Dissolution of high-level nuclear waste solids

Item Type text; Thesis-Reproduction (electronic)

Authors Voss, James Wilson, 1954-

Publisher The University of Arizona.

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DISSOLUTION Of HIGH-LEVEL

NUCLEAR WASTE SOLIDS

: . \ ' by

James Wilson Voss

A Thesis Submitted to the Faculty o f the

DEPARTMENT OF NUCLEAR ENGINEERING

In P a rtia l F u lfillm e n t o f the Requirements For the Degree o f

MASTER OF SCIENCE

In the Graduate College

THE UNIVERSITY OF.ARIZONA

1 9 7 6

STATEMENT BY AUTHOR

This thesis has been submitted in p a rtia l fu t f in m e n t o f requirements fo r an advanced degree a t The U n ivers ity o f Arizona and is deposited in the U nivers ity L ibrary to be made ava ilab le to borrowers under rules o f the L ib rary.

B r ie f quotations from th is thesis are alTowable w ithout special permission, provided th a t accurate acknowledgment o f source is made. Requests fo r permission fo r extended quotation from or reproduction o f th is manuscript in whole or in part may be granted by the head o f the major department or the Dean o f the Graduate College when in his judgment the proposed use o f the m aterial is in the in te res ts o f scholarship. In a l l other instances, however, permission must be obtained from the author.

SIGNED:

APPROVAL BY THESIS DIRECTOR

This thesis has been approved on the date shown below:

R. G. Poste c / " f y c

DateProfessor o f Nuclear Engineering

ACKNOWLEDGMENTS

I would Tike to acknowledge the assistance which I have

received from Dr* Norman A. H i!b e rry$ Dr. Morton E. Wackss and

Dr. Roy G, Post. A ll have provided invaluable guidance in th is

work. I would also l ik e to acknowledge the patience o f my

colleagues> especia lly John Boegel, as they gave me many hours

o f th e ir time providing he lp fu l advice. F in a lly s I acknowledge

the strength and patience o f my w ife , Sandra Lee, as she helped

me through th is portion o f my career.

TABLE OF CONTENTS

Page

LIST F TABLES ® ® « * * « » » • » * « e * * * o « « o

LIST OF TLLUSTRATIONS . . , . .. . . , % ............................. .... . v i

ABSTRACT , , . . . . . . . . . . . . . . . v i i

1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . 1

2. ANALYTIC EXPRESSION RELATING TO RELEASES OFRAOTOISOTOPES FROM WASTE FORMS . . . . . . . . . . . . . , . 3

Solution Behavior o f Waste Forms . . . . . . . . . . . . 3Temperature D is tr ib u tio n in Waste Solids . . . . . . . . 8

3. RADIOISOTOPE RELEASE FROM WASTE FORM WITHSUBSEQUENT ENVIRONMENTAL TRANSPORT . . . . . . . . . . . . . . 1 2

4. NUMERICAL EXAMPLES . . . . . . . . . . . . . . . . . . . . . . 17

PUREX Waste Description . . . . . . . . . . . . . . . . . 1 7Description o f Reference B o ros ilica te Waste Glass . . . . 21Primary Radioisotope Release . . . . . . . . . . . . . . 25Radioisotope Transport through the Environment . . , . . 27

5. DISCUSSION AND CONCLUSIONS . . . . . . . . . . . 4 . . . . , . 3 4

APPENDIX A: LISTING OF MAJOR RADIOISOTOPE COMPOSITIONIN PUREX WASTES . . . . . . . . . . . . . . . . . 39

APPENDIX B: WEIGHT FRACTIONS OF MAJOR FISSION PRODUCTRADIOISOTOPES . . = . . . . . . . . . . . . . 42

APPENDIX C: WEIGHT FRACTION OF ACTINIDES INBOROSILICATE GLASS . . . . . . . . . . . . . . . . 44

APPENDIX D: TABULATION OF MAXIMUM PERMISSIBLE CONCEN­TRATIONS (MPC) OF VARIOUS ISOTOPES IN WATER . . . 45

APPENDIX E: RADIOISOTOPIC RELEASES FROM WASTE FORMSVITREOUS FORM, LEACHANT AT 298K . . . . . . . . . 47

i v

V

TABLE OF CONTEMTS-^Contimied

APPENDIX F: RADIOISOTOPIC RELEASES FROM WASTE FORMSDEVITRIFIED FORM, LEACHANT AT 298K, . ,

APPENDIX G: RADIOISOTOPE RELEASE FROM WASTE FORMSVITREOUS FORM, LEACHANT AT 372K , ,

APPENDIX. H: RADIOSOTOPIC RELEASES FROM WASTE FORMS ,MODELED FORM AT ONE DAT OF LEACMING,WASTE AGE — 10 YEARS V ? .

APPENDIX I : NDMERICAL UNITS , . . . . . V . . . ,LIST OF REFERENCES , . . . . . . . . . . . . . , . .

