this case, E  is  the resuspension factor.  It
should be noted  that AHRAW uses input constants developed by externally
applied models or rationale.  The result  from exercising this step is
the adjusted receptor inventories, R2, in Fig. 4 -  10  .
         fa)  Convert to Conoentrat-ions,  After calculating dispersion
to zones for each environmental receptor and adjusting for inter-
receptor transfers during the release time increment, a simple step
is taken to convert the inventories, in  Curies, to concentrations in
each zone, as shown in Pig.  4-10.    The dispersion parameter, DISPH,
is land surface  area or water volume as  appropriate.  For ground water,
the dilution volume for the leachant is  the effective volume of the
ground water plume flow during the time  increment.  It is convenient to
convert from Curies to micro-Curies in this step.  The concentrations
are accumulated  in the matrix R2TOT,  The pathway analysis, discussed
later in this section, makes use of the  integrated deposition during
each release time increment for terrestrial food products.  For this
purpose, deposition is retained in the non-accumulated matrix, GNDBP.

. ;;y\ -::-- :: :;::;:::;::;:-:;-: ::c-^:ve:v:.:-


uCi y/cm

yCj y
--.-."--.-..-; .'-.-'-•"":""•-.-
.::;:;v:"-:;;-;V::' - '-LAND' SURFACE *



"" 	 """X

.../ 2
yC i/crn

yC i /era

pC i /cm


C ,oS,sPN )
Ns . S

yC i/cm






               Figure  4  -10,  Conversion of adjusted inventories to  concentrations.

          (d)  Residual Activity in Subsequent Time Increments.  The above
discussion describes the step in calculating the net concentrations asso-
ciated with the time increment during which a calculated release occurs.
The next  step is to determine the average residual activity during all
subsequent environmental time increments.  This requires accounting
for physical and environmental decay and additional transfers between
the environmental receptors.  This is followed by summing up, within
each environmental time increment, the residual activities from the cur-
rent and  all previous release increments.  The sequence for doing this
between two time increments is illustrated in Pig,4  -  11 .  The transfer
coefficient A2 is evaluated in a subroutine (TRINP - Transfer to envi-
ronmental input) and includes two factors:  radiodecay, and environmental
decay, applied over the time interval from the middle of the previous
time increment to the middle of the time increment being evaluated.  The
method used for determining these factors is described in the following
subsection.  There are removal and fixation processes that gradually
remove each nuclide from effective environmental movement; these pro-
cesses lead to the concept of environmental decay.  It is difficult to
obtain appropriate decay constants to fully implement this provision in
the model.
     The  air suspension from a release is fully accounted for within the
release time increment and there is no direct residual during subsequent
times (A2 = 0.0, via input of a large environmental decay constant).
That is,  any release to the air is deposited on the surface or is swept
out of the study region by air movements within a few days.  This is a
very short time compared to time increments of several years or more,
and there is therefore no subsequent direct residual.  There is, however,
a resuspension component fed back to the air by inter-receptor adjustment
(land surface to air)  for each time increment,
     For  ground water transport, the factor A2 for each environmental
time following release is evaluated for the cumulative time since re-
lease.  This is detailed in a following subsection.
     After accounting for the decay processes and the delay associated
with ground water transport, each quantity R2, carried forward to the
subsequent environmental time increment is then adjusted for interreceptor

                                                       PHYSICAL ANO
                                          PHYSICAL AMD
                                   6ROUND yATEft TRANSPORT
                                    COEFFICIENT FOR TOTAL
                                      TIME SINCE RELEASI

                                        ADJUST   FOR    INTERRECEPTOR   TRANS F-ER

                                        CONVERT   TO   CONCENTRATION  COMPQNENTS
                                                   ACCUHULATE, INTO TOTALS  FOR  TIME  INCREMENT
                                          REPEAT   FOR  NEXT  TIHE  INCREHENT
                          Figure   4-11.  Sequence for residual activities  in  time increments
                                               subsequent  to  release.

transfers  (described earlier and illustrated in Fig. 4-9), converted
to concentration components R2CON  (also described earlier and illustrated
in Fig.  4-10), and accumulated in the net matrix of environmental input
concentrations, R2TOT.  As indicated in Pig.  4-n , this sequence is
repeated from time increment to time increment, over all time subsequent
to each release increment considered,
     Transfer between zones of the region following the initial disper-
 sion is not provided in AMRAW, with the exception of ground water which
can have withdrawal for usage in any appropriate zone.  Programming for
 interzonal adjustment can be added to AMRAW with a sacrifice of addi-
tional computer storage, running time, and input data requirements.  At
this time, the unavailability of appropriate data for this additional
model refinement does not justify the additional complexity.  However,
transfer from any zone to areas putside_ of the study region can be simu-
lated in &MRAW as presently programmed by appropriate adjustment of the
environmental decay constants.  Also, it should be noted that environ-
mental effects which accrue to the population in one zone include any
components which would otherwise accrue to the populations in other
zones if inter-Eonal transfer were calculated.
         (e)  Decay Factors.   The  physical and environmental decay fac-
tors used in the calculation of residual activities in environmental
time increments subsequent to a release are described here.
      Radiodecay is handled in RMRAW by a decay factor, DECPAC.  If all
of the selected nuclides had simple one-step decay to a stable form, an
exponential calculation could easily be used in AMRAW.  However, many of
the actinides have complex decay chains with daughters first displaying
a buildup with time followed eventually by a decline.  In AMRAW, the
effective decay factor between two times is determined as simply the
ratio of inventory quantities for the two times from AMRAW input data,
This may be done since the decay behavior of any released fraction is the
same as that for the total repository inventory.  That is, the complex
decay-buildup equations are done externally by the ORIGEN code, or equi-
valent,  which is more accurate than any simple model which could be used
within AMRAW.       specifically, the radiodecay factor for carrying
forward the residual activity from one time increment to the next time
increment is the ratio of the average inventory in the two adjacent in-
crements.  For example, consider two ten-year increments ending at 80

     :90 years respectively, and evaluate  the radiodecay factor for Sr-90.
     -'aver age repository inventory during  the first  time increment is CX
     " )/2, where the X values represent input data:  grams  of Sr-90 at 70
        years (after start of repository  inventory), respectively,  Simi-
       the average inventory during the next time increment, using data
      cases in Vol. II, is {Xon + X   )/2.   Then  the decay  factor becomes
;.•:: ;•• • •                          Ow    :?U

              „__„„   X80 + X90   1.91 x 107 +  1.4B x 1Q?
              DECFAC = = - ;£-= — = - 7 - J        {4-26}
                        70    80   2.43 x 10  *  1,91 x 10

                     = 0.781,

•'jljsing the basic exponential decay relation [My67J ,  activity -  exp (-Mt) ,
lathis factor for a ten-year interval, corresponds to a decay constant of
.,-A-v».;itJ 0.781/(-10) » 0.0247 y"1 and  hence a half life of  £n 2/0*0247 =
;.v2-0.Q y.  This is a reasonable approximation of  the literature value of
::;27.'7.  It should be noted that the decay factor is dimensionless and
Devaluation by use of nuclide mass is the same as use of activity.  When
-;:l5uildup of a radionuclide occurs over a  time interval this  is automati-
:':;G;ally- accommodated by this method; a DECFAC value  >1.0 indicates build-
 oli;.,': Also, it should be noted that this  method  properly evaluates an
?:jej|fective decay factor for nuclides  in equilibrium with longer lived
".pa-cents .
iS;:::-;;  '/; ground water transport calculations are      from the  time of re-
      • to the beginning and to the end of the subsequent time increment
    'jiiriterest and then averaged.  The  decay factor in these  instances is
           with inventory values for  the  corresponding times,
          ground water calculations where  the time  increment of interest
           the increment is subdivided and the intermediate  values obtained
               n the average for the  whole time  increment.   The inventory
          each intermediate value of  DECPAC is determined  by linear inter-
          -between inventory values for the beginning and end of the whole
          above discussion applies  to the  terminal storage phase which
          - '.releases only after  a  fixed initial inventory has been accumu-
          hen AMRAW is run for  the  repository operations phase, potential
          are calculated only for the repository accumulation period,

Evaluation of DECFAC for environmental times which follow the end of
the accumulation period proceeds as discussed above.  However, during
repository operations, the accumulation process masks decay processes
and a modified evaluation of DECFAC becomes necessary.  For this condi-
tion, the decay factor is based upon the factor for the first time
increment after closing the repository, with adjustment for the size of
the time increment of interest relative to the reference increment.
This may be illustrated with an example.  Consider:   1) a release during
a time increment from 20 to 25 y after start of the repository,  2) re-
pository closing at  30 y, and  3) time increment immediately  after clos-
ing is from 30 to 40 y.  Then,
                  DECFAC .
                           0.5  (1
For Sr-90, this becomes
       DECFAC = 0.5  (1 + 4.91 x  1Q7/6,2S x  10?) = 0.891
which for the five year time interval is within 1% of the 0.882 value
which would correspond to the literature value of 27.7 y half-life.
For a long lived nuclide, X,  = X   ,     DECFAC becomes 1.0 as it should,
     The environmental decay factor is simply exp{-A At), where A  is
                                                    e            e
the environmental decay constant and At is the time interval over which
the factor is to be applied.  A  is input to AMRAW as ECD with values
for each combination of radionuclide, zone, and receptor.
         (f)  Ground Water Transport Model .   In Section 4.C.2,  a multi-
barrier concept is discussed as it applies to a geologic isolation
repository.  By selecting a stable geologic structure free from water
penetration and by using a high-integrity container, the initiation of
release of radioactivity can be prevented or impeded.  For a hypothe-
tical breaching of the container, the rate of release can be reduced
by selecting a low-leachable solid waste matrix (such as borosilicate

      - Into which  the  nuclides are incorporated.   In addition to these
      'barriers ,  there  is  a fourth barrier provided by the geologic
||i^|!uBl--surrounding the repository which can inpede the migration rate of
         lcies  through the  geosphere to the biosphere.  Here,  an analysis
       '-- transport processes of the last barrier is the domain of ground
      : transport  s t ud ie s .
      In considering movement of solutes (dissolved nuclides) through the
 geologic medium it is well understood that generally solutes move due
 to the connective movement of the transporting solution, in this case
 water.  In addition, other complex physico-chemical interactions such
 as solid~phase sorption, hydro-dynamic dispersion and diffusion also act
 to control the movement of solutes relative to the solvent |Br?4] .
 effect of these interactions is thus to cause the nuclides to      at
 generally lower velocities compared to the velocity of the water and*
 also taking into account radioactive decay, result in the consequent
 reduction of releases to the biosphere £Bu76] .
               (1)   Flow in Saturated-Unsaturated Porous Media.  Consider
 the case of instantaneous release of radioactive waste frosts a storage
 tank.   Essentially this type of release first brings the waste into
 contact with the soil moisture moving as unsaturated flow.  The pre-
 dominant direction of unsaturated flow is vertically downward until the
 flow reaches the saturated  zone where the moisture content on  a  volumetric
 basis,  6, has reached effective porosity e  (i.e., 0 =  e) and  flow  is
mainly  lateral,  in some sites  [EP&75] the unsaturated zone  (i.e., 6 <  e)
way be  sufficiently thin so  that interactions  during transport  may be
considered small.  In other  sites, like the Los Alamos low-level  burial
site {EPA75J , the unsaturated zone may be so  thick that  it may  be diffi-
cult to characterize an interaction between the burial ground and the main
asjoifer underneath,
     Consider further a different type of release whereby  interconnection
of aquifers by offset faulting  (Pig.  4-12} introduces ground water into
the disposal horizon and allows it to come into contact  with the  inven-
tory of waste  (container failure is assumed here for purposes of  ana-
lyszs) ,  -pjje contaminated ground water leachant may then move through
the disposal formation and into the upper aquifer as shown in Fig, 4-12.


                                                  DISPOSAL HORIZON
                                                    LOWER  AQUIFER
           Figure  4  - X2.  Movement of  leachant from
                            disposal horizon to upper  aquifer,

For this release scenario, the upward movement through the disposal for-
mation can be considered equivalent  to the downward movement unsaturated
flow described previously in the release from the waste tank storage.
             (2}  Generalized Formulation for Ground Water Transport.
The equations governing ground water transport through saturated-
unsaturated media may be formulated  in the most general form by first
assuming that, where flow of both air and water is  involved, the air
phase is continuous and is at atmospheric pressure; therefore, there are

 no air pockets  trapped in the main ground water flow system CRe?5j.
      The. generalized formulation for flow in saturated-unsaturated porous
 media as developed fay Duguid and Reeves [Re75, Du?6, MS] consists of
 the following:   a)  equation of continuity of the fluid, b)  equation of
 continuity  of the  solid,  c)  equation of motion of the fluid, d)  consoli-
 dation equation for the medium,  and e)  equation of state for the compressi-
 bility of water.   Combination of all of these equations will yield one
 governing equation for flow through porous media [Re75].
      The equation  of continuity of the fluid [Co66J is given by

where JS is the saturation i.e., volumetric fraction of porosity which  is
Bolid, and v   is the velocity of ths fluid relative  to the solid  [Re75J.
Bird  [Bi&O] defines v_  as the superficial velocity,  i.e.,  the volume
rate of fluid through a unit cross sectional area of  solid  plus fluid.
The velocity of the solid, v  is carried here to keep the equations  gen-
eral but this parameter is not retained for the simplified  formulation
presented later.   The term velocity is used here interchangeably with the
Darcian- flux of fluid relative to the solid.   The equation  of continuity
for imcompressible solids is
(1  - e)  + 7 •  (v (1 - e))  = 0.              (4-28)
              »  s       *
Here, the term  (1  -  e)  represents the volume concentration of the solids,
     For anisotropic media the equation of motion of the fluid is repre-
sented by Darcy's  law  [Sc74]  given by
                             v   = - K •  VH                        (4-29)

ishere E is the hydraulic  conductivity tensor and H is the total hydrau-
lic bead.  Generally, the tensor K accounts for directional properties
{anisQtropy} that arise in  formations such as layered sediments.  It is
defined as

                                   k Pf9
where k is the intrinsic permeability tensor, g is the gravitational
factor, and V  is the fluid viscosity.  If a continuous sattirated-
unsaturated flow domain exists, then the total hydraulic head H at ele-
vation z, relative to an arbitrary datum z  c
manner defined by DeWiest  [0w65, Re75], i.e.,
vation z, relative to an arbitrary datum z  can be expressed in the
            Tj __ __

                   Z         p
                    O         Q
 The term p,  is  the pressure at  elevation z,, and p  is the pressure
 at the arbitrary datum z .   Thus H may be written, using  consistent  units,
                                H = 2 + h                         (4-32)
                                            Pi  ~ Pm
 where CF represents the incremental pressure in the fluid.   Substitution
 of Eq.  4  -  32  into Eq. 4  -29 yields the resulting equation of motion

                         V   = - K • (Vh + Vz).                   {4-34)
                          X S

      Although  Eg.  4 - 28 considers the  grains of the solid medium to be
 incompressible,  the granular skeleton  of the medium as a whole is con-
 sidered to  be  compressible, in which case the geometric quantities
 describing  porous  media may be functions of certain dynamic quantities,
 notably of  the existing stress [Sc74J.   Thus in a study on the consoli-
 dation  of porous media, Biot [Bm40] developed the three-dimensional
 consolidation  equation [Re75]  given by

                          (X  + 2n ) ?2T - 72o                    (4-35)
                            s     s

 where X  and n  are the Lame1  constants, i is the dilatation of the
        s      s        2
 medium, and the  term V a represents the total stress.   The dilatation

 is defined  as
                                 T = E
•where  5. .  is  the  macroscopic strain tensor, i.e. of the bulk of the
    ium.   (In  a study of flow through porous media, the flow of fluids
    not the consolidation of the medium is of primary interest in gen
;::;..;-. The  equation of state for the fluid compressibility g* [Dn68J is,
ifor: ;an  isothermal case
                      Pf = Pf e   1  o  = pf e
                               I' = lpfg.                         (4-37)

   • '  4>
;3;he.:'p-,,  here is the fluid density at pressure p  , and 3' is the modified
             of compressibility of water.  The term h is defined  in
       :  this  point a number of functional relationships should be noted
       -continuing with the formulation of  the generalized flow equa-
       -As  indicated by Eq. 4-37,  the fluid density p  is a function of
::j3r.ejs'sure heacL   The hydraulic conductivity (often called permeability
;-;piay-:seepage coefficient)  and the porosity e are both functions of posi-
         pressure head [Re75] , i.e.,

                              K = K(x, h)                         (4-38)

                              e = e{x, h)                         (4-39)
            a position vector.  In saturated regions the dependence of
            is due  or»ly to nonhomogeneity of the medium, and in unsatur
            g K varies both with position and time even in homogeneous
           to its dependence on pressure head [Re?5].
                   K  and saturation 0 (Eq.  4-27)  may be used to define
                moisture content 6, such that

                      0{x, h) = 0(x, h) e(x, h) ,                  (4-40)

Eq. 4-40 simply shows that as the medium approaches saturation  (0 ->  I) ,
the moisture content approaches the numerical value of the porosity of
the medium.
     Equations  4-27  and  4-28  can be written first in expanded forms
and then combined to yield the resultant expression
                       f s                £      s

                   + ? */p   v  )  + EV  7 «  (0P-)  =0.           (4-41)
                        V A  itS '      S     \   f/

The  last  term  in Eq.  4  - 41  is  essentially  a  higher-order effect and
may be neglected  [Re 75], thus
                               *   p
                                   f  vfgj =o.                     (4-42)

     The  equation  of motion (Eq, 4-34) can be multiplied by p   and
the divergence  of  the  result  obtained to give
f • (p
                                       p   K •   C?h
When Eq.  4-43  is  substituted  into Eg.  4-42 the following equation
is obtained

                      Epf If + ^e  if + 0Pf ? '  Vs
                              p   K •  (7h -f  7z)   -                (4-44)
                               f               1

     Eq. 4 - 44 can be simplified by  searching  for a relation for  the
gradient V • v  .  The porosity may not  vary considerably with the
pressure head h, in which case chain-rule differentiation on  Eq, 4 -  40

                               30     3#
                               5T = E 3? '                       (4-45)

 from which it  also follows that

                         d§_ 3h     30 3h     30                  ,„  _
                         dh a? = E 9k ^ = E  3^ •                 (4'46)

 Assuming a constant modified coefficient of  compressibility of water,
 3',  the fluid  density given by the equation  of state (Eg;. 4  -  37 )  is
 differentiated with respect to time to give
                          3t    H  \Kf         3t
     The equation for consolidation  of  the  medium {Eg, 4 - 35 )  is  seen
as a second-order derivative,  and when  integrated twice, yields
                           s + 2ns)  T =  Q  +  f                    (4~48)

where f = f £x, t) ,  The function  f here  must satisfy  the Laplace equa-
tion V f » 0 for all time  [Re75] , i.e. this  condition enables Eq. 4-48
to transform back to Eq.  4-35   when Eg.  4-48 is double -differentiated
The Lame' parameters A  and n  are considered  constant.  For the case
where all the displacement u is in the vertical direction, e.g. u =
u  , it was shown [Dw69, Re75] that  f =  0.   Thus  from Eq. 4-48
                              3T _   ^£
                              at ~ a 3t
^s+    s
                                        2r\  }.                     (4-49)
                                         s f
The lumped parameter  a is the coefficient of consolidation  of  the
     Introduce the transformations

                        ~               T = ? - u.               (4-50)
 but since u is considered a continuous function, the operational order
 on Eq. 4-51  is immaterial, thus

                       7  . v  = JL (tf  • u) « — .                 (4-52)

 The expression for h in Eq. 4 - 33  can be written

                              a -  pfgh

which is  substituted into Eq. 4 - 49 to give

                            T~ = a  p g v|-                         {4-53}

                            a: = a p g,                           (4-55)

Here, a1 is the modified coefficient of compressibility of the medium.
Eq. 4 - 54 is next combined with Eq. 4 - 52 to obtain V • v  , i.e.

                                       , 3h
                            ?- vs » a' ~.                       (4-56)

     Finally, Eqs. 4  - 40, 4 - 46, 4 - 47, and 4-56 are substituted
into Eq.  4  - 44 to yield the governing equation for saturated-unsaturated
flow in porous media

—- = 7 '   K • (Vh + Vz)
dt        I
     terms'a'  and p'  are defined in Eg. 4-55 and Eq. 4-37,  respec-
 tively;  z is  the elevation head defined in Eq. 4-33,
      Inspection of Eq.  4-5? shows that it is nonlinear on acccount of
 the dependence of both  the moisture content 0 and the conductivity tensor
 K on the pressure head  for unsaturated flow.  Furthermore, the disadvan-
 tage of  such  a nonlinear formulation in three dimensions is that in a
 large-basin oriented study,  the  added numerical computational  complexity
 practically restricts the  size of  the region that may be modeled.
      The  following is a discussion of a simplified version of  the  Duguid-
 Beeves solution  [Re75]  of  the generalized flow formulation,  giving a  one-
 dimensional flow with two-dimensional dispersion relation  which  is adapted
 in  this analysis,
               (3)  Simplified Formulation for Ground  Water Transport.
 Strictly, the  governing formulation for saturated-unsaturated  flow in
porous media  (Eq.  4-57)  is .valid for both saturated and  unsaturated flow
because the unsaturated region is  considered in the movement of  the
 species from the point  of  release  through the unsaturated  zone to  the
water table (saturated  zone)  where  flow is mainly lateral.   The  Duguid-
Reeves transient model  [Re7.5, Du76,  ANS]  is  first discussed here before
presenting a simplified version  of  that model,  which  is  used in  AMRMf,
This model and a number  of one-dimensional models [Ch69, Kn64, Ls74,  Rt72]
were studied to ascertain which  predictive method to  use in determining
the effects of solid-liquid phase  interactions  on the  movement of  dis-
solved nticlides in porous media.  The  Duguid-Reeves model  is now in
"Standards for Evaluating Radionuclide  Transport  in Ground  Water at Nuclear
Power Sites/" American National  Standards ANS-2.17 (in review}  CANS],
     For saturated-iinsaturated flow, both a  vertical  dimension and a
horizontal dimension are considered,  generating a vertical  plane.   The
equation of motion for the fluid given  by Eq.  4-34 along with  the  govern-
ing formulation for flow (B<5- 4-57}  are written together to  form a coupled
set of equations


- K
— a'
                             dh   3t
      = ? •  K
                                                (Vh 4-
 Prom these  equations,  a single equation can be written in which the
Darcy flux (v  )  appears  as  a variable,  i.e.
      3h     _
      3t " ~ ? ' Vfs'
     For  a defined  position vector x,  the conductivity tensor K is  a
 function  of pressure head,  namely K =  K{h>;  this is verified  by the form
 of Eq,  4  - 38.   When flow interactions in the unsaturated zone are
 considered negligible  (i.e. the unsaturated  zone is sufficiently thin),
 then only saturated  flow in the lateral direction is considered.  Thus,
 from Eg. 4 -  40 , 0 ->• s as 0" -*• 1»  and Eq. 4 - 5?  becomes
                          {Vh + Vz)  .
     As was pointed out in an earlier discussion in this section, the
conductivity tensor accounts for directional properties  (anisotropy) .
If the coordinate system is selected such that it is made parallel to
the principal components of conductivity, then only the principal com-
ponents of the tensor are required  [Re75].  Assuming further that the
solid medium is homogeneous and isotropic/ in which case the conducti-
vity will not vary with direction, the tensor K reduces to a scalar
[Bi60, Kr67] , i.e. K •* K.  Equation  4-34 thus becomes
and using this result, Eq. 4-59 takes the corresponding form
     (a'  +  93
   - K V  -  (Vh +  ?z)
where a' and B  are defined in Eq. 4-55 and Eq. 4 - 37 , respectively

                              e  =  epfg                           (4-37)

     In dealing with saturated flow,  a generalized storage  coefficient

F is defined such that

                             F = a1 + 6$'
or, using Eqs.  4-55 and 4-37,

                           F = pfg  (a + 68)                      (4-62)

 Substituting Eg. 4-62  into Eq.  4-61,  the result is
                         F ~ = K V •  
     Consider a confined aquifer of thickness w.  Next define a storage
constant P  and a transmissivity T  such that

                    F  = Fw               T  = Kw.               (4-66)

Substituting these definitions  (Eq. 4-66) into Eq, 4-65 yields
Eq. 4-67

                            V2 H - 5* || .                       !4-67)
Duguid and Reeves note that in  using this predictor relation, the boun-
dary conditions of  leakage should be applied when  appropriate.
     For  the case of  flow through an unconfined  aquifer,  the modified
compressibilities of  both the solid medium  («*}  and the water  ($  )  are
not significant compared to the vertical movement  of the  free surface
 (water table)  [Re75].  Thus Eq, 4-67 simply reduces to
                               7  H =  0                           (4-68)

which is the Laplace equation  {Kr67J.  Equation  4 -  68  is valid  for
steady-state flow in confined  and unconfined  aquifers  [Re75].
     A further approximation of the equation  of motion  {Eq. 4 ~ 60 )  for
the fluid velocity v-   (also termed Darcy  flux in  this  analysis)  can be
obtained next.  If the predominant bulk flow  is in the  x-direction,
Eq. 4-60 along with Eq. 4 - 32 can be written
The gradient dH/dx relates to the basic  concept  of  a  continuum.   Thus,
from elementary calculus  [Kr67] Eq.  4  -  69  can be approximated
                             fs x
    term AH/^X is the approximate hydraulic gradient  in  the  direction  of
the flow  {ic-direction); it is constant over the  increment Ax for  a  homo-
geneous, isotropic solid medium.


     The pore velocity  (also  called seepage velocity) is obtained by
                                                      , by the effective
 dividing  the  fluid  velocity in the x— direction ,  vf
 porosity  [Bi60,  Re75].
               (4)   Simplified Formulation for Radionuclide  Mass Trans-
 port.  A  formulation  for  the general  movement of the  carrier  fluid  (water)
 has  so far been  discussed.   In order  to completely  describe the uiove-
 ment of dissolved constituents (radionuclides) in ground water through
 porous media,  a  formulation for the mass transport  of the radionuclides
 must also be  obtained.

     It was pointed out at  the beginning of this section that, with
 respect to the migration  of radionuclides,  these rmclides may have com-
 plex physico-chemical interactions with the geologic  medium fBt»76] ,
 These  interactions, which fall tinder  the general category of  sorption,
 can  cause the  nuclides to move at  velocities lower  than  the carrier
 water  itself.  In general,       nuclides (e.g. Th-229, Th-230) are
 very strongly  sorbed  on many geologic media; others (Sr-90, Np-23?) are
 moderately sorbed, while  nuclides  like  1-129 and Tc-99 are  sorbed very
 poorly, if at  all {Bu76,  Rt73a],
     A measure of the retention of the  species on the porous  medium is
 called the distribution coefficient K,  [Bu76, Gf74, Gv66, Lv?2J,  In
 general, K  is a function of the pH of  the  ground water,  the  concentra-
 tion of dissolved salts (e.g.  sodium  chloride),  solution temperature,
 and in     cases , concentration of the  dissolved nuclides  themselves
 {Bu76J  «  Equilibrium condition  are  assumed  for all  relative physical
     Symbolically, K  can be  represented by
                                K  =  -                           (4-71)
where  f  is the fraction of the  amount of species  that is sorbed
on the solid medium per unit mass of the  medium, and  f is the fraction
of the amount  of  species remaining  in  the solution per unit  vol-
ume of solution.  The usual units of K  are in cm  /g.   Simply, a higher
K,       strong sorption, and conversely;  Th~229,  for  example, has a
K, over 10,000, while 1-129 has a K, near zero [Rt73a] .
 a                                 a


     A retardation factor R, is defined such that
                             Rd = 1 +  e                         (4~72)

where p is the bulk density of the porous medium and  e is the solid
porosity defined in Eg.  4-39.  Here, p must have units of g/cm  to
obtain a dimensionless R .  The pore velocity is normally divided by R
to obtain a measure of the approximate rate of travel of the radionuclide
(see Eq. 4 - 80 in subsequent discussion).
     The most general  form of the single species radionuclide mass trans-
port equation for saturated-unsaturated media as developed by Duguid and
Reeves  [Du76, ANS] is  given by