SO

53

56

58

59

LIST OF TABLES

Table : , ■ Page

I . Relative D issolution o f Elements in Glass . . . . . . . . . 5

I I . Chemical Content o f PUREX Process Liquid Wastes . . . . . . 19

I I I . Heat Generation Rate o f PUREX Waste . . . , . . . . . . . . 20

IV. Composition o f Reference Borosi1ica te Glass . . . . . . . . 21

V. Solution Rates o f Reference Borosi1ica te Glass , . . . . 24

VI. Radioisotopic Releases from Waste Forms . . . . , . . . . . 28

V I I . Major Radioisotopes Released from Ten Year Old WasteForms . . . . . . . . . . . . . . . . . . , . . . . . . . . . 29

VIIT. Ion Exchange Holdup Factors fo r "Typica l" Western U.S.Desert Soil . . . . . . . . . . . . . . . .... . . . . . . . 32

IX. Concentrations o f Radioisotopes Dissolved fromD e v itr if ie d Reference Waste as They Are Transportedthrough the Environment . . . . . . . . . . . . . . . . . . 33

v i

LIST OF ILLUSTRATIONS

Figure

T. Steady State Temperature (K) versus Radius (M) fo r Ten Year Old Waste . ................ ... ........................................

ABSTRACT

A work has been done to explore the release o f radioisotopes

from h igh-leve l nuclear waste so lids by d issO fution, I n i t ia l l y , a

generalized expression describing the dissoTutibn o f a waste form

as a function o f time and temperature is derived. Discussion o f the

element sp e c ific d isso lu tion behavior is included. The environmental

transport o f dissolved radionuclides is next discussed. Equations

describing the flow ra te .o f radioisotopes from a waste form, the

d ilu t io n o f radioisotopes as they are transported in a groundwater

environment, and the radioactive decay o f radioisotopes due to ion

exchange w ith the s o ils are developed. F in a lly , the derived

equations are used in a sample ca lcu la tion invo lv ing the d isso lu tion

o f a b o ro s ilica te glass h igh -leve l waste form and the subsequent

environmental transport o f the dissolved radionuclides.

v i i i

CHAPTER 1

INTRODUCTION

Commercial nuclear power has been under development fo r nearly

t h ir t y years. During th is time period, the recycle o f uranium and

plutonium has been considered essentia l to fuel cycle economy and

conservation o f uranium resources. This strategy has been strengthened,

by the lin k between the L ight Water Reactor (LWR) fue l cycle and the

Fast Breeder Reactor (FBR) fue l cycle.

The LWR and FBR fuel cycle re la tio n is a complex one. Some

fuel cycles include a syne rg is tic re la tio n between the two. Others

show the FBR as an evolutionary step past the LWR, w ith the eventual

phase out o f the LWR systems. Within both s tra te g ie s , the need fo r

uranium and plutonium recovery by nuclear fu e l reprocessing isl ?essentia l. 5

The need fo r uranium and plutonium recovery by nuclear fuel

reprocessing may be s a tis fie d by several d if fe re n t means. One Such

method may be the reprocessing o f nuclear fuels by government owned

in s ta lla t io n s . Another p o s s ib ility is fo r the reprocessing step to be

carried Out by commercial reprocessing p lants. Neither is being done

at the present. The choice o f government reprocessing o f spent nuclear

fuel is techn ica lly feas ib le . CommerciaT fue l reprocessing, while

1

being te chn ica lly fe a s ib le , is not le g a lly possible a t the present, as

a va rie ty o f regulatory questions re s tr ic ts the licens ing o f any com­

mercial nuclear fu e l reprocessing p lan t.

One regulatory issue which is Currently being addressed by the

Nuclear Regulatory Commission, surrounds the d isp os ition o f h igh-leve l

nuclear wastes. H igh-level nuclear wastes contain nearly a l l o f the

radioactive f is s io n products generated by the fis s io n in g o f nuclear

fue ls . Current reprocessing technology generates these h igh^ieve i

wastes in the form o f liq u id s . -

At present, government regulations require th a t these high-

level l iq u id wastes be s o lid if ie d w ith in f iv e years o f th e ir genera­

tio n and be transferred to a Federal Government Nuclear Waste

Repository w ith in ten years o f 1iqu id waste generati on. While

regulations state tha t the s o lid if ie d h igh-leve l waste must be

"chem ically, the rm a lly , and ra d io ly t ie a lly s ta b le ," i t has been

determined th a t S pec ific waste form properties are needed to ensure

, that, the environmental impact o f h igh-leve l nuclear waste disposal be

pred ictab le and environmentally acceptable.

For complete environmental assessment o f the impact o f nuclear

waste d isposa l, a great deal o f inform ation is required about nuclear

waste form behavior. Two items whiCh are w ith in th is need are the

descriptions o f waste form d isso lu tion and o f environmental transport

o f radionuclides. This work addresses these two subjects by developing

generalized models fo r each phenomenon.

CHAPTER 2

ANALYTIC EXPRESSION RELATim TO RELEASiS OF ;RADIOISOTOPES FROM WASTE.FORMS

Radioisotopes may be released fTom a waste form by d isso lu tions

v o la t iliz a t io n s and p a rticu la te d ispersion. This work analyzes the dis»

so lu tion o f waste sol id .

This d isso lu tio n meG.hanism has been re ferred to as the leaching

mechanism. However, the act o f leaching implies oply the percolation

o f a liq u id about a s o lid which says nothing o f the mechanisms involved

in the leaching process. This work views the act o f leaching as the

so lu tion or d isso lu tion o f waste form.

Within th is Sectionj one model characteriz ing the d isso lu tion

o f s o lid is developed. A second discussion evolves a model re la tin g

the d isso lu tion o f a waste form to the environmental transport o f d is ­

solved radionuclides.

Solution Behavior o f Waste Forms

. The d isso lu tion o f waste forms is a complex phenomenon. TheA

so lu tion process is both temperature and time dependent. In add ition ,' 5the so lu tion process is element s p e c ific ; The element sp e c ific behav­

io r is discussed f i r s t .

I t has been observed tha t a lk a li metals, being h igh ly so lub le ,

dissolve most read ily from waste s o lid s .5 ’ ® In a d d itio n , s o lu b il i ty is

seen to decrease:as ion ic radius increases w ith in a valence s ta te .

. : ■: ' ' ■ 3 '

these observations are consistent w ith experimental evidence revealing

advanced d isso lu tion behavior o f sodium and cesium from waste so lid s .

In: contrasts cerium, an abundant element in h igh-leve l nuclear wastes,

is seen to dissolve from waste so lids a t a rate much slower than the 5a lk a li metals.

Mendel compiled a tab le demonstrating the p re fe re n tia l disso­

lu tio n o f various elements from po ten tia l waste glasses. Mendel

studied experimental d isso lu tion resu lts obtained by several d iffe re n t

researchers. While several d iffe re n t experimental techniques were used,

the comparison o f atomic ra tio s o f various elements in the glass forms

and in the solutions lead to Mendel1s resu lts shown below in Table I .

The time dependent behavior o f the d isso lu tion o f waste formsshas been described by equation ( I ) *

■ L = A e " 1/2 + B • ( 1)

where L = so lu tion rate o f waste form

8 = time

A = ra te constant re la ted to d iffu s io n o f io n ic species through waste m atrix

B = rate constant re la ted to corrosion o f waste m atrix

Equation ( ! ) is seen to have a S in g u la rity a t e = 0 sec. Since experi­

mental measurements to which th is expression has been f i t tend not to

be fo r times less than two hours, the equation is considered not to be

va lid fo r these small times.

This expression has been fu rth e r extended.to the arrhenius form

in equation (2) . ^

5

fab le I . Relative D issolution o f Elements in Glass,

Glass Type Relative D issolution Reference

S ilic a te glass Gs>Sr>Fe>Zr Eliassen and Goldman^

Lead glass

Phosphate ceramic

Cs>Al>Pb>SrsCe :

Nas Cs>Sr>Zr-Nb>Ru,Ce

PaigeR' - ' g ■' ' : . Allemann

Boros11ica te glass .

Borosi1ica te g1 ass

Gs a Na>Zr-Nb>Ru»Ce

Na>Si>B>Cs>Sr>Ge 3 Tb

QAllemann

E l l io t and Auty®

BorosiliCate glass

Phsophate glass

Na>B>Si

Cs>Na>Sr>Ru>Ce

Heimerl e t al . ^

Mendel and McElroy^

where a»b = constants m atrix speGffie)

AHd - activation-energy o f d iffu s io n {element and so lid m atrixsp e c ific )

AHc = a c tiva tio n energy o f corrosion (element and so lid m atrixsp e c ific )

R - gas constant

T - absolute temperature o f so lid m a trix -so lu tion in te rface .

Equation (2) then predicts th a t a t short tim ess the d iffu s io n

o f radionuclide species from the waste surface is the dominant e ffe c t.

A fte r long times s the corrosion o f the waste m atrix becomes dominant.

The separation between short and long times is on the order o f 10 sec-

onds, based s t r i c t l y on an order o f magnitude argument.

The Constants a and b are dependent upon several fac to rs .

These include so lu tion v e lo c ity , so lu tion pH, so lu tion chemical compo­

s it io n , and surface condition o f so lid m atrix.

Addressing the surface condition in p a rt ic u la r , i t is observed

tha t the surface energy o f p a rtic le s on a jagged surface is higher than

fo r a smooth surface. Thus, less energy is required to remove those

p a rtic les on a jagged form. This means th a t i f a piece o f a waste form

has a very rough surface, i t w i l l d issolve fas te r than a piece w ith a

smooth s urface.

This surface condition is o f special importance in regard to

measurement o f so lu tion rates Of waste forms. Solution ra te measure­

ment methods vary w idely, ye t nearly a l l require a high degree o f waste

form subdivis ion. This may include the grinding Of a waste m atrix to

- - - ; : . . : ' ' \ ^ : / - i ^ ;■ - ; - " ^ ::: 7

a powder3 w ith subsequent d isso lu tion o f a specified set Of waste par­

t ic le sizes. Then, in l ig h t o f the previous discussion, i t is apparent

tha t the degree o f suhdivisiOn o f a waste m atrix w i l l have an e ffe c t on

the resu lts o f the so lu tion rate measurement.

The various s o lu ti on rate measurement methods vary the soTutioh

flow rates. Some techniques have s ta t ic so lu tions , some have cycled

so lu tions , w hile others have continuously flow ing so lu tions. This too

w i l l a ffe c t so lu tion ra te measurement re su lts .

Results obtained from the various measurement methods vary.