                  RJ e IT ~ v '  (8D  • ?c) + V •  (v,, c)
                   d   3t                          fs
                               *\ a
                         *  (Rd at +  A6Rdc) = °                    (4"73)

where c is the concentration of the  dissolved species, 5" is the dis-
persion tensor, and X  is the radioactive decay constant.
     In general, for simulation of radionuclide transport, Eq. 4 - 73
may be used together with either Eqs. 4-34 and 4 -  58  or Eqs. 4-34
and  4 _ 59 .  Duguid and Reeves {Re75] observed that in a numerical solu-
tion of Eqs.  4-34 and 4 - 58 in conjunction with Eq. 4 - 73, the com-
ponents of the flux will be discontinuous where the advective-transport
term V  • (v  c) is comparable to or  greater than the  dispersion term
(second term in Eq. 4 - 73).  In the case of fine-grained sediments
where the coefficient of dispersion  is small, Duguid  and Reeves recom-
mend using Eqs. 4-34 and 4 -59.
     The Duguid-Reeves  transient model [Re75]  employs a finite-
element Galerkin method to numerically solve Equation 4-73 along
with Eqs.4-34 and 4 - 59, for instance.  The method was shown to be
superior to other numerical methods previously used,  in  that stability
was significantly increased.  As a result of improved stability, Duguid
and co-worker were able to increase step increments in size and time
accordingly, thereby reducing the computer time and storage core re-
quired.  However, the average computing time for this procedure is
approximately 4 1/2 minutes.  Because of the computational nature of the

ftMRAW code itself, this numerical method was not adapted for use in the
ground water transport calculations in AMRAWj instead, a simplified ana-
lytical solution ie the basis of the ground water transport algorithm
employed in this analysis.
     In the mass transport equation (Eq. 4 ~ 73) , it should be pointed
out that the dispersivity D is generally a fourth-rank tensor which
contains 3  or 81 components.  If isotropy is assumed, however, it can
be related to two constants:  namely, longitudinal and transverse dis-
persivities [MIS] ,  The longitudinal and transverse components of dis-
persivity can be obtained from tracer studies conducted in the aquifer •
under investigation.
      The component, D. .,  of the dispersion tensor for isotropic media
 has the general form' [Re75]
                         &           (a  - a }
 where 6 . ,  is the Kronecker delta [B160, Kr67}, am and a  are the trans-
       it                                        J?      i> >
 verse and  longitudinal dispersiviti.es,   respectively? }v  is the mag-
 nitude of  the Darcy flux,  and v.  and v, are the components of the Darcy
 flux. Note that the subscript fs in the previous Darcy flux term (v  )
 has  been dropped for simplicity.
      The following major assumptions provide a simplification to the
 radian uclide mass transport equation (Eq. 4 - 73) , and form an important
 basis for  the simplified Duguid-Reeves two-dimensional model itself;
 1) the porous medium is infinite , homogeneous , and isotropic with sim-
 ple  boundary conditions;   2}  porous region is fully saturated;  3)  sorp-
 tion of the dissolved radionuclide species is governed by a linear
 relationship;   4)  mechanical dispersion is dominant over molecular dif-
 fusion;  5)  chemical reactions are rapid such that instantaneous equi-
 librium exists between the dissolved and sorbed constituents,  6} fluid
 flow is uniform and steady;   7}  flow is parallel to the x-axis;
 8} concentration of the radionuclide species in the soil region is zero
 at time equals zero; and 9} a single species without a decay source is
      The use of the second assumption above yields 8-»-e as $-*•!, and
 Eq,  4-73 becomes

             R . |f- - 7 • CD « 7c) •*• ? •  (- c) -f XR e = 0.        {4-75}
              Q ot,                       e        d

Also, from assumption 6, the Barcy flux v can be considered constant t

thus Eq, 4 - 75 reduces to

               R , rr ~ V •  (D * 7c) + -  • ?c + AR,c = 0.         (4-76)
                a at                  e          a

     If the dispersion tensor is assumed to ' apply to a homogeneous but

anisotropic solid medium, then using assumption 1, Eq. 4-76 aiay be written

in a form giving two-dimensional dispersion  with one-dimensional flow as

 where the components of the coefficient of dispersion are given in

 Eq,   - 74  as

                            v                      v

                   D=aT~            D   = a  — .            (4-78)
                    xx    L e              yy    T e              \    i
 The term v  is the fluid velocity (as distinguished from pore velocity

 which was defined earlier as fluid velocity divided by the effective

 porosity)  in the predominant x-direction of flow;  a  and a  are the
                                                    I»      T

 longitudinal and transverse dispersivities, respectively, and should

 be  determined from in-situ studies in the aquifer.   Dividing Eq. 4-77

 by  R  yields

                       D. ,                     j   v

                  Ei"Tf                U = i~ii-             (4-80)
                        a                     a

 Here,  U  is  called the  pulse velocity,  and is the approximate rate of

 travel of the dissolved radionuclide and can be used  to estimate the

 approximate travel time of  the  species [AHS].

     Eq. 4-79   can also be written

                              2        2
                     DC   ^,3c  ^3c   ,

                     ^ ' \ ~2 ~ Ey  7~2 + Xc  ' °              H-81)
                             3x       3y



                             DC _ _§£     _3£
                             Dt "" 3t     3x *

 Hie term Dc/Dt is a special kind of total derivative and is called
 the "substantial derivative" or, more logically, the "derivative follow-
 ing the motion" of the radionuclide in the x-direction.
     Although for saturated~unsaturate<3  flow with two-dimensional dis-
persion the vertical and horizontal dimensions must be  considered, the
resulting rectangular plane  source approaches that for  a line source as
the distance from the source becomes large compared to  the source width
 [ANS].  Appendix A provides  development  of the equivalent line source
equation from a plane source equation-   Hence, for the  instantaneous
release from a vertical line source through the point 
 this chapter.  Separate calculation for one rmelide at a time with Eq.
 4-83 or Eg. 4-84, followed by adjustment for decay (or buildup)  by DECPAC,
 needs some interpretation.  If the radionuclide of interest has no radio-
 active parent, has a short-lived radioactive parent,  or if a radioactive
 parent has the same K, as the daughter, the simplified method described
 here correctly accounts for decay and for a decay source with no further
 adjustment,  A short-lived daughter of a long-lived parent may be appro-
 ximated by setting the K, value for the daughter equal to K, for the
                         a                                  a
 parent,- the daughter inventory in this case is dependent upon the parent
 and in effect, moves with the parent.  If both parent and -daughter are
 long-lived/ the method described here overstates daughter concentrations
 if the daughter       faster than the parent and understates daughter
 concentrations if the daughter moves slower than the  parent.  An inter-
 mediate value of K  assigned to the daughter in such  a case can provide
 an approximate corrected representation.  A complete  interpretation of
 the validity of these simplified calculations depends upon inspection
 of the K, values determined for a specific site for the nuclides in
 decay groups to be considered in conjunction with water velocities/.
 travel distances,  and other aquifer parameters.  For  nuclides where the
 travel time to a usage or discharge point exceeds the time range to be
 calculated (i.e.,  K, exceeds a "border value?" see Section 7,A.2,a. in
 volume II), the calculation method becomes moot.
      The definitions given in Eqs. 4 - 72 , 4 -  78 , and 4-80  are used
 to write Eq. 4 - 84,  relative to the point (x^ = D, y^ = G)
                                  (x-k_v t]
                                      2 D
                          exp -
                      v t
k,v t
 3 p
               M1                     1                    r
     k  ^ 	              k  =              k     4 _±
          4ir(aa)VR,           2   Rd            3     Rd
              jLi  j.    ci
     k  = 4 —                       M                    pKrt
      4     R.                  M' = —          R. =  1  + —&    (4-84b)
             d                                     a         e

Here, v  is the pore (or seepage)  velocity (= —I, and z  is the aquifer
       p                                   \   e /       a         ^l
thickness.   Eq. 4-84  is in a subprogram CRATIO in AMRAW.

     Equation  4-84 obtains  the  concentration  in  ground water at  time t,
distance x from the source,  and at a  distance y  from the plume centerline
for specified  aquifer  and nuclide  parameters.  At y  » Q, the concentra-
tion is a maximum and  it drops  off rapidly with  distance from the center-
line.  It is shown in  Appendix  A (Eq. A-15) that there is a value of y,

                         y  = yy =  2.08(aTK}*5  ,                    (4-84c)

at which the concentration  calculated by Eq,  4-84 is equal to the average
concentration  across the plume  width  (in the  •vicinity of the peak with
respect to time).  This is  the  basis  of input to AMR&W-A for the corre-
sponding zone-dependent parameter  YY.  appendix  A also shows that the
effective width  (width ~ 2y) of plume where the  concentration drops to
0.1% of a valne  at the peak, from  Eg. A-14, is
                            y = 10.5 (a x) a  ,                     (4-84d)

The value y  is  input  to AHB&W  as  the zone-dependent parameter YW.  The
subprogram CRATIO in AMR&W  first determines the  average concentration
across the plume pe_r Ci released,  by  using y  = y as explained above,
                             •*             3     y
This concentration is  (yCi/exn )/Ci or (Ci/m )/Ci.  Next, CRATIO  calcu-
lates the volume of water with  the calculated average concentration which
seeps past the  location of  interest during a  time increment {or  sub-time
intervals).  This volume (denoted  in  CRATIO as GNDD1S or GND1NG) is cal-
culated as the product of the effective plume width  y t aquifer  thick-
ness z , seepage velocity v , porosity e, and the duration of the time
      a                    p                                   3
increment.  The product of  concentration per  Ci  released,  (Ci/m  }/Ci;
and the associated water volume, m ,  is diinensionless (Ci/Ci), repre-
senting Ci passing the location of interest during a time increment, per
Ci released at an earlier time.  This product, denoted as CRATIO in sub-
program CRATIO,  is returned  to  subprogram        {see previous Section
4.D.l.d and Pig. 4-11) where it is averaged for  sub-intervals in the
time increment  (see a  following paragraph for discussion of sub-intervals)
and adjusted for radiodecay.  Finally, the transfer  coefficient A2  (Fig.
4-11) emerges for use  in the main  program, where multiplication  of A2
by a quantity released in Ci obtains  the quantity in Ci passing  the


location of Interest during the time increment.
     An example calculation is presented here to illustrate application
of Eq. 4-84 and the subsequent calculations in predicting radionuclide
concentrations at      usage point, e.g., at 10 km from the repository
area,  consider an offset fault which results in ground water coming in
contact with a portion of the canisters in the repository inventory, and
that this event constitutes a leach incident.  Consider further that this
leach incident takes place during the time interval 900 - 1000 years
(after beginning of repository operations), and release of C-14 by leach-
ing is being studied.  Then, as was determined in the example calculation
for leaching given in Section 4.C.2, the activity leached into the ground
water preliminary input receptor during the time interval of interest is
10.1 Ci.  However,       first calculates a transfer coefficient norma-
lized to a 1 Ci release and then applies the coefficient to the calcu-
lated release.
     Next consider that the contaminated ground water, normalized to a
1 Ci release, enters an unconsolidated aquifer with the following pro-
perties taken from the application in Volume II:  v  =1.46 m/yi e =
                                       3           -P                3
0.15; a  = 50 m; a  = 6 m; p =2.3 g/crn ; z  ~ 50 m; and K  = 1.4 cm /g.
       Ij          T                        ad,
The C-14 concentration is to foe determined at a usage point x =* 10,000 m
after a time in the environment, assumed here for illustration, of
160,000 years.  From Eq. 4-84c, y = 2.08{6 x 10,000)  = 510 m.  The
retardation factor can be immediately estimated using Eq. 4-72:  R  =
1 + (2.3)  (1.45/0.15 = 22.47.  Then from Eq. 4-84:  M1 = 1/50 = 0.020
                                       k                7
Ci/m; k  = (0.020) (22.47)/(4 TT (50 x 6} 2) = 0.00208 Ci/m ; k2 « i/22.4?
- 0.044; k, = (4)  (5Q}/22,47 = 8.9 m; k  = (4) {6)/22.47 = 1.07 m.
          -J                            ^J
Substituting these values in Eq. 4-84, yields the C-14 concentration
prior to accounting for decay.

 c =    0.00208 Ci/m	  J  [10,000-(0.044){1.46}(160,000)J2 m2
     (1.46 m/y)(160,000 y)  '"    |(8.9 m){1.46 m/y){160,000yj
                      (1.07 ra)U.46 ra/yHl&Q,ODQ
                               -9     3
                     (8.90 x 10   Ci/m ) (0.340)

                    =  3,03 x  10~9  ci/m3

                    =  3.03 x  1(T9  yci/cm3  .

 The example calculation is  continued after first discussing travel time
 and the use of sub-intervals  of time in  AMRAW.
      The travel time of the C-14 at the  emergence point can be approxi-
 mated using the pulse velocity U defined in Eq.  4-80:
 U - v /R  = (1.46 m/y)/22.47  = 0.065 M/y.   Then,

              approx, travel time = ^~^e—7~~ ~  154,000 y.

 Thus,  it would tales approximately 154,000  y for the maximum concentration
 "peak" of C-14 to occur at  a  distance of x = 10 km.
      It is helpful to describe the procedure in estimating the average
 radionuclide concentration  in ground water in MLEAW.   Presently,  as
 specified by input data for applications in Volume II, fifty times are
 used from the start of repository operations up to a time  horizon of a
 million years,  with shorter time increments such as 5, 10,  100 and 1,OOO y
 at the beginning anfl increasing time increments  later, such as 10,000 and
 100,000 y.   Results of preliminary sensitivity  analysis runs on the ground
 water transport model discussed in Section 7.a  of Volume II indicate that
 generally the width of the radionuclide  concentration  peaks at half-
 height is more than 2,000 y.   This means that for time increments up
 to 1,000 y (e.g.,  9,000 ~ 10,000 y), the average nuclide concentration
 is simply taken as the arithmetic  average  of the concentrations calcu-
 lated  at the beginning and end of  the time increment (e.g.,  at 9,000 and
 10,000 y).   When  the  time increments are 10,000  y or higher,  however,
 this simple  averaging procedure  would be in  error because  for these  large
 time increments, narrow peaks  associated with low K, values  can be
 "missed,"  Hence,  in        each time increment of >_  10,000 y is  sub-
 divided  into  1000  y sub-intervals  if K,  <  1  and each increment >  100,000
y  is subdivided into  1000 y sub-intervals  if K  <  1 and into  20,000  y
 sub-intervals if K >  1  (broader peaks permit longer sub-intervals)»  The
concentration is calculated at the end of  each time period,  and the
average concentration  is obtained by  dividing the  sum  of all  these

calculated concentrations by the total number of time periods in the
increment.  AS discussed in earlier Paragraph 4.D.l.e/ a decay factor
DECFAC is applied to account for radiodecay in all of the components  for
average concentration calculations.  To illustrate the application of
DBCPAC, continue the example calculation where it is found that the aver-
age concentration of C-14 in a plume 10 kin from the repository after
160,000 y following release of 1 ci during a leaching interval from 900
                                                         -9       3
to 1000 y, and prior to accounting for decay is 3,03 x 10   yCi/cm .
The inventory values for C-14 at times of 1000 y, 100,000 y and 200,000
               4           -1              -6
y are 3,59 x 10 , 2.26 x 10   and 2.28 x 10   g, respectively.  By linear
interpolation, as performed within &MR&W, the approximate inventory at
160,000 y is 9.04 x 10   g.  The decay factor beeouses siatply

             DECFAC = 9-04 x lo" /3.59 X 1Q4 = 2.52 x icf

and the concentration corrected for decay during transit becomes

 .  C «* (3.03 x 10~9}(2.52 x 10" } = 7.64 x 10    pCi/cm  (or Ci/m  )

still normalized to a 1 Ci release.
     The effective plume width, from Eq. 4-84d  is y   =  2,570 m.  The
time sub-interval for the 100,000 to 200,000 time increment  and K  =
1.4 > 1.0, in accordance with the above  discussion,  is  20,000  y.   Hence,
the associated water volume is
                                                             H  3
      GNDINC = 2,570 x 50 x 1.46 x  0.15  x  20,000 =  5.63 x 10  m  .
Multiplying by the average concentration obtains the activity passing
during the internal,

         CRATIG = (5.63 x 10 ) (7.64 x  1Q~15}  =  4.30 x 10~° Ci
                                              =4.30 uCi .
In subprogram TRINP, the above  calculation is called for all sub-intervals
in the time increment and averaged to  obtain the transfer coefficient
 (A2) for the time increment.   If we consider only the sub-interval for
illustration, the main program  obtains the corresponding activity trans-
ported following the 10.1 Ci calculated release as simply

                 (10.1}(4.30 x 10 6) = 4.34 x l(f5 Ci  .

     Also, the main program establishes average ground water concentra-
tions, after accumulating contributions from all releases and adjust-
ing for transfers to other receptors, by dividing the net activity by
the associated water volume for the time increment of interest.
          (g)  Accumulate Conoentyat-iona.  The product of the Transport-
ta-Ejwironmerrfc portion of the Environmental Model is a matrix, R2TOT,
of net total concentrations accumulated for each of the four environ-
mental input receptors, and the land surface deposition matrix, GNDEP,
for each zone of the study region, at the end of each time increment
considered.  This matrix furnishes the environmental concentrations for
use by the second part of the Environmental Model which performs the
pathway analysis and calculates dose to man.
          (h)  Sample Calsulations,  In Section 4.C.1, a sample calcula-
tion is given for the probabilistic release to the preliminary environ-
mental input receptor for air during the 400 - 500 y interval as a
result of volcanic explosion.  The release is 1.1 x 10   Ci, representing
a quantity, RlJ, released to the air in the immediate vicinity of the
repository from either an instantaneous pulse or a  slower release over
period of time within the time increment.  A sample calculation is now
given to illustrate the steps in obtaining the corresponding environmen-
tal input concentrations in Zone 2, using data from the base case des-
cribed in Vol. II, by the Transport-to-Environment part of the Environ-
mental Model.
              Figure 4-13 uses appropriate portions of Pigs. 4 - 8,
4-9, and 4- 10, and illustrates this sample calculation.  Consider
first, the airborne component.  A2 has a value of 1.0 indicating no decay
for a time interval coincident with the release interval.  Use of an air
dispersion code, externally to AMRAW, obtains the integrated concentra-
tion per unit release in Ci-y/cm -Ci, in various grid subdivisions
of Zone 2.  The weighted average in the zone in this example is ZONALQ -
5.31 x 10   , a value input to &MRAW, which represents the average
integrated concentration from a diffused unit release pulse moving across


1. 1

x 10-*
C i
. I 	 '

i.f3 x IfT15

2.12 « ID"20
                           RESUSPEHS !OM

                          (2,1k  x  10'27!
                                                     RELEASE  TO LAND
                                                        IN  ZONE,

                                                      2.14  x  10'6
                                                           X  10
                                                                                     M  I
                                                                                     +J O


                                                                                    4J M
                                                                                     J3 -H

                                                                                    -H O
                                                                                     W Q)

                                                                                     d W
                                                                                     0) 03
                                                                                     0)  CO
                                                                                     CP r-J
                                                                                     U  04
                                                                                     P O
                                                                                     tfl -H

                                                                                    ^ W5
                                                                                     rt O
   •H >
 M 3* Vi
-H o a>
 r0 ^1 -M
   H C
 O O -4

4J CM g
 M    -H
 O 0) -M
 |*5, g
 W O >!
 d ^*3
 rt    o
 J-i C o
EH -H in
                                                                                    - 1
          8,81 E-20 (x 32.6}
                                                         8.7S E-1J  U 40.3)

the zone.  Then,  for the  given  release  of RlJ = 1.1 x 10   Ci,  multiply-
ing by A2  and  ZGNALO obtains  the  integrated air concentration  in the
                       —2&        3
zone of M2 = 5.84 x  10    Ci-y/em .   Next,  this is  adjusted for any
transfers  in from other receptors,  in this  case as  resuspension from
land surface.  Removal from the air need not be performed at this point
since this    taken into account by the external air dispersion code,
The resuspension  integrated concentration {explained below)  is  2.14 x
  -27        3
10    Ci-y/cm  which when added to  the  airborne plume component yields
                                              -27        3
a total or "adjusted"  value of  R2 = 2,70 x  10   Ci-y/cm .   Note in
passing that resuspension dominates the air concentration.   Multiplying
by 10  converts units  and obtains concentration of  R2COH =  2.70 x 10
yCi-y/crn  , also accumulated into  the net total air  concentration R2TQP =
         -21         3
2.70 x 10    yCi-y/cm  ,   The  term "accumulated" is  used here because
the code goes through  this process  for  each receptor.   For  air,  however,
integrated concentrations do  not  carry  over to a subsequent time incre-
ment ? the  code sets R2 =  0 to accomplish this beyond the present illus-
     Next, consider the ground  deposition onto land surface, again
referring  to Pig. 4-13.  From air dispersion code calculations, the
average deposition per unit release is  the  input value ZONDEI1 = 1.93  x
  —15      •?                                                      —5
10    Ci/cm -Ci.   Multiplying  this by  the  release  RlJ = 1.1 K  10
                                             ~20      i
Ci obtains ground deposition  DEP  =  2.12 x 10    ci/cm2 .  Multiplying
                                         14    2
by the area of ground, AREAG  =  1,01 x 10   cm  (equal to dispersion
area for acne, DISPN)  yields  the  total  deposition in the zone,  DEPGND =
2.14 x Id"""  Ci, which  is  carried  into the receptor  R2.   It  is here that
any other  events  releasing directly to  land surface are added to R2
(omitted from this example for  simplicity).   The "adjust" step  transfers
a small fraction  of the land  surface inventory into the air,  This re-
                           3                             2
suspension factor is Ci/cro air concentration per Ci/cm  ground concen-
                                                              -9  -1
tration.  The value input as  flDJi (E in Eq.3 - 25)  is 1, K 10    cm   ,
and it is applied as a step transfer by making ADJ2 (F  in  Eq.4  - 25)
sufficiently large (=  20),  Then, the integrated resuspension eoncentra-
tion is the zone  land  surface inventory,  R2  = 2.14  x 10  Ci, divided
                                14    2
by the zone land  area, 1.01 x 10    can  (giving ground concentration),
                                              -9  -1
multiplied by the resuspension  factor,  1 x  10   cm    (giving air con-

centration}, and multiplied by the duration of the time increment, 100 y,
giving the integrated concentration, 2.14 x 10    ei~y/em » which is
consistent with the units used for the air receptor.  Continuing with
the land surface receptor, the small amount of material which continu-
ously cycles through a resuspended status is a neglible removal and the
adjusted R2 for land surface is also 2.14 x 10   Ci,  Multiplication by
  *r                                            -| A   O
10  and division by land area DISPN = 1,01 x 10   can  obtains the eon-
                             -14       1
centration, R2CON * 2,14 x 3.0    pCi/cm .  This concentration is the
current time increment deposition, GNDEP, used subsequently for terres-
trial food pathway calculations, and is also accumulated into the net
total land surface concentration, S2TOTt used subsequently for direct
exposure pathway calculations.  Residuals from each previous release
increment are carried forward (see Pig. 4-11 for the steps) , consider-
ing physical and environmental decay and inter-receptor transfers, and
the release increment discussed here is carried forward to subsequent
environment time increments.  Each such increment makes an additive
component to the resuspension air concentration, and the net total,
R2TOT, increasing the air and land surface concentrations to larger
values than shown here in this sample calculation for one release incre-
     Similar calculation steps apply to releases to the other environ-
mental receptors.  The deposition to land surface illustrated above is
handled in the same way for deposition onto surface water of area,
(see Fig. 4 - 8), giving deposition onto water, DEPWTR, which when
divided by the water volume yields the concentration in water,
A sample calculation for transport in ground water is included in the
earlier Section 4.D.1- (f).(4).

      2.   Environmental Pathways.   The second part of the Environmental
Model is the Environment-to-Man Pathv/ays Model, in which pathway analysis
is performed and dose equivalent rates to man are calculated.   In dis-
cussion that follows,  frequent  use of AMRAW nomenclature is used as an
aid in correlating with associated input data which is required.  This
model is entered for each increment of time with the calculated con-
centrations for each environmental input receptor.  These concentrations,

                                                  TO m





n 1






UF i



"V trnlt-1



O ss:

fr— 4





-For Land Surface, the net total  accumulated concentration  applies to the Direct  Exposure pathway,
 and current deposition concentration  applies to the Terrestrial Food pathway.
                      Figure 4 -  14,  Main environme.nt-to-man  pathways.

 as determined in the Transport-to-Environment Model discussed previously,
         1}  Air.  Integrated air concentration, R2TQT, uCi-y/cm  ,
         2)  Land	Surface.
             a.  Accumulated ground concentration, R2TOT, yCi/cm  ,
             b.  Integrated deposition for current time increment,
                 GNDEP, pCi/cm  ,
         3}  Sur£_ace^Water _.  Accumulated water concentration, R2TQT,
             yCi/on , and
         4)  Groun_d^Hater_,  accumulated ground water concentration at
             point of use, R2T0T, pCi/cm .
     The matrix, R2TOT, contains the net total concentrations accumulated
 for each of the four environmental input receptors, for each zone of
 the study region, at the end of each time increment considered.  Simi-
 larly, GNDEP is the land surface deposition matrix for each current time
     There are a number of potential pathways through the environment
 from the input concentrations to radiation dose commitment to man,
Fig, 4-14 shows the main pathways.  For each of the first three recep-
tors , the first main pathway (mode 1) involves external dose sources and
the second main pathway (mode 2} involves internal dose sources.  For a
 specific site, the ingestion pathways from ground surface and surface
water to food and drink are each subdivided into a number of subpaths
for the various categories of terrestrial and aquatic foods as appro-
priate.  In fact, in AMRAW any of the main pathways may be divided into
subpaths if needed.
      The basic pathway  relationship  (Fig. 4 - 15}  is  that  a  transfer
 coefficient  is used to  transform a  radioactive  material concentration
 in a receptor to a corresponding dose commitment rate  for each specified
 organ.  The  transfer coefficient, C,  must  contain  elements  to represent:
      1}  Concentration  or dilution to the  consumed or  exposure quantity

     2)   The amount of exposure or consumption per year  (VOL1KT),
     3)   Dose rate conversion per unit of exposure or consumption,  for
         the specified organ  (DOSF&C).
Hence, the transfer coefficient is expressed as
                            x VOLINT x DOSFAC
where C and the component factors use a set of units consistent with
the environmental  concentration to obtain, dose or dose rates in the
same units for all pathways, to permit smnmation.  Table 4-4 details
the units for each factor in AMRAW for the main pathways.  Any siabpaths
follow the scheme  of  the corresponding main pathway.
                         ENVIRONMENTAL  JMPUT
                      RECEPTOR  CONCENTRATION
                                         TRANSFER COEFFICIENT
                      DOSE COMMITMENT  RATE
         Figure 4 - 15.   Basic  pathway relationship,

                      Table  4 -  4 .   Factors  Comprising Environment-to-Man Coefficients
Main Pathway
Exposure (
or Food
Production Rate
Conversion of
Value to
Average Rate
Dose Factor
Dose Rate


mt otn/y*
cm /y


, 4*









1 or 2


          *Food pathways divide into  sub-paths  (not shown).
          tTransfer coefficient yields average  dose commitment rate during time interval in which integrated dose commitment


     The air pathways involve integrated air concentration and the ter-
restrial food pathway involves integrated food concentrations.   These
are converted to  average dose rates during a time increment by dividing
by the length of  the time increment, as shown in Table 4 - 4 to provide
consistent units  for summation with other pathways which directly  pro-
duce average dose rates.  The use of dose rates instead of the corre-
sponding integrated doses during each time increment permits inspection
of output tables  for trends where the size of time increments varies.
         (a)  Integrated Food Concentrations*   Before describing the
component factors of the transfer coefficient, a discussion of food con-
centrations will  be helpful.  If there is a uniform and continuous de-
position rate,  equilibrium concentrations of each radionuclide are
approached in various components of the terrestrial environment and in
terrestrial foods.  Following an acute deposition, there is a transient
response for  food concentrations.  Fig. 4-16 illustrates the response
of concentration  of Sr-90, in uCi/g, in above-surface crops, milk  and
meat  following  a  unit acute deposition of 1 pCi/cm .  These curves are
typical in general characteristics to those for other radionuclides,
ftbove-surf ace-food crops have a maximum concentration initially, due  to
foliar  deposition, followed by decay through wash-off.  Milk and beef
are initially  at  zero and increase with contaminated food intake,   Move-
ment  of radionuclides down through the soil horizons eventually removes
them  from further intake, and biological elimination, processes produce
an exponential  reduction of the concentrations in foods.  The peak con-
centration  for  the example illustrated occurs at approximately 2d  for
milk  and at  50d for meat.   Appendix B  presents a detailed analysis  of
the equations  from the TBRMOD code  [K176] and the food concentration  re-
sponses for  several radionuclides.  The area under each curve for  a given
radionuclide,  integrated in terms of years, represents the integrated
food  concentration, yCi-y/g.  The analysis  (Appendix B)   shows  that  the
time  constants  for transfer downward from, foliage through soil horizons
to the  soil  sink   (beyond root zone) override the significance of physical
half-life  such that virtually complete integration is attained in  less
 than  five  years,  even for the longest half-lives.  Therefore, as AMRAW is
typically  implemented with time increments greater than five years, a
 calculated release accumulated during one release time increment,  treated


   3n  _.
                                                       Meat [=] yCi/kg

                                                       Mi!k  =
                                                       Above-surface food [=] yCi/m
        Above-Surface Food


Time,  days
                                                                                             _  4
                                                                                             -  3
                                                                                             _  1
                    Figure 4  - 16,   Response  of concentration  of Sr-90  in

                                     food to unit deposition.

as an acute release, results in terrestrial 'food consequences which are
completed within the following environmental time increment.  It is ad-
vantageous to base the terrestrial food on the concept of integrated
concentration following an acute deposition.  There is an equivalence
of the ratio of the equilibrium concentration in food (uCi/g) to a unit
continuous surface deposition rate {pCi/cm~-d} with the ratio of the in-
tegrated concentration in the food {uCi-d/2) to a unit acute surface
deposition (yCi/em ).  This equivalence provides for a simple application
of terrestrial code output {converted from unit of day to year) to obtain
integrated concentrations.
         Cb)  Local Dose and Nonspesifia Dose,  Some, of the pathways {or
subpaths) discussed above have a direct effect on populations within each
geographic zone considered.  These ares  immersion in air, inhalation,
exposure to contaminated land surface, and submersion in and ingestion
of contaminated water.  Dose to man by organ resulting from these path-
ways, in mlllrems per year per individual, is collected as "local dose
rate" for each zone.  All of the pathways concerned with production of
agricultural commodities produce effects which are not localized to the
zones in which the food is produced; most of the food is exported,  Dose
to     by organ resulting from these pathways is collected as manreros of
population dose per year as "nonspecific dose rate."  Accordingly, for
this last category, food production rates are involved instead of indi-
vidual consumption rates.  Data input to AMRAW for each subpath includes
a flag which identifies the dose category to which the calculations accrue.
         (a)   Component Faetovs foT Transfer Coefficient.  The three fac-
tors:  BIOFAC, VOLIHT, and DOSFACf are obtained from output tabulations
by existing computer codes or other sources and supplied to AMRAW as in-
put data for each subpath, along with data designating the number of sub-
paths under each receptor and mode (see Table 4 - 4 ) and designations of
dose category.
     The first factor, BIOFACr expresses the concentration or integrated
concentration in food and drink per unit concentration in the associated
environment.   For terrestrial food, this is the integrated concentration,
uCi-y/g per unit of acute deposition, pci/cm , as discussed previously.
Codes such as TERMQD [Ki?6] or FOOD [Ba76] may be used to perform calcu-
lations for preparation of AMRAW input.