, Most methods are reproducible w ith in a fa c to r o f ten, ye t since the

values obtained from d iffe re n t methods on s im ila r waste forms vary, the

meaning must be questioned, the d ifferences mentioned above along w ith

many others account fo r re su lt va ria tions .

Calculations using the resu lts o f any so lu tion ra te measure­

ments must be performed w ith caution. Recognition o f weaknesses in the

test methods and thus so lu tion rates is demanded.

The actual meaning o f so lu tion ra te measurements is usually

qu ite c lear. As most methods tend to create a set o f “worst possible"

d isso lu tion eonditions, measured so lu tion rates generally serve as up­

per 1im its . Thus, ca lcu la tions made using measured values re f le c t th is

same upper T im it behavior.

One p a rtic u la r measurement o f the so lu tion ra te o f b o ro s ilica te

glass, done at B a tte l!e Northwest Laboratory, has been performed to

determine the time and temperature behavior o f the so lu tion ra te . The

measurement has been done using the so ca lled Dynamic Method in which a

1 gram sample o f -45 +60 mesh p a rtic le s (p a rtic le s o f mean diameter be­

tween 0.56mm and 0.42mm) o f glass are placed in a s ta in less stee l "tea

bag", and Suspended in d is t i l le d water a t various temperatures. The

water is continuously ag ita ted about the sample and changed a t frequent

in te rva l s. Data from th is measurement have been f i t to equation (2) by

the Least Squares Method to determine the various constants. The v a l­

ues obtained are shown below:

a = 1 . 6 2 X 1 0 5 ug/(m2s1/ 2)

b = 2.12 X 103 yg/(m2s)

AHd = 3.0% X 103 J/mole

AHc - 1.20 X 104 J/mole

Temperature D is tr ib u tio n in Waste Solids

The energy balance equation predicts the temperature o f a so lid

with time, as Seen in equation (3).

vkvT+q'' ' = pc (3)

where T - temperature (K)

e - time (s)

K - thermal conductiv ity o f s o lid (W/mK)

q ' ' ' === volumetric heat generation ra te (M/m3)

p = so lid density (kg/m3)

c = s o lid sp e c ific heat (J/kgK)

The surface temperature o f the waste so lid becomes o f fundamen­

ta l importance in determining the so lu tion rates o f waste s o lid s , as

expressed e a r l ie f. Determination o f the surface temperature requires

deta iled knowledge o f the environment which the waste w i l l be placed

in to . Even i f a l l necessary inform ation is known9 the descrip tive so­

lu tio n o f equation (3) is not a t r i v ia l one.

The energy balance equation has been solved fo r One p a rtic u la r

steady sta te case. A waste cy linde r o f varying thermaT properties des­

cribed below is buried in some s o il w ith a l l can ister she ll material

and overpack neglected.

Figure 1 shows the steady sta te temperature d is tr ib u tio n fo r a

waste cy lin d e r and the close proxim ity s o il. The fig u re was developed

fo r a waste form w ith a heat generation rate o f 15,420 W/m which cor­

responds to the heat ra te o f a ten year ou t-o f-rea c to r b o ro s ili cate

glass form. The radius o f the cy linde r is 0.1525m, seen to be a t the

in te rsec tion o f the two curves. The ambient temperature is 300K. The

points labe lled 1 corresponding to TEMPI are fo r the thermal conductiv­

i t ie s o f the waste form and s o il both 1.OW/mK. The points labe lled 2

corresponding to the variab le TEMPI0 are fo r a waste form conductiv ity

o f 10.0 W/mK and a s o il thermal conductiv ity o f 1.0 W/mK.

The energy balance equation was solved fo r th is ca lcu la tion by

f i r s t assuming th a t the steady s ta te condition existed. The geometry

considered was th a t o f an in f in i te r ig h t cy linder. Four boundary con­

d itio n s were used since the problem is o f two regidnS, one region w ith

and one region w ithout heat generation. The f i r s t boundary condition

is tha t the f i r s t rad ia l distance de riva tive o f temperature is zero a t

the center o f the cy linde r. The second and th ird are co n tin u itie s o f

■ ; 10

heat f lu x and temperature a t the c y lin d e r-s o il in te rfa ce . The la s t

boundary condition is the ambient temperature at some distance from the

cy linder.

One meaning o f th is type o f ca lcu la tion , aside from the disso­

lu tio n im p lica tions , is re la ted to phase changes which various waste

forms undergo a t elevated temperatures. As discussed la te r , d e v i t r i f i ­

cation o f a glass waste form may occur a t a rapid ra te w ith elevated

temperatures, as i t s rate is described by an arrhenius equation.

V Another impTication o f th is Calculation is th a t fo r heat con­

duction to the environment, the thermal conductiv ity o f the waste form

does not change the in te rface temperature or the temperature p ro f ile in

the surrounding environment. In the f ig u re , the two temperature curves

are seen to merge a t the waste form surface, and Coincide from tha t

po in t on.

A ll o f these fac to rs , phase o f waste form, surface temperature

o f waste form, and temperature p ro f i le in the close proxim ity o f the

waste form, have a marked e ffe c t on the conditions fo r d isso lu tion .

The constants in the d isso lu tion equation w i l l be d if fe re n t fo r each

phase o f each form. Also the temperature fo r d isso lu tion w i l l have

d ire c t e ffe c t on the d isso lu tion rate o f a waste form.

11

1=TEMPI 2=TEMP1C

Figure 1

6.50

6 .03

4 .50

4 .00

3-50

2 .50

0 .00 0 .10 0.20 0.30

Steady State Temperature (K) versus Radius (M) fo r Ten Year Old Waste

CHAPTER 3

RADIOISOTOPE RELEASE FROM WASTE FORM WITH SUBSEQUENT ENVIRONMENTAL TRANSPORT

The mass flow ra te o f the radioisotopes in to the environment *

m, from a waste form is the product o f the so lu tion rate o f the sOTid,

L, and the exposed surface area o f the s o lid . A, provided the mass flow

is independent o f the concentration o f radioisotopes in the Solution^

m = L * A . (4)

Thus, the concentration, C , o f radioisotopes in a so lu tion ' • ' 0 : .

which is Teaching the waste form is the quotient o f the rad io isotope;

mass flow rate and the volumetric flow rate o f the so lu tio n , V^, as

shown in equation (5 ), ’

r - 2L - L ACo ' Vf ~ -Y J - (5)

I t is important to recognize tha t Co w i l l vary w ith time and

waste surface temperature ju s t as the so lu tion rate does. Calculations

which fo llow in th is work w i l l consider constant so lu tion rates and

thus constant concentration, CQ. However, recognition o f the actual

time and temperature va ria tion is made.

Once radioisotopes have been dissolved from waste form, th e ir

subsequent environmental transport may be estimated, and a n a ly tic a lly

described. Equation (5) expresses the concentration o f io n ic radionu­

c lide species in a d isso lv ing so lu tion as i t re la tes to the so lu tion

12

■ '■■■ : : -"V . •. ■ ■ . : . . ;■ is. rate o f a waste form. As the radionuclides are transported through the

environment th e ir concentrations are reduced by several in te ra c tio n s ,

o f which only d ilu t io n and exponential decay are considered in th is

work.

Considertng radionuclide d ilu t io n f i r s t , i t is seen by equation

(6) tha t the concentration o f radioisotopes whioh reaches man, C, is

expressed as the concentration a t the waste form, CL, d ivided by the

dilution factor, 0. :

■ c = c0/D • ; (6)

This d ilu t io n fa c to r is the number o f equivalent volumes o f un-

contaminated water th a t the radionuelide mixes w ith during environmen­

ta l transport.

Concentrations o f radionuclides are fu rth e r reduced as the

radioisotopes decay exponentia lly w ith time during environmental trans­

port. Thus fo r the 1 th rad io isotope, the concentration which reaches

man, C|, is expressed as in equation (7).

C1 = C01 (e ' " h / D ( 7 )

where C = the concentration o f i a t the waste form

A.. = the decay constant of i

t . = the time required fo r i to be transported to man

The transport time is found by d iv id in g the distance which

radionuclides must trave l to reach man by the speed a t which the radio­

nuclides move through the environment- The radionuclide ra te o f tra ve l

is somewhat less than the groundwater speed. The reduction o f the

speed is caused by the ion exchange o f the radionuclides as they trave l

through some aqu ife r m ateria l.

Ion exchange is a phenomehon in which some dissolved species

are held by ion ic bonds a t s ite s w ith in a s o lid ; the s o lid being aqui­

fe r m aterials fo r the case o f radionuclide transport. There is a com-

p e tit io n fo r the dissolved io n ic radionuclide species as they are moved' ' IA - ' - : • ' " ' ■ '/ - ' ••• ■ . '

through the biosphere. Thus, the dissolved species w i l l be continu-" ■ ■ • • ■ is ■;

a l ly exchanged through environmental transport.

The problem a t hand is to re la te the chemical behavior o f the

ion ic radioisotope species to th e ir transport. I f M+m and A+n repre­

sent ions o f radionuclides and n a tu ra lly occurring exchangeable aqu ife r

minerals respective ly carrying charges +m and +n, and X is assumed to

be a reactive Chemical rad ica l in aqu ife r m ate ria l, the equation fo r

the ion exchange reaction is as in equation (8).

nM+rri + m(AXrt) + n.(.MX ') + mA+n (8)

The equ ilib rium constant fo r th is exchange, K, is defined by

equation (9).

[ « g n n C " f (9 )

[M+m] n [AXn] m

Since in r e a l i ty , a very small fra c tio n o f the ava ilab le ex­

change s ites in the minerals is occupied, [A+n] and [AX ] may benassumed constant. This allows the d e fin it io n o f a useful d is tr ib u tio n

c o e ffic ie n t.

\v t iv«. i v- « u i w i v i w i c v i u u i w.i i

(1 0 )

W = the weight o f minerals

Consider, then, a species o f rad ionuclides, i n i t i a l l y lo ca liz e d

to a waste form. The flow ra te o f the rad ionuclides, F_, may be ex-• * a

pressed as in equation ( 11),

Since p is not known exactly , i t is convenient to use a value

o f 1, the usual value being 4 or 5. Thus, by assuming in addition th a t

the area o f flow fo r the radionuclides and groundwater are equal,

equation ( 11) reduces to equation ( 12).

where V - the ve lo c ity o f the radionuclides

V = the ve lo c ity o f the groundwater

I - the ion exchange holdup fa c to r

The transport time o f the radionuclides, t , is then the d is ­

tance, X, which radionuelides must trave l to reach man divided by the

ve lo c ity o f the radionuclides in so lu tion .

where F, = the flow rate o f groundwaterwp = the ra tio Of weight o f minerals to volume o f water

per u n it volume o f aqu ife r material

Thus, the concentration o f each radionuclide transported to man may be

Calculated.

fli l(TX)C = f ^ e V (1 4 )

f ' • . .