     For aquatic foods, BIOFAC is simply the nuelide-dependerit bioac-
eumulation factors for each class of aquatic food considered, pCi/g in
the food per yCi/cm  of water concentration.  Tabulations such as those
by Thompson et al. [Tp72] and OKNL  [OHN1.75] provide this information.
For ingested water BIOFAC is xmity  fdimensionless), although it could be
set at less than unity if water treatment may be assumed.
     Contamination of meat and milk from contaminated drinlcing water
uses BIOFAC obtained for each radionuclide as the product of the stable
element transfer factor  (meat or milk as appropriate) and the water con-
sumption rate.  With unit conversions this becomes (yCi/g)/{jiCi/cm ) , as
with aquatic foods in Table 4-4.
     The second factor, VQLINT, expresses the consianption, exposure or
food production rate for each zone and subpath.  For immersion in air
or water, or direct exposure to contaminated land surface, VOLINT is
the average fraction of a year during which individuals are so exposed.
For inhalation, the value is respiration rate, cm /y, and for ingestion
of water by people it is the intake rate, can /y.  As explained above,
pathways concerned with production of agricultural commodities produce
effects collected as "nonspecific dose rates."  Accordingly, VOLINT for
these paths are food production rates/ g/y-
     The last factor, BOSFRC, is the dose commitment conversion factor
for each radionuclide, organ, and exposure mode combination.  External
exposure modes are air immersion, land surface direct exposure, and
surface water submersion.  Internal exposure modes are air inhalation,
and ingestion of food or drink.  Dimensions are as shown in Table 4 - 4.
Codes such as EXRBM 111  [Tr73, Kl?6] and INEEM  (Kit75, K176] provide dose
conversion factors for external and internal sources, respectively,  AMRAW
is presently dimensioned to handle up to eight organs, including total
         (d)  Operation of Code,  Each subpath is provided with a flag
to denote whether results are to be accumulated as local or as non-
specific dose rates.   For each time increment, zone, and organ, the AMRAW
main program:  (1) considers each of the four environmental receptors in
turn, {2) calls subroutine TKMAN to obtain and return the summation trans-
fer coefficient C for all subpaths associated with the respective receptor,

contributing  to  local dose  rate,  arid then  calculates the  corresponding
dose equivalent  rate, and  (3)  repeats for  nonspecific dose rates.  This
process  is repeated  for all organs  for the given  zone,  for all other
semes, and for all other time  increments.   The nonspecific dose category
accumulates from all zones.
     It  should be noted that the  Environment"to-Man Pathways Model is
fully dependent  upon input  data determined by other external models and
codes,   fhe model within AMBAW serves to perform  the arithmetic for the
many combinations of parameters to  produce the output dose rate matrices.
The dose rates calculated in the  environmental model are  the last items
of output by  AMRAW-S.  They are subsequently entered into AMBAW-B, the
economic model,  where consequences  of dose are evaluated, beginning with
the application  of health effect  incidence rate factors for each organ
dose rate.
          (e)  Sample Calculations,   In  Section 4.D.I, a sample calcula-
tion is  given which obtains environmental  input concentrations of Sr-90
for air  and land surface receptors  in Hone 2, associated with probabi-
listic volcanic  release during the  400  - 500 y interval.  Continuing,
using data from  the base case described in Vol. II, a sample calculation
is now given to  illustrate the Environxnent-to-Man Pathways Model part
of the Environmental Model  (Fig. 4 - 14),
     Table  4-5 shows the  calculation  sequence for the air and land
surface  receptors, for one  zone (Zone 2} and one organ  (total body),
This table is the applicable portion  of Table  4-4 , with typical numeri-
cal values (see Vol. II) indicated.   As pointed out in the earlier
Transport-to-Environment sample calculations, the receptor concentrations
shown represent only the quantities  from the sample release increment;
in AMRAW, residuals from previous release  increments are  accumulated,
increasing the land surface total (R2TOT),  and the corresponding resus-
pension increases air concentration  (R2TOT).  In Table 4 - 5 / modes 1 and
2 under each receptor represent external and internal main pathways/
respectively.   There is one subpath  under  each main pathway for this
example.   For other zones, additional terrestrial food subpaths {above-
surface-crops, milk, and hay-fed-meat)  are  included under mode 2 for
land surface.

                            Table 4-5.  Sairple Calculation, Environmental Pathways ia Zone 2, Total
                                        Body Dose Rates from Sr-.90 Following Volcanic Explosion Release
                                        to Air in 400 - 500 y Time Interval
Input Receptor
Main Pathway

Coefficient C

R2TOT = 2.7 x 10~21
f 3

_ — .

l-o y/y

1/100 y
u» u 	 "~ 4
0. 0 mrem/y

— _.

7.3 x 109 caj}3/y

1/100 y
i a v in3 mrem

J» * »3 X 4-v/ ^
3.5 x 10 mrem/y

= 2.1 x 1(T14
Direct Exposure

Direct Exposure

0.4 y/y

0.0 • ""••' TT "
0,0 fflrent/y
= 2.1 je 10
. , 2
Ingestion Terrestrial
Meat (Range Fed)
Q r^ pci-y/g
1.2 x 10 g/y

1/100 y
1 7 x 102 ^S?^

i , .. in!0 mrem/y
i . JL X 1U "
2,3 x 10 mrem/y

     A subroutine in AMRAW  (TRIKP)  calculates the  transfer  coefficients,
C, for each mode under each receptor  (for given radionuclide, zone,
organ, and duration of environmental  time increment).  The  main program
then multiplies the respective receptor concentrations at the time of
interest by the transfer coefficient  values to obtain dose  commitment
rates.  To illustrate the calculation of C, consider the subpath for
meat in Table 4-5 (last column),  Note that C =  BIOPAC x  VOLINT x
DOSFAC/DELTE.  Here, BIOFAC is the  integrated concentration of Sr-90,
(pCi-y/2}/EpCi/cm ), in range-fed meat animals following &  unit deposi-
tion of Sr-90 on the land surface.  VOLINT is the  total meat production
rate, g/y, for the zone considered.   The quantity  represents mass added
during grazing in the zone and does not include meat added  in feed lots
after export from the contaminated  zone.  With use of total meat pro-
duction, the subsequent dose rate is  routed to the nonspecific dose
category by input of the appropriate  flag values in AMRAW.  If local
dose rate to an individual is preferred for ingestion pathways, the
individual meat consumption rate is used for VOLINT and the appropriate
route flag is used.  DOSFAC is the  dose conversion factor for dose com-
mitment for ingestion, mrem/yCi, or rates, (rarent/y)/{pCi/y).  DELTE is
the duration of the time increment, used for conversion from an integrated
value to an average value.  The subroutine (TBMMJ) calculation of c
accumulates for all subpaths under a  mode and does not preserve component
subpaths nor intermediate values for  a given subpath.  It is of interest
here to trace the intermediate values implied by the calculation sequence.
                                                            -14     .  2
First, multiplying the ground deposition quantity, 2.1 x 10    pCi/cra ,
by BIOFAC obtains the integrated concentration in  the meat, 1.1 x 10
yCi-y/g.  Then, multiplication by VOLINT obtains the total  contamination
activity in meat produced during the  time increment, 1.3 x  10   pci.
Division by DELTE converts to the average rate, 1.3 x 10    yCi/y.  Finally,
multiplication by DOSFAC produces the dose rate, 2.3 x 10   mrem/y.  When
routed to nonspecific dose rate, due  to use of total production rate, the
                  _4                                     -7
result is 2.3 x 10   rnillimanrem/y, converted to 2.3 x 10   manrem/y.
It should be noted that the location  of the division by DBLTE in this
sequence has no effect or the numerical result.  If the division is left
until the end, it can be shown that the result after multiplying by DOSPAC
is integrated dose, 2.3 x 10   mrem,  which when divided by  DELTE becomes

dose rate, 2,3 jc 10   mreffi/y, as before.
     The other subpaths in Table 4-5 are similarly calculated.  In
this example, since Sr-90 has no gamma emission, there is no external
mode exposure (DOSFAC = 0.0).  Factors which <3o not apply are assigned
a value of unity within aSB&W.  In the main program, the dose rates for
each mode under each receptor are routed to the appropriate category
(local or nonspecific) in accordance with routing flags.  As indicated
above, nonspecific dose rates to the population become stated as man-
rams /y.  Vol. II discusses the sources of input data for the several
factors for an iinp lament at ion example.

     This section gives a mathematical  development of the portion of the
Waste Management Systems Model upon which the AMR&W-A coiaputer code is
based.  It is necessary for computational purposes that all of the inde-
pendent and dependent variables be discrete.  However, a continuous
representation with the transformations At •*• dt, Axay -*• dxdy of the
equations involved are given first,  This facilitates an easier under-
standing of the model by replacing subscripts with continuous variables,
After the continuous representation is  discussed, the corresponding
discrete equations are given as they appear in the AMRAW code,
     1.  Continuous	Representation.  The variables and subscripts have
the following meanings;  T is the variable time, t is a release time of
radionuclide from the waste site to the Preliminary Environmental Recep-
tors, T is time of interest for population doses, r is a space variable
in the rectangular coordinate system (x, y, z) in which the origin of
coordinates is the land surface directly above the waste site, i is a
subscript denoting a release event, j is a subscript for the environmen-
tal receptor which is of current interest, and m is a subscript for any
environmental receptor other than j,  Generally, the space variable
representation may be considered two-dimensional since we are mostly
concerned with concentrations on the land or in surface water.
     The starting point of the computation is the introduction through
data statements of the quantity of the  radionuclide in grains as a func-
tion of time, X{t).  For simply decaying miclides [My67] (i.e., no radio-
active parents)
                         X(t) =  X(0) exp(-At)                     (4-86)

where X(0)  is the amount of the nuclide at some reference time, and the
radioactive decay constant, A, is related to the half-life,
A = ,693/t  ,_.  If u  is the specific activity in Ci/g of the particular
          1/2       o
radionuclide of interest, then

                           Y(t) = X{t) * 

is the radioactivity in Ci at time t for the radionuclide.


     Nuclides in decay chains, like many transuranic isotopes, have com-
plex simultaneous buildup and decay.  The time-dependent quantities for
these nuolides have been previously computed in the ORIGEN computer
code, and are provided to the AMRAW code for each time t in data state-
ments.  A radiodeoay factor DC(t»T)  between two times t, and. T may be ex-
pressed as the ratio of nuelide quantities for the two times.  For
nuclides released at time t, the subsequent distribution and radio-
active decay is computed by means of the transfer coefficient &2{t» T,
r), to be discussed below.
     The next phase of the computation relates to the release model
which determines release mechanisms moving the nuclide from the reposi-
tory to the preliminary environmental receptors.
     A versatile method for computation with release mechanisms is to
introduce a probability density function P..(t) which represents the
probability of release by release mechanism i to environmental receptor
j during the time interval (t-dt, t),  The resulting generality allows
computations to be made either with acute release from mechanism i by
setting P, . (t) , for example, equal to the delta function 
for each instance.   Information is provided  to subroutine FAULT by in-
put data from externally  computed data values. Consequently,  the  fol-
lowing result

                       =  j  P, . £t)  * Al, , {t}                  (4.-871
                      3   f     J i}         iU                        '

gives the expectation value for the transfer coefficient  from  all  re-
lease events at time t to receptor j.
     Since we are considering the contribution to population  doses
from each different  environmental receptor in turn, the subscript  j may
henceforth be dropped for simplification, except where confusion is
possible.  It should be noted here that the  four receptors are treated
slightly different.  This is due to deposition onto land  surface arid
surface water of material which is released  to air.  This is discussed
in detail in Section 4.D.  The  following discussion is- for the receptor
ground water as an illustration;  the other receptors are  handled by
adding appropriate terns,
     Let Z(r) be a dimensionless function which gives the fraction of
                                       -j-               ->-
released nuclide deposited at position r.  In AMR&W, Z(r)  is a discrete
function for the zones, giving  the fraction  of the release which ends
up in each zone.  This zone allocation factor involves external calcu-
lations with air and land dispersion models.   For ground  water the fac-
tor serves to indicate delivery via a  ground water path to a given
geographic zone.  The space dependent  source term is then
                   q(t, r) = Y(t)  •    - 2(r)               (4-88)

giving the activity in Ci at position r from  nuclide released at time t.
The sum over release events is finite; therefore, q can be considered
to be an expected value.  Similarly, all functions developed in the
following sequence of equations  (except G  in Eq. 4-89) can also be »
considered to be expected values.  However, in AMRAW, the summation
occurs at the step represented by Eq, 4-87,   Therefore, the expected
value symbol is omitted from the subsequent equations*

      The next  step  of  the  calculation  involves  transfer  from the recep-
 tor  of  interest  at  release time  t to population dose  tine  T,  and to the
 receptor of  interest from  other  receptors.   The introduction of two
 transfer coefficients, Al  (already  discussed) and  A2, requires  further
 explanation.   Each  environmental input receptor is a  volume  of  air or
-water,  or  area of land surface.  Some  potential release  events  may pro-
 vide initial depositions which serve as concentrations at  environmental
 input receptors.  However,  other potential release events  may involve
 secondary  distribution processes,   An  example is leaching  of  a  waste
 deposit process by  circulating ground  water.  This release process re-
 quires  a geologic faulting event to cause a  major  non-healing fracture
 through the deposit, coupled with the  presence  of  ground water,  for
 leaching to  occur.  However, particularly with  deep burial, release by
 leaching to ground  water is not  in  itself a  release to the environment.
 In addition, transport is  required  before contamination  concentrations
 accrue  in  an aquifer contributing to the biosphere.   The use  of  the two
 transfer coefficients, Al  and A2» then provides the flexibility  to cope
with the physico-chemical  aspects of such two-stage release and  trans-
port processes.  Section 3-D. provides a detailed  description of these
      The coefficient A2.(t, T, r) is a time  transfer  coefficient,  account-
 ing  for radioactive and environmental  decay  occurring between release
 time t  and population dose  time  T.   In addition, the  coefficient can
 account for special transport processes within  one receptor.  The  coef-
 ficients A2 are computed from AMRAW input data  in  subroutine  TRINP.  For
 the  receptors air,  surface  water, and  land surface, the  calculations
 are  done completely within  this  subroutine.  For ground  water,  subroutine
TRINP calls function CRAT1Q for  ground water transport calculation of
concentration ratios.
      Some quantity  of the nuclide enters the receptor  j  from  the other
receptors, and it is thus necessary  to add terms to the  A2.ft, T,  r) to
                                                       •>  J      ->-
account for these processes.  Two sets  of functions E (r)  and P  (r)
account for transfer between receptor  terms  and  are provided  to  the
AMRAW code as input data.  E (r)  is  the maximum fraction of the  nuclide
in receptor m which can be  transferred to receptor  j.  F (r)  gives the
f racfcional rate of  transfer of the nuclide from receptor m to receptor j.

      Then, the transfer  fraction term of nuclide from receptor m to
||iceptor j is given by
                   (t,  T,  r} = E  (r)  1 - expf-P  (r) - 6J           (4-89)
                                IT)     j_        \  Kl       /J
v-.v/here 6 =  /dt  (range of integration is period during which transfer
'.;'• is considered) .

 If rapid transfer  is expected, F  (r) is given a large value, while for
 slow transfer, Pm<3r> takes a smaller value,
      Thus , in the  following equation ,

            H(t, T,  r} =  I G  (t, T, r) • &2  (t, T, I) • q .           -j.       ->
                     R(t, T,  r)  =  S(t, T, r)  • DS(r),               (4-93)

  where  R(t,  T,  r)  is  the activity in  Ci/oa   or Ci/cm  at time T and posi-
  tion r due  to release  in  the time interval  (t - dt, t) ,

     Integrating over all release times prior to T, Eq, 4  -93 becomes
                        T                      T
           RT(Tf r) =  |R(t, T, r)dt = DS(r) " /S(t, T, r)  •  dt.   14-94)
Here, RT(T, r)  corresponds either to the total activity per unit volume
for ground water or surface water, activity per unit area for land
surfacer or integrated activity for air, at time T and position r due to
all previous release events,
      The  coefficients  for transfer  from environmental receptors  to popu-
 lation  dose  are now considered.   Pathway analysis  considers  two  cate-
 gories  of pathways  from environmental concentrations  to population dose:
 1}  local  dose  rates for persons  in  the  vicinity of position  r, and 2)
 nonspecific  dose rates to persons at undefined  locations  from  foods  grown
                            ->•                       ->
 xn  the  vicinity of  position r.   The coefficient A3i(r)  is  the  local  dose
 transfer  coefficient,  and A32(r)  is the nonspecific dose  transfer coef-
 ficient.   These two coefficients are discussed  in  Section 4.D. and are
 computed  in  subroutine TRMMi,  The  dependence of A3l  and  A32 on  various
 organs  of the  body  is  suppressed here but is included in  the complete
      The  local dose rate  at time T  is then

                    Ml(T,  r) * RT{T, r)  •  A3l(r)                    (4-95}

 and the nonspecific dose  rate at time T is
(t)  =  //RT(T,  r)  •  A32fr)  •  dr.               (4-96}
     The quantities Ml and M2 given here represent population dose  rates
only from receptor j for a specific radionuclide.  The total dose rates
are obtained by summing over all receptors and radionuclides.   The  double
integral in M2 is to obtain the total contribution to the nonsoecific
dose from all spatial locations.
     2,  Discrete Representation.  The  discrete  equations may be obtained
from the continuous equations by replacing the continuous variables with
, iperscripts and subscripts, and integrals with  finite sums-  To prevent

confusion, time-dependence is represented by superscripts, and all other
independent variables are represented by subscripts.  Release time t is
labeled by the superscript a, and population      time T is likewise
labeled by the superscript g.  The space dependence, or the variable r
is replaced by zone dependence denoted by the subscript k.  It should
                                          r*       R
be pointed out that the time increments At  and At  are not uniform in
the AMR&W calculations and the superscripts are thus necessary.  The
discrete form of dr is not needed; all other subscripts retain their
original meaning.

     The final objective is to represent JSqs, 4-95 and 4-96 in the
continuous representation in discrete notations.  The resulting expres-
sions explicitly contain all the calculations in the AMRAW code for
ground water, except the transfer between receptor calculations.  As
mentioned in the discussion of the continuous representation, the other
receptors are slightly more complicated and need minor modifications.
     The quantity of radionuclide assumed available for release in the
time increment At  is the average of the radionuclides available at time
t  and time ta~ .  Thus X° = —  [X(t°) + X(ta~ }] , and the activity cor-
responding to Eq, 4-86 for the continuous representation is

                              01    a
                             Y  = X  • UQ.                        (4-9?)

     The probability density function at release time t  is P,,» and
the first transfer coefficient is Al.,,
     Thus, corresponding to Eq. 4 -87,

                                  I P3. Ala,                      (4-98}
                                  I  30   13                           f

is the expectation value for the transfer coefficient.
     The term 2   is the zone-dependent factor which gives the fraction
of the amount released to receptor j that ends up in that receptor for
Zone k.  The zone-dependent source term is then» corresponding to
Eq. 4 -88,


     In the continuous case, the second transfer coefficient was  intro-

duced as a given function A2(t, T» r}.  In the discrete  case,  the com-

putation of the second transfer coefficient is rather  complicated,  and

its representation as a continuous function needs some justification,

           FY ft                                     -A,            fa Q

     Let A2.f be the discrete analog of A2.(t, T, r) .  Then  A2.^  is deter-

           3                    aB        -1                    -1
mined as follows,  A quantity, S, , is computed in subroutine  TRINP for

each population dose time greater than or equal to the release time
\T  >. t /  For  the  case  where population dose time equals the release

time (T  =  ta),
     Subsequently, A2 p  is defined recursively by
or, in general,

                            ^«P    TT   *«y
                            A2.  =   it   A,  r

where   « I  represents product summation and  y  ranges from a to fJ.

Thus, for example,

                  _^4    11   jy     11    12     3,3     14

                  n 1c   1 ^ *V.^>. ^t n Ic     T V"    T Ic     ™i Ic     *i 1?

This computational form was chosen  since it can be  easily used to

handle radioactive decay.

     Now, letting E  . (r) , F , (F) , G  . (t,  T, r)  and  DC(t,  T)  be replaced

by E ,, , F  .,  , G  ,, i and DCa&, respectively,  the transfer to receptor 1
    Hrjk   nijk   ™"lV               "                                    J
from receptor m corresponding to Eq. 4-89  is  given  by
                    v      lfc
                  mjk    mjk
and, corresponding to Eq. 4 -90,

                       ap    r  osS    ,-aB    a
                      H., =  ) G  ,, *  A2 ,  •
                       jk    £, rrgk     mk

is the total transfer to receptor j from all other receptors.

     The quantity

                       ag    r.   a0      ag    a
                                     * A2   •  a
is the corresponding term representing transfer from receptor j tap through

time T  to all other receptors,

     The final source term corresponding to Eq, 4 - 92 is then

                     ^ - 4 • < * $ - L£

     The local dispersion factor depends on both the zone and the

receptor, and is thus represented by DS,..

     So, corresponding to Eq. 4 -93,
is the activity at time T  in Zone k due to release in the time interval
     Summing over all release times up to population dose time T /

corresponding to Eq. 4 -94,
is the total activity at time T in Zone k.

     If the population dose rate transfer coefficients are represented

by A31. and A32 , , the resulting local dose rates are given by

                         MlP  = RTBfc -"A31.,                     (4-105)

and the resulting nonspecific dose rates corresponding to Eq. 4  - 96 are

                                     ^                           {4-106}


Tliese last two equations represent the final output of AMRAW-A.


Page Intentionally Blank

                               CHAPTER  5
     The AMR&W Code is written in Fortran IV language.   The two parts  of
the codes are:  1} AMR&W-A which contains the Source Tens,  the  Release
Model, and the Environmental Model, and 2} AMBAW-B which contains  the
Economics Model.  They are being run separately but may be  joined  if
desired.  There is an advantage to running the first part independently
to determine sensitivity of environmental concentrations and dose  rates
to variations in input.  Similarly, there is an advantage to running the
economic model independently to study the response to varied economic
parameters.  User's manuals are Volume IV for AMBAW-& and Volume VI for
AMRAW-B.  This chapter provides a brief description of  &MR&W-A; similarly,
Chapter 6 in Volume V describes AMBAW-B,
     The present dimensioning of &MKAW-A is as follows;
     1)  Radionuclides;  25.
     2)  Environmental receptors:  4, designated by programming as Air,
         Land Surface, Surface Water, and Ground Water.
     3)  Release Model events:  9 events  or event combinations under
         each of the 4 environmental receptors.   Each may be input with
         up to 4 conponent factors.  Each of these factors  may be  flagged
         far type of function {constant,  step, ramp, exponential,  or
         delta)  and specified by three appropriate function parameters.
     4)  Environmental pathways:  2 main  pathways (modes) are programmed
         for each environmental receptor.  Dimensioning provides for up
         to 6 subpaths for each receptor  (each mode under a given  receptor
         is divided into the same number  of subpaths).
     5)  Geographic zones:  8.
     6)  Human organs:  8,  Typically, one of these is  total body, but
         there is no restriction.
     7)  Time increments:   50.

With this dimensioning, the code runs with 256 k bytes of core storage,
10 cylinders  (1459 k bytes) of disc storage, and requires 21 minutes
of CHJ time in the UNM IBM 360/67 coraputer.  The range of subscripts for
variables is specified by input data and may be any "value within the
above dimensioning with the exception of environmental receptors which
are fixed within the code at four.  Dimensioning may be increased if
necessary, limited only by available core storage or other system re-
quirements.  Also, some exchanges of dimensioning can be used for spe-
cial cases without increasing storage requirements.  For example, 9
Release Model events, each with 4 component factors represent 36 storage
combinations  (-9x4),  If release is described by an involved function
representing dynamic repository simulation (see Section 4.C.l.d), AMRRW can
be dimensioned as one release event with up to 36 component factors if
needed.  The number of geographic zones, presently dimensioned at 8 is
limited to 9 because of programming for the variable "NPRINT" which
controls output options.
     Large output matrices for local and nonspecific dose rates are
written onto disc to conserve core space,  Complete output is then writ-
ten onto magnetic tape for retention but ouput may be diverted directly
to printer by job control statements if preferred.  Printed output is
subsequently obtained from the tape as needed.  If AMH&W-B is to be
coupled to AMRftW-A for a combined run, &MRAW-B may access the disc for
dose rate input data.  The operation demonstrated at UNM is separate
running of AMRAW-B.  For this purpose, the dose rate portion of the
AMRAW-A output is obtained from tape,
     AMRAW-A has provisions for running more than one case, per submis-
sion.  This can ber  13 more than one set of conditions for a waste
management phase such as terminal storage, or 2) aiore than one phase,
such as repository operations and terminal storage.  A full set of input
data is read in for each case.
     There are three subroutines in AMR&W-A which evaluate transfer co-
efficients between sequential sections of the systems model (Fig. 4-2).
Subroutine FAULT handles the Release Model {see Section 4.C.I)  and provides
the transfer coefficients used to accumulate releases to four preliminary
input receptors from all release events considered.  This subroutine uses

function RI£ACH when an event involves leaching into ground water.  Sub-
routine TRINP handles transport from the preliminary input receptors to
the environmental input receptors  (see Section 4.D.I}, providing trans-
fer coefficients which account for physical and environmental decay and
ground water transport delays.  Hhis subroutine uses function CRATIO for
the ground water transport calculations.  Ose of the transfer coeffi-
cients from TRIM? by the main program leads to net environmental concen-
trations for input to pathway analysis.  Subroutine TKMftN handles
evaluation of transfer coefficients between environmental concentrations
and population dose rates (see Section 4.D.2) for the various pathways,
     A directory of fiMSAW-A output tables is given, in Table 5-1.  Output
is divided into six sections, separated by divider pages,  to output
control parameter, HPEINT (see Vol. IV)r controls which of the 10 types
of tables are output and whether for all zones and organs or for only
selected zones and/or organs.  If all tables are output as currently
implemented, 627 tables are obtained.  If dimensioning for zones is
increased from the present 8 to the program limit of 9, 68 additional
tables could be generated.  If in addition, Section 6 tables are re-
quested for all 50 times, 810 more tables would result, for a possible
total of 1505 tables.  Clearly, discretion is called for when specifying
requested output, particularly for the Section 6 group.  In practice, an
adequate sampling of Section 6 dose stunraary tables is obtained with 2
zones and 5 times, yielding only 20 tables from this section.  In Table
5-1, the complete title for each type of table is stated, including the
variable name called for and the units for the tabulated values.  Each
table as printed is identified with the appropriate radionuclide identi-
fication, zone number, and organ name as appropriate.

                              Table 5-1.  Directory of AMRAW-A Output Tables

SECTION 1.  Data Input

1,  Output listing of AMKRW input.

SgCTION 2.  Release to Environment

1.  Release Fractions by Each Cutset, RELOOT
2.  Release Increments to Preliminary Environmental
    Input Receptors, R1J, from All Release
    Events , Ci
3,  Concentrations at Environment Input Receptor,
    R2T0T.  Units:  JP = 1 pCi-y/cm3, JF « 2 pCi/csa2 ,
    JF - 3 and 4
        3.  Local      to Individual

1,  Average Annual Local Dose to Individual, MAM1L,
    mren/y .

SECTION 4 , _ Monspecif ic_ _ jPpseu_ tj3__Pppulatiant

1.  Average Annual Nonspecific Dose to Population,
    HAN IN, manre»/y .
                                                                  cr of Table Combinations
           (8 in each
          (8 in each
                     (4 in each

                               Table  5-1.  Directory of       Output Tables  (continued)
       SECTION  5.   Total  Dose j>yReceptors

       I.   Average  Annual Local Dose to Individual,
           MAM2DF for JF  = 1 to 4,       for Total,
           mretn/y,  Total  for All  Kuclides.

       2.   Average  Annual Nonspecific Dose to Population,
           MAN2KF for JF  = 1 to 4,       for Total,
           manrem/y, Total for All Nuclides-

       SECTIOM  6.   Dose Summary Tables

       1.   Average  Annual Local Dose to Individual,
H          MAN1L, in Zone , mrem/y.

       2.   Average  Annual Nonspecific Dose to Population,
           MANHT, manrem/y.
      Total Number of Tables


      a.  All output tables, except Section 6 are for 50
          time steps, 0 to 10° years.

      b.  Individual zones may be specified.

      c.  Section 6 may call for a table for each of all
          times beginning with 100 y or skip some times;
          5 tables result if call for every ninth time.