Given equation (14), a sp e c ific waste form w ith i t s d isso lu tion

ch a ra c te ris tics , and a maximum concentratioh o f radionuclides which may

reach man, the required is o la tio n o f rad ioactive wastes may be calcu-

la ted. This required is o la tio n would be expressed in terms o f the d is ­

tance from mans X, and depends on the Velocity o f water through the

environment, Vs the sorption cha rac te ris tics o f the environment. I , and

the quantity o f water which may flow through the environment, V^-D.

A note must be added about th is environmental transport model.

Many sophisticated computer codes modeling th is behavior have been

w ritte n and are in use. This simple model has been derived fo r ease in

hand ca lcu la tions . Assumptions have been made in th is theory. One is

in assuming bulk quan tities such as s ing le sorption cha rac te ris tics o f

an environment. This may be true in a small increment, but ce rta in ly

is not true on a Targe scale. The radionuclides have been modeled as

moving only in one d ire c tio n , while in fa c t they w i l l tend to spread in

a manner s im ila r to m ateria l in a plume dispersion. The important fac­

tors in constructing th is simple model are th a t hand c lacu la tions may

be performed, and w ith proper se lection o f averaged p rope rties , the

resu lts w i l l be conservative.

CHAPTER 4

: NUMERICAL EXAMPLES : ^

In order to demonstrate the use and meaning o f the ana ly tic

expressions previously presented, a series o f sample oalculations w i l l

be performed oil a typ ica l waste form. The ca lcu la tions w i l l include an

analysis o f rad io i sotope release by s o lu ti on $ and a sample analysis o f

radioisotope transport through the environment.

The type waste form which w i l l be considered is b o ro s ilica te

glass produced from PUREX waste. This section w i l l q u a n tita tive ly de­

fine the b o ro s ilica te glass and the PUREX waste whichs a fte r c a lc i­

nation, is mixed w ith the glass.

In add ition , the b o ro s ilica te waste form f i t t e d to the so lu tion

rate expression in Chapter 2 is studied in terms o f i t s radioisotope

release and subsequent environmental transport. For ca lcu la tiona l pur­

poses , i t is assumed th a t the radionuclide content to be specified fo r

the reference waste form w i l l e x is t in the modeled form*

■ PUREX Waste Description

This analysis considers nuclear wastes generated by the LWR

fuel cycle* While in the reacto r, the LWR fue l w i l l acquire a f is s i le

fuel burn up o f 2.85. TJ/kgU (33000 MWD/MTU) over a three year p e r io d .^

The fue l considered.w ill have been removed from the reactor 160 days

p r io r to reprocessing.

17

The nuclear fuel is processed in the PUREX process. This PUREX

process uses concentrated n i t r ic acid in aqueous so lu tions and t r ib u ty i

phosphate in kerosene to separate uranium and plutonium from the f i s ­

sion products in spent reactor fu e l. The re su lting liq u id wastes are

n itra te s . The chemical content o f these liq u id wastes is described in 18

te I I .

The h igh-leve l PUREX wastes are h igh ly rad ioactive and s e lf ­

heating. The to ta l fis s io n product a e t iv itv in the l iq u id waste isq a ' ' '

0.451 EBq/m (1.22 x TO C i/1 ). The to ta l actin ide a c t iv i ty , assuming - \ ■ . ; . • . - '

0.5% loss o f uranium and plutonium in reprocessing, is 4.28 nn~

(115.8 C i/1 ). Thus the to ta l radioisotope content is 0.455 EBq/m^

(1.24 x 104 C i / 1 ) T h e major radioisotope composition in the PUREX

waste a t 160 days o u t-o f-re a c to r is lis te d in Appendix A. In add ition ,

in Table I I I , the volum etric heat ra te o f PUREX waste as i t varies w ith

time is l i s t e d . ^

The analysis next considers th a t the PUREX liq u id waste is

s o lid if ie d by the ca lc ina tion process. This process drives the waste

n itra te s to oxides, removing the n itra te s and water as o ff-g a s . The

c a l c i n e d product is then suspended in a glass m atrix , s p e c if ic a lly in

a boros H i cate glass m atrix. This fo rm .is discussed in the next

section.