(25 in each
{25 in each


up to 8
up to 8


(8 in each
(8 in each

Environ ,
(4 in each
{4 in each



Page Intentionally Blank

                              CHAPTER  6
                       APPLICATION OF MODEL
     The computer code that implements the Radioactive Waste Management
Systems Model is totally dependent upon externally generated input data.
One function subprogram calculates nuelide-dependent leach rates as a
function of leaching duration when called upon by the Release Model.
Bnother function subprogram calculates the nuclids-dependent concentra-
tion ratios for points of usage versus the point of release as a func-
tion of ground water transport time intervals,  Both of these subprograms
depend upon input data for values of all parameters used.  All other
calculations in AMRAW are arithmetic operations which collect appropriate
numerical components from the input data for the calculations, accumulate
totals from contributing increments, and route results to the appropriate
output tables.  The nature of the input data dictates;  1) the waste
management phase studied, 2} the inventory ace-omulation of radionuelides
and their buildup and decay, 3) release scenarios, whether probabilistic,
discrete events, statistical occurrence or dynamic repository simulation,
4} transport to environmental receptors via air dispersion to each geo-
graphic zone, ground water transport and by other transport mechanisms,
5) nuclide concentrations in food associated with depositions, 6) agri-
cultural production and exposed populations, and 7} dose commitment rates
associated with calculated intakes and exposures.  The flexibility in
AMRAW implementation permits use of various existing and accepted codes,
reviewed and published data compilations, and estimates by experts in
various fields, for preparation of input data,
     Chapter 4 provides a step-by-step discussion of data needs in the gen-
eric sense.  Volume II, Part 1, presents a base case which illustrates data
acquisition for terminal storage at a specific repository site in bedded
salt.  Other cases illustrate sensitivity analysis showing the effects
on calculated results of variations in selected input parameters, and
consequence analysis showing consequences following discrete release events
and the effect of the time of occurrence.  Part 2 of Vol. II demonstrates
other applications of the model.  These include a case demonstrating pre-
liminary application to the repository operations phase, discussion of


application to ground surface storage, m case demonstrating a preliminary
application to another geologic setting {repository in shale) , and a
discussion of model feasibility for application to other radioactive
and nonradioactive hazardous materials.
     Volume III describes the aMR&W-B part of AMR&W and demonstrates
implementation for the base case dose rates obtained with AMRAW-& arid
for several consequence analysis cases.  Volume IV is the &MR&W user's
manual which provides specific information on input data formats and
sequence.  Part 1 of Vol. IV is for AMBAW-A and Part 2 is for &MR&W-B.

                             APPENDIX  A
                      GROUND WATER TRANSPORT
     1.  Line Sourc_e Equivalent of Plane Source.   The solution of the
radionuclide      transfer equation (Eq. 4-79),  from Duguid [AHS ],  for
the instantaneous release from a rectangular plane source of width f,
parallel to the y-z plane and centered at the origin is
     C S51
where M"  is the      (or Curies used here)  per unit area of the plane
source, obtained by dividing the released quantity of a particular radio-
nuclide by the product of the width f and the aquifer thickness z  .
Other parameters are as defined in Chapter 4.
     It is now desired to obtain the equivalent solution for the instan-
taneous release from a line source located at the origin and parallel
to the z-axis.  The line source equation compresses the plane source
into a width which approaches zero, providing for simpler calculations,
     The form of the error function is
. , M" .
4 (WE t}"5
- k_v t) "
2 p
. k3Vpt

erf H
: (••

^ .
                                       u  2
                         erf u = -r- I   e   dn                     (A-2)
                       2  f
                   u = — I
erf u =  " (erf u)  = —  ~      e   dr.
                                                         e"U       {A-3}
Consider the error function factor in the exponent of Eq.  A-l,  and use
Taylor's series to approximate the error functions.  It is implicitly
assumed that width f/2 becomes small when going to the line source.

compared with distances y from the plume centerline.
         2/E t
       . erf
               2/E t
                                  = erf
                        2E t     4VE
                           y /       y
                   2/E t      \2/E t
                      y     •  \   y /
                           exp -
                      E t
Substituting from Eq. A-4 into Eq. ft-1, simplifying, and  also substituting

M' = M" £ (release per unit of aquifer thickness), obtains
               c =
                            exp -
                   4-rr/E E  t
                       x y
                          (x -
                                2 p
                                                    2  1
                                         4E  t
Using the following substitutions from Chapter  4;
                                                3    R,

                                     C4 = ¥T
     E  =
— a v
R, Vp
                 4  3 p

Eq. A-5 becomes
exp —
v t *
kjv t
3 p
k,v t
4 P
which is Eq. 4-84 in Chapter 4 and is equivalent to an equation by
Duguid  [ANSj  for the line source.  As shown later, with input of an
effective value of y  (parameter YY) , Eg. A-6 as calculated in AMR&W pro-
vides the average concentration within the equivalent plume width (param-
eter YW, the width within which C > .001 C   ).
     Figure A-l shows computer generated plots of concentration versus
y at a distance of x - 10 km for the plane source (f = 3000 mi ,  Eq. A-l
and the line source Eq. A-6 for a 1 Ci instantaneous release in an aqui-
fer of thickness z  — 50 m.  Other values of parameters used are from
the application in Volume II:  a  = 50 m, a  = 6 m, and v  = 1.46 m/y.
                                Lt          T             p
The plots shown represent the distributions at the time of peak passage
at distance x; any consistent pair of time t and retardation factor R.,
applies.  The areas under the two curves are equal, indicating equiva-
lency of the two source concepts.
     Figure A-2 presents isometric views of 3-dinension computer plots of
the concentration distributions in peaks at the time of arrival of the
maximums at a distance of 10 km, for a plane source (length 3 km)  and the
equivalent line source.  The computer plots are normalized to the same
maximum ordinate value; actually, the line source peak is approximately
3.4 times as high as for the plane source (as in Fig.  A-l)  such that the
volumes within the solid surfaces are equal.  It should be noted that the
leading face,  as a peak approaches, is steeper than trailing force.   The
integrated volumes

                Volume -  z   j  §  C{x, y) dy dx ,  Ci,            {A-7)
                         aJ J
                           G  O

                  1 K 10 V
                                                          Line Source
                                                                    Plane Source (3 km width)
                                         Distance y from center line, km
                            Figure A-l.   Transverse distribution of concentration
                                          of peaks at distance of 10 km  for plane
                                          and line sources.

                                     (a) Plane source,
                                       leading face
                                                     (b) Plants soyrce
                                                       traiI ing face
ic)  Una sourca,
   leading face
                                                                                           (d) Line source,
                                                                                              trai1!ng fact
                      Figure  A~2.   Concentration distribution  10 km from the  source for
                                      plane  and  line  sources with instantaneous  release.

 calculated by computer show that an  instantaneous  release  of  1  Ci  is
 properly accounted  for fay Bgs. A-l and A-6  for  a plane  source and  a
 line source, respectively.  This proving  step has  showi that  porosity  e,
 contained in the denominator of the  original Duguid equations,  should  be
 omitted as is done  here.
     Figure A- 3 illustrates the spreading out of a peak, both longitu-
 dinally and transversely, as travel  distance increases.  Again,  the
 computer plots are  normalized to the same maximum  ordinate value?  actually
 the maximum concentration  decreases with distance such that  the volumes
 within the surfaces  (see Eg. A-7) are constant,
     2.  Calculation of :Sffe ctiye Plume Width _ an_d JPr an .s verse  Distance
 to ^Average Cgncentratipri,  The effective  plume width YW and the  trans-
 verse distance corresponding to the  average concentration  YY  are input
 to AMRAW for each travel distance involved  in calculations .   The deri-
 vation of equations used for obtaining the  input data values  is  pre-
 sented here.  Consider Eq. A-6, and  simplify it for the time  of  arrival
 of the centerline peak concentration.  The  time of peak arrival  at dis-
 tance x is
                        ,    V  x R_
Then  (x - knv t) => x - r— * -*- - =  0, and the first term in the ex
           2 p         Kg      Vp
ponential drops out.  The denominator  of the second term becomes
                    k,v t - 4 — - • v   • - = 4a x
                     4 p      R     p    v      T
The coefficient becomes
V t
p 31

T{aLaT)% XRd
R P v
d P
Equation A-6 for peak distribution at x becomes

                                                              line source, at
                                                              of 10 and 20 km

                                           \4a  x
                   2 2
          A exp -(By)
where A

                       2     1
                      B  *** f-TT-V-r,-
The transverse distance y = — y   (Figure A-4)  for decrease  in  concsntra-
                            ^  Wf

tion to 0.1% of the centerline peak valtie is obtained  from
                           = 0.001 - exp
The effective plume width  (YW for AMK&W input) becomes
The average concentration across the pl»uine width  is
                        C =
                            J     '
                             C dy
                                           — vr

                                           2 Yw
 It can be shown that
          C dy = erf
                                           =  erf  2.63

and 0.9998 < erf 2.63 < 1.0000.  Therefore,  the  integrals  are equal to

3 significant figures.

                             A j   exp - B2y2 dy

Substituting for B from Eg, A- 10,
                                     = °-337
At what value of y does Eq* A-8  yield 5" directly?  Prom A-8,
                        0.337  a  =  A exp - (B y2}
                               2    Jin 0.337
                                 - j-,.:,.04-
                               y ~  B   *                           (A-13)

This is the traverse  distance  corresponding to the average concentration,
input as YY to AMR&W.
     To illustrate  evaluation of AMBAW input parameters, again consider
values of parameters  from the application in Volume II:   a  = 6 m.  For
a travel distance of  x =  10 km (10,000 m),  from Eq. A-9b,
                B  -  	1—._ - 	i	„ = 2.04 x 10~3
                    2 (ax)'5
Then,  from Eq. A-10

                           5.26      5.26
                                  2.04 x 10~3
and from Eq. A-13,
                                   2.04  x 10

It may be noted that YW  an<3 TfY depend only upon a  and x; as sucb,  AMRAW
could calculate YW and ¥¥ but these values are included as input data
(for x values  appropriate to each zone) for greater flexibility,
     In summary, substituting for 8 from Eq. A-9b, the effective plume
width, from Eq. A-10/  is
                              = 10.
and the transverse distance corresponding to the average concentration/
from Eq. A-137 is
                              -  2.08(aTx)
               y  = YW
                Figure A-4.   Effective plume dimensions.

     The transfer  coefficient  used  in AMR&W for environment-to-man
pathways  (see Section 4.D.2) includes a component factor, BJOP&C, which
relates radiomiclide concentration  in food to a unit concentration in a
corresponding environmental input receptor.  In AMRAW, the calculations
for terrestrial  {land surface  receptor)  pathways are based upon the con-
cept of integrated food concentration following an acute deposition.
There is a numerical equivalence between:   1} the ratio of the equili-
brium concentration in food, uci/g, to a unit continuous surface depo-
sition rate, MCi/cra -d, and 2) the ratio of the integrated concentration
in the food, uCi-d/g, to a unit acute surface deposition, yCi/on
     A systems analysis methodology developed at the Oak Ridge National
Laboratory by Booth et al. [Bh71] has a three-fold purpose of:  1)  pre-
dicting intakes by man, 2} estimating dose commitments, and 3} identi-
fying "critical" exposure pathways resulting from radioactivity releases
to a terrestrial environment.  An important part of this methodology is
a generalized dynamic model simulating selected terrestrial pathways
which assumes that fallout is the only source compartment and that
man is the ultimate receptor compartment of interest.  The model is
implemented by the computer code TERMOD  (Ki76].  A similar code, FOOD,
was developed at Battelle Pacific Northwest Laboratory by Baker et al,
     Discussion is presented here to support the observation that integrc
of concentrations in terrestrial foods versus time is virtually complete
within a period of five years after an acute deposition,
     1.  Introduction.  The mathematical compartment models depicting
terrestrial pathways, as developed by Booth and co-workers [Bh?l] is
shown in Pig. B-l.  The objective of this model is to obtain predictions
of radionuclide intakes by man through consumption of milk, beef, and
plant parts contaminated as a result of fallout.  Pig. B-l indicates a
fallout rate, pCi/m -d, but it is shown later that the system equations
may also be solved for an initial one-tiroe deposition, in units of pCi/
m .

                    FALLOUT SOURCE
                        • - day!
       FOOD CROP
          1 e. m
- r.
  e,s •

                           SOiL POOL FOR
                           THE FOOD CROP


-.1 I
'9.' _?
* rr,9
* 1
T» A

                          INPUT  TO MAN  1  t^Ci/cioy)
       Figure B-l,   Compartment  diagram of  the terrestrial
                      food pathways by which  radioactivity can
                      be transferred to  man [Bh713.
     Considering  the  above-surface food crop  (ASF) first,  a fraction S
of the fallout deposits on the food and a fraction S  {where S  + Sn =
1,0)  deposits  on  the  soil surface below the food crop.  The radioactivity
enters the ASP crop by deposition and  is retained either by external
adhesion to, or foliar absorption into, the crop's edible parts.  This
crop is assumed to be continuously harvested during and after fallout,
with biomass removal  balanced by crop  growth.  Transfer rate coefficients,
T, are shown between  the  various compartments in Fig, B-l,  Washoff from
ASF to the soil surface below is represented by t   .  The half-time for
                                                e t s
this is generally taken as 14 days  (taken as  30 days  for desert graaing
land in Vol. II), corresponding to T    = 0.693/14 =  0.05 « d~  .  The
                                   e fs
other removal  of  ASF  radioactivity is  by harvesting the crops/  represented

by T    , and transfer directly to man.  Contamination on the soil  sur-
    e ,m
face moves down into the  subsurface  soil pool  (root  zone)  at the rate
T   , and from there, moves below the root zone into the soil sink at
the rate T   ,.  This model does not  consider root uptake by ASF but
          p,d                                      *      J
simulates this instead by the link T    between, the soil pool and nan,
Root uptake can be shown  to represent at most only a few percent of
ASF concentrations.
     Next, consider meat  and milk production.  A fraction  S  of the fall-
out deposits on pasture grass  (or rangeland vegetation as  appropriate),
Washoff to pasture soil surface is per T    and root uptake in per r
                                   *   g,r           ^        *    r,g
again radionuclieJes in the pasture soil migrate to the soil sink at
rate T  ,.  Meanwhile, transfer to meat and milk via consumption of
pasture grass is by t     for meat {beef) and T    for milk.  The .trans-
                     grb                      g,c
fer rates from meat and milk to man  are T,    and T   , respectively.
                                         b,m      c,m
The milk compartment variable C(t) is the concentration of radioactivity
in milk produced by a cow grazing on the contaminated pasture.  In the
Booth model, radioactivity is transferred from the grass directly  to the
milki this simulation is  used mainly because the milk of grazing cows
can be in transient equilibrium with the forage radioactivity after
about two days.  The beef compartment variable B(t)  is the radioactivity
in the meat or muscle of  cattle grazing on the contaminated  pasture,
Radioactivity is directly transferred from the grass to the meat as in the
milk compartment; removal is via radiodecay, biological elimination, and
slaughter of the cattle.  Transfer to uncontaminated feed  lots terminates
intake of radionuclides.  The parameters d  through  d  in  Fig, B-l are
dietary correction factors which account for cleaning and  trimming of
food.   The gradual accumulation in the soil sink effectively removes
radionuclid-es from food pathways and limits the duration of impact fol-
lowing deposition.
     AMRAW applies this model only for determining the concentrations in
ASF, meat and milk, in relation to deposition.  Intake rates of these
foods and corresponding dose commitment rates are handled  in AMRAW,
     2<   Formulationof the System Equations.  Referring to Fig,B-l,
the conservation equation describing the rate of change of contamination
of above-surface food crops, E(yCi/m }, [Bh71]  is