19

Table I I . Chemical Content o f PUREX Process Liquid Wastes*

Component Concentration (kg/m^)

hydrogen 1.058

iron X v: ' .n ickel : 0.265

chrpnium 0.529

n itra te 174.1■

phosphate 2.380 :' • ' a

uranium 12.70

plutonium . . ' 0.106

neptunium 1*270

americium 0.370

curium 0.106

Total f is s io n products 76.19

*based on a waste production rate o f 3.78 x lC fV /k g l l

20

Table I I I . Heat Generation Rate o f PUREX Waste

Time Out o f Reactor (YR) Heat Generation Rate (W/m3)

160 days 5.04 1+041 2.73 E+04

-5:'-. ; ' / ' ■: ' 5.05 E+0310 2.91 E+0320 2.06 E+0330 ■ v-v' .. 1.60 E+03 :40 1.25 E+03

’ so 9.80 E+0260 7.70 E+0270 6.10 E+0280 4,80 E+0290 3.80 E+02

TOO 3.00 E+02120 1.90 E+02140 1.30 E+02160 8.54 E+01180 5.91 E+01200 4.29 E+01220 3.25 E+01240 , 2.58 E+01260 2.14 E+01280 1.84 E+01290 1.74 E+01

V ' . ; . 21

/ v :Descr1ption o f Reference B pros llica te Waste Glass

A b o ro s ilica te glass contains and SiO^ as i t s major

cdnstituents. The boros11ica te glass considered in th is analysis is

Savannah River P lan t's Mix #18. I ts chemical composition is lis te d

in Table I f . 20

Table IV, Composition o f Reference BorosiTicate STass

Compound Wt% o f Glass F r i t

s122 ; ' t : ' . I 52,5

Na20 22.5

B203 10.0

Ti02 10.0

CaO 510

Production requirements fo r bo ro s ilica te glass vary from

1.4 x TO*17 m3/J (1.2 1/1000 MWD) to 5.8 x TO*7 m3/J (5.0 1/1000

This analysis w i l l consider a production ra te o f 2.3 x ld “37m /J

(2.0 1/(1000 MWD)). For th is value, waste oxides are about 22 wt% o f

the b o ros ilica te glass product.

The heat generation rate o f the b o ros ilica te product is

calculated from the heat generation ra te o f the PtiREX waste as shown

... 'V -';;--; : : ; : : . .. ; ■ - ■ 22

in Table I I I . The glass heat generation rate is calculated from

equation (15). ; \

% = <i P V tBV ■ ( , 5 )where q^ = the heat generation rate o f b o ro s ilica te glass (W/m)

qp = the heat generation rate o f PUREX waste (W/m^)

- the production ra te o f PUREX (m^/kgU)

B = the f is s i le fuel burnup o f the fue l (J/kgU)

Rh = the volume o f b o ro s ilica te glass produced per energy generated (m /J )

In th is ana lys iss Rp = 3.78 x 10“ 4 m3/kgUs B = 2.85 TJ/kgU (33000 MWD/

MTU), and Rp is 2.315 x 1 0 "^ m^/J. Hence, qp is described in equation

(16).

qb - q0 ; 3 M -------- .) ,5 .30 (16)p m PUREX waste m buro-glass

Thus, to determine the heat generation rate o f the b o ro s ilica te glass

products the data in Table I I I need be m u ltip lie d by 5.30, as shown

above.

The reference b o ro s ilica te glass has several measured proper­

tie s which held describe i t . Solution rates o f th is glass under v a r i­

ous conditions are shown in Table ,22

The constants fo r the d isso lu tion equation calcuTated e a r lie r

are used w ith the d isso lu tion equation to calcu late d isso lu tion rates

fo r use in th is section. Temperature conditions selected are 298K and

372K as the d isso lu tion temperatures. The time fo r d isso lu tion is a r­

b i t r a r i ly selected to be one day. In th is manner, d isso lu tio n rates

are calculated and shown in Table V.

23

Table V . - So lu t i on Rates o f Reference Boros11ica te Glass

Component Leaching Solution Rate «Leached Condition (ug/mzs) (atoms/m s )*

137cs r 0.013898Sr 1 0.0467

125Sb ./ i

0.261 n h9ma ipria aCLi n i aes

• bulk glassi

1U o U d-U I

603.0 3.96 £+18'137CS : : 2: / : 0.019090Sr 2 0.832 « ■*

; ,25sb ■ 2 . o0.230n m n/ia ipfia: aCuinluGS

. bulk glass. ; c <

2W o u 1U4

535.0 3.50 E+18 ;137Cs 3 0.39490Sr 3 0.749

125Sb 3 1.01alpha actin ides ■ 3 0.0435bulk glass 3 2350,0 1.54 E+l9 ,bulk glass 4 61.2 . 4.01 E+l7modeled glass modeled glass

5 176.3 1.15 E+18• ' • 6 248.0 1.62 E+18

Conditions:

1 - glass in H20 a t 2S8K (23°C)

2 - glass heated to 773K (500°C) fo r 1 month 3 in H O a t 298K (25°C)

3 - glass heated to 873K (600°C) fo r 1 month ( d e v i t r i f ie d ) s in H90a t 298K (25°C) d

4 - glass in H O a t 372K (99°C)

5 - glass in H O a t 298K (25°C) surface temperature fo r e - 1 day

6 - glass in HgO a t 372K (99°C) surface temperature fo r e = 1 day

*Based on a calcine molecular weight o f 190g/mole and a waste glass molecular weight o f 92g/mole.

A few additiona l properties o f the reference.waste glass are

known. These are described below.

The density o f any waste glass varies w ith waste:oxide content.

A ll data ind ica te th a t expected densities w i l l range from 2900 to

The thermal s ta b i l i t y o f b o ro s ilica te glass is well known.

Glass undergoes two steps to thermal i n s ta b il i ty * d e v i t r i f i ca ti on and

m echan ica l;in s ta b ility .