                            dt-slFtt)  -V2                      ^

where I"{t) = deposition as function of time,

        X  = X  4- ~--— — -f- T     effective removal  constant, d
         a    R     ft     e,s                                  '

        A  = radiodecay constant, d   f

      T    - crop harvest rate, m /d,

                                                                      3 2
         a = soil surface area producing food crops for one person, 10 m , aid

      T    = fractional transfer rate, foliage to soil surface, d  *".
       6 tS

Other parameters have been discussed previously.  It should be noted here

that this model expresses ASP contamination in terms of crop area? appli-

cation in AMBAW requires conversion to pCi/f (typically using 100  g/m

for the conversion).  The equation for soil surface below the food crop,

S(lJCi/m2) is
S2Ftt)' vC±/m               (B-2)

where X  — X^ •+• T    , effective removal constant, d
       s    R    s,p                                 '

    t    = fractional transfer rate, soil surface to soil pool, d

    T    = fractional transfer rate, crops to soil surface, d
Subsurface soil pool concentration, P, is yCi associated with one person's

food supply, typically 1000 m .  This changes as


                          ^ = ATs,PS ~ V                        (B-3S

where X  =AT+T    +T  ,, effective removal constant, d  ,
       p    R    p,m    p,d

    T    = fractional transfer rate, soil pool to roan, d  ,

    T  „ = fractional transfer rate, soil pool to soil sink, d  ,  and

    T    = fractional transfer rate, soil surface to soil pool, d
     s ,p


Moving to  the pasture pathways,  pasture grass contamination,.  G,  UCi/m ,

responds as

                      f -S3F(t)  -  \,G+TR                    (B-4)
where X  » A_ -<• T    +V/AD,  effective  removal constant r  d  ,
       g    R    g»r    c7 g  g'                                 '

    T    = fractional transfer rate,  grass to soil,  d  ,

 V /A D-  = fractional grass consumption rate,  d   (related to T ,  and
  o' g g              s           *                             g,b

           i   , Pig, 8-1} , and
            g, c

    T    » fractional root uptake rate ,  soil  to grass ,  d

Pasture soil contamination, R, pci/m  ,  changes as
                              = T   G  -  *  R                        (B-5)
                           dt    g , x     x

                                                           _ i
where A=A+T    +T   ,, effective removal  constant,  d  ,  and
       r    R    r,g    r,d

    T    = fractional transfer rate, pasture  soil  to  soil sink,  d
     r ,ct

Soil sink lumps sinks for  crops and pasture areas  in  D, pCi/m  as

                      f~ = T   ,R + -£~-  P  - A_D,
                      dt    rfd      A        R

Contamination in milk, C,  yCi/A, varies  as
                              « T   G  - A C                         (B-6)
                           dt    g , c     c

where X  = A  + t .„,  , effective removal constant, d   ,
       c    R    rnxlk

                                       *•- 1
  T .  ,   = transfer rate from udder, d , and

    T    = transfer rate, grass to milk, m /£-d,

Contamination in beef, B, pCi/Kg varies as

                           f - T,bG  ' XbB                         CB-?)


 where A  = A  + T    ,  effective removal constant, d   ,

    t,   , = fractional rate of removal of beef nerd, d  , and

     T    = transfer rate, grass to n?eat, m /kg-d,

      All the above equations represent the change with tints of the radio-

 activity in each compartment.  Subsequent expressions for intake to man

 are omitted here; AMBAW provides this step.

      3.  Equilibrium Solutionsfor Constant Deposition Rate.  If the

 deposition source, F(t}, is set equal to a constant value, P, yci/m -d,

 and the rates of change of compartment values     set equal to zero

 (e.g.  dE/dt = 0), the equilibrium values are obtained;
                        E = S,F/X                                   (B-8)
                             •L   St
                        S = (S_F + T   E)/A                         (B-9)
                              2     e ,s    S
                        P = AT    S/X                               (B-10)
                              s,p   p
                        G = (S P + T    R)/X                        (B-ll)
                              "5     X f *s    y
                        R - T    G/A                                (B-12)
                        D =
                        C =  T    G/A                                 (B-14)
                            g,c   c
                       B »  T   ^G/^.                               (B-15)
                            g,b   b

     4,  Transient  Solutions ...for Unit Initial Deposition.   The substitution
F(t} = P   <5{t) , where  5 (t)  is  the  Kronecker delta function, represents

a pulse or  acute deposition, may be  applied immediately before t = 0 such

that F(o) = P  .  Then,. the  solution  of Eq.  B-l is [Kr67]

                                        -A t

                            E(t)  =  S.P e    .                       (B-16)
                                   i  o

For the soil surface below the food, the solution of Eg. B-2 is, noting
that S = S0F  at t =  0,
          2 o
                      S-F  T
                                 -X  t    -A t
                                                  2 o
     The initial  condition for the subsurface soil pool is P = 0 at t =

0.  Then, using Eq, B-3,   the solution of Eq. B~17 is {Kr6?}
                                  S-.F T    T   A
                             	I  o e,s s,p	

                              (X  -X ) (A  -X ) (A -X )
                               s  p    as   pa
-A t
                                       -X t
(A -A )e     +  (X -X  )e
  as           pa
                               (A -X )e
                                 s  p
A r -At    -A t]

      p    -  s  I JB-18)
Subsequent solutions of B (t),  C(t)  and G{t)  yield [Kr67]

                     B(t) = -TT-
                                   S.,F T
                                  	3 o g,b
          X t
where X
           X  +• X  +  f(A  -fX  }2 - 4(X X -T   T   }
            g    r    L g r _ g r  r,g gfr -»
           A  + X   - f(X  +X )   - 4(X X -T   T   }
            9   r    L g  r _ g r  r,g g>r
      C(t) = S
               3 o  g,c
                                        -X t
                                    (X -A )(X -A ){A -A )
                                      c  1   12   2  c

                                                               X t
 G(t} = S3FQ
               £A  -A  MA  -X  } (X -A.)e
                c 2   2 r   c  1
                                             \  -X.)(X.-X )(X -X )e
                                              c  1   1  r   2  c
where A  and X  are  defined in Eqs.  B-20  and B-21r  respectively.  As

noted earlier, the term A  in Eq. B-18  is  the  soil surface area required
to  furnish food  crops  for  one man  (taken  as 1000  m ),
     As an example,  consider 1-129.  The  long half-life  for this  isotope .
 C1.7 x 10  y) illustrates  the dominance of the  other transfer coefficients
over the physical decay constant,  Subsituting  values  for parameters  used
by  Booth et al.  [Bo71, 101763 for average  U. S.  conditions into Eq. B-16
B-19  and B-22 obtains the following food response equations,  respe-
tively, following deposition of F = 1
                              0.1 e
                                   -(5.2 x  10~2)t
B(t) - 2.30  1(2.06 X
                                          ~(2.08 x
                      (1.42 x
These are plotted in Fig. B-2, along with the corresponding curves for
soil surface, subsurface pool, and pasture grass.  The above-surface food
concentration is a maximum initially and decays primarily by washoff.
Milk concentration quickly builds up to a maximum at 3 days and meat
reaches a maximum at approximately 80 days.  The curves in Pig. B-2
have differing scale factors.  To place the peaks in perspective, Table B-l
summarizes the peak values in the units determined by the compartment
model, and converted to common units of pCi/g.
               Table B-l.  Peak Concentrations in Foods
                           Following Unit Deposition of 1-129
     Above-Surface Food
                                 0.1 yCi/m
                              3 x 1D
                              4 x 10   yCi/kg
1 x 10
3 x 10
4 x 10

             Hi Ik,  C
                                    Pasture G rags ,  G
                                           x 10
                                       Above-Surface Food, E
                                       uC!/in2 x 1 O2
                     Figure B-2 .
                                                         Subsurface Pool, P
                                                            pCi x 10-2
                                                       Soil Su rface, S
                                                       PC i/m2 x 0, 5
                                                       Meat, fi
                                                       PC i/kg x 10
                                              Time, days
Linear plot of 1-129 concentrations in response to
unit initial deposition of 1

 It may be  noted  that  above-surface food dominates the peak -rallies, but
 as shown in  Fig. B-2,  concentrations in meat have longer residence times.
 Fig. B-3 is  a semi-log plot of food concentrations showing that they
 drop virtually to  zero within 5 years.   Shorter half-lived radionuelides
 have greater decay constants, A ,  and increase the effective removal
 constants.   Fig. 4-16   shows food  concentrations versus  tine for Sr-90.
     5«  Integrated_Concentration  in Food.   Integrating  above-surface
 food concentration from Eq.  B-16 over time,
                    ~0                CO
                                      /-A t
                                      e   a dt = S, F  /X .          (B-27)
                                                 •>•  o /  a
                 0               0
 Comparing with the equilibrium value of S for a continuous deposition
 rate,  P, it  is seen that the total time integrated concentration in
 above-surface  food (area under curve in Fig. B-2  or Fig, B-3)  following
 a  unit initial deposition is numerically the  same  as the equilibrium
 concentration  with a continuous  deposition o£ one  unit per unit  time.
 The same is  true for milk and meat but  the integration is  complex and
 is not given here.  Overall,  the analysis shows that the time  constants
 for transfer downward  from foliage through soil horizons to the  soil sink
 dominate the significance of physical half-life such that  complete  inte-
 gration is practically  attained  in less than  five  years.   AMRAW  is  cur-
 rently implemented with time  increments no shorter than 5  y and  most
 are 10 y or  greater.  Thus,  it is  concluded that the  deposition  accumu-
 lations onto land  surface during one  time increment and treated  as  an
 acute  deposition for input to the  following time increment results  in
 integrated food concentrations which  have virtually complete integration
within that  following increment.

  30 -
  20 -
  10 L.
Above-Sur face
   Food, E
      uC i/m  x
                                                                                           -  2
                                                                                           -  1

                                T i me, days
I ,000
                    Figure B-3,
                        Response of concentration of 1-129 in  food  to
                        unit initial deposition of 1 yCi/m2.

the value of adverse or unwanted effects measured
in economic units, usually dollars.  Total damages
are a summation over causes and time; marginal damages
are total damages divided by a reference production

a mobile core such as salt which moves upward
injecting into the more brittle overlying rock.

a volcanic vent or pipe, typically less than 1000 m
in diameter, drilled through enclosing rocks by the
explosive energy of gas-charged magmas (mobile,
possibly molten r rock material) ,

a sorption parameter relating amount of material
soirbed on solid material and amount remaining in

health effect
leash Incident
local dose
"committed dose equivalent" is sometimes referred to
here as simply "dose,"  Dose equivalent is the pro-
duct of the absorbed dose from radioactivity and the
quality  factor, loosely called biological dose,
expressed in units of rem or millirem  (inrem) .
Committed dose is the sum of future dose accrual
(generally over 50 yj resulting from a radioactivity
intake.  Dose expressed in roan-rests is the sum of dose
to individuals in a given population.

the rate at which dose (committed dose equivalent)
accrues following an intake or during .exposure to an
external source.  Where an intake rate is also
involved, reference is made here to "dose committment
rate" (committed dose equivalent rate} .

an unwanted health effect such as leukemia, a cancer,
or serious genetic effect , equatable to a death for
damage estimation purposes,

a combination of events that introduces circulating
ground water to the waste inventory and starts dis-
solving waste components.  Time delays for the leach
process and migration via ground water flow retard
the environmental effects,

committed dose equivalent to individuals located in a
given geographic zone, in mrem.

nonspecific dose
offset fault-ing



committed dose equivalent to an undefined population
from consumption of largely exported agricultural
products, in man-rent.

a nuclear species characterized by the number of
neutrons and protons in the nucleus.  Dsed here at
times in lieu of the more descriptive term:  radio~

movement producing relative displacement of adjacent
rock masses along a fracture and resulting in a
separation or gap.

based on probability, which is the number of times
something will probably occur in & given amount of
time.  The probabilistic mode refers to operations
with probabilities included in the calculations.

a nuclide which is unstable or radioactive.

a breach of containment which allows radioactive
material to migrate through the geosphere.  A release
may or may not be directly to the biosphere.

the process of material deposited onto land surface
being picked up by wind action and resuspended,

The product of probability of occurrence of an event
and the consequences of an occurrence.  As used in
economics, risk refers to the chance of damage or

an overall term referring to retention of a species
on a solid by any of several processes such as
absorption, adsorption, and ion exchange.

adjective and noun, respectively, pertaining to
natural processes resulting in the formation of
volcanoes or lava flows.

a violent explosive form of volcano ejecting material
into the atmosphere.
non-explosive carrying of material by any of three
mechanisms:  magma transport, volatile transport,
or hydrotherma1 transport.

                              VOLUME  1

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Am72    Amarantos, S. G. and J, H.  Petropoulos, "ft Study of Leaching
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Bi60    Bird, R. B.,  W, E. Stewart, and E, H, Lightfoot, Transport
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Bo76    Brooking, D, G.t "Shale as a. Repository for Radioactive Waste:
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Bu75    Burkholder, H. C., M, Q, Clovinger, D. A. Baker, and G, Jansen,
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Bu76    Burkholder, H, C,, "Methods and Data for Predicting Nuclide
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Bu76a   Burkholder, H. C.» "Methods and Data for Predicting Nuclide
        Migration in Geologic Media," Proc., ERDA?6a, pp, 658-666.

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C£77    Claiborne, K. C.» "The United States Program for the Safety
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Co66    Cooper, H.f "The Equation of Ground Mater Plow in Fixed and
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Da70    Danckwerts, P. V., Gas-Liquid Reactions, McGraw-Hill Book Company,
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         of Wastes from the LWR Fuel Cycle," Proceedings of International
         Symposium in Denver,  CO, July 1976, CONF-76-Q7Q1.

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         for Mathematic Computations,  Prentice-Hall,  1977.

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         Obtain Minimal Sets from Fault Trees," Aerojet Nuclear Company,
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         active Isotopes  from Waste Solids to the Environment.  Part I:
        Background and Theory," ORNL-TM-4333, Oak  Ridge National Labora-
         tory, 1974.

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         Management of High-Level Radioactive Wastes," ORNL-4762, Oak
         Ridge National Laboratory, February 1972.

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         for the Description of  Radionuclide Transport in Solids," ARH-
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         263, p. 223-228,  March  1965.

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G077    Goldberg, S, M., S. E, Logan, and M. C, Berbano, "An Assessment
        Methodology of Environmental Risks Associated with Radioactive
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