D e v itr if ic a tio n is a phase transformation in glass, in which

the supercooled liq u id s truc tu re o f a glass c ry s ta lliz e s . Four main

factors d ire c tly a ffe c t the d e v it r i f ic a t io n o f a glass; 1) time,

2) temperature, 3) nuciea tion , and 4) in te rna l s truc tu re .

I t has been observed tha t the rate o f d e v it r i f ic a t io n may be27expressed in the arfhenius form as in equation (17).

3500 kg/m3. 23924825$26 This work calculates a density o f 3000 kg/m3

fo r the reference glass

to 1.4 W/mK.

The thermal conductiv ity o f b o ro s ilica te glass varies from 1.0 ,/my 23,24,25,26

(17)

where A - constant

E = a c tiva tio n energy

R - gas constant

T - absolute temperature

:: : ; ' ' / ' ; 25

Thus, d e v it r i f ic a t io n is a k in e tic process which w i l l proceed

to some degree a t a l l temperatures. I t may be expected th a t a nuclear

waste glass w i l l eventually completely d e v it r i fy , even a t low tempera-

v; tures. .' ;

The se lf-hea ting nature o f nuclear wastes provide more advanced

temperatures, and thus higher rates o f d e v it r i f ic a t io n . I t has been

observed tha t a t temperatures over 870K, the d e v it r i f ic a t io n o f the

" reference glass proceeds r api dl y . ^^9 Whi1e the e ffec ts o f d e v it­

r i f ic a t io n on a glass are varied, data in Table V demonstrate tha t the

reference glass so lu tion rate may increase w ith d e v it r i f ic a t io n :. V ■■ . ■ .;:v 'v ' ■ : . 24

Mechanical in s ta b i l i ty o f glass begins a t about 973K, as the

glass takes on a mol ten behavi or. This behavior becomes more severe

w ith increasing temperature u n t i l a t 1373K to 1473K, the glass behaves

as a viscous l iq u id . ^

Waste form geometry is Of ye t uncerta in i This work assumes a

canister geometry o f 0.30m in diameter by 3.0m long.

Primary Radioisotope Release

The radioisotope release by d isso lu tion is to be calculated fo r

the reference b o ro s ilica te glass. To demonstrate the possible range o f

releases which may re s u lt from the waste formy fourteen d is t in c t cases

w i l l be considered as shown below:

a - v itreous product w ith leachant at 298K fo r c y lin d r ic a l mono­

l i t h and fo r monolith broken in to cube p a rtic le s 0.1 mm on

a s ide, w ith waste age a t one and ten years o u t-o f-re a c to r;

b - d e v it r i f le d product w ith leadhant a t 298K fo r c y lin d r ic a l

monolith and: cubic pieces w ith one and ten years o u t-o f-

reactor ages;

c - yitreous product w ith leachant at 372K fo r c y lin d r ic a l

monolith and cubic pieces w ith and ten years o u t-o f­

reactor ages;

d - the modeled glass in c y lin d r ic a l monolith form a t one day

o f leaching w ith the leachant a t 298k and 3721.

the ca lcu la tion o f rad io iso top ic release by so lu tio n , u t i l iz in g

the data o f tab le V and the previously described a na ly tic expressions,

requires some prelim inary explanation. Table V l is t s sp e c ific 1 each

rates o f ^% r, ^ C s , ^ S b , alpha ac tin ides , and bulk glass. Those

radioisotopes not s p e c if ic a lly mentioned w i l l be assumed to be released

from the waste form by corrosion. Thus, the actual rad io iso to p ic re ­

lease is the release o f the waste forms times the weight fra c tio n which

those radioisotopes make up o f the m atrix. These weight frac tions are

found in Appendices 8 and €.

The a na ly tic expressions presented describing the concen­

tra tio n s o f radioisqtopes released from waste forms were o f the general

form shown below in equation (5 ).

Co = V ; (5)

where C. = concentrations o f radioisotopes

m - mass flow rates o f radioisotopes

= volumetric flow rate o f leachant

■ 27

To assure tha t calcuTatipns are not weighted by the estimation o f a

volumetric flow rate o f a leachant, the mass flow ra te o f radioisotopes

alone w i l l be calculated in the units o f (MPC-m^/s)s from Appendix D.

Thus, the po ten tia l mass flow rates o f radioisotopes from the/ •

reference waste glass are shown below in Table VI w ith sp e c ific re­

leases shown in Appendices E, F, G, and H.

Calculations performed to a rr ive a t values found in Table; V II

show some addi t i onal i nformation o f i n teres tv Those radi o i sotopes

which are o f major in te re s t a t a waste age o f ten years are revealed.

These are tabulated below in Table V II.

Radioisotope Transport Through the Environment

This section w i l l discuss the releases o f radioisotopes pre­

viously calculated as they are moved through the environment. In par­

t ic u la r , radioisotope transport in a r iv e r type environment and in a

typ ica l desert environment w i l l be considered.

Equation (14) shows tha t concentrations o f radioisotopes a t

some po in t in the environment is as shown below.

For a r iv e r environment, one in which the decay o f radioisotopes during

the transport may be neglected, th is equation may be reduced to the

form o f equation (18).

28

Table VI. Radioisotopic Releases from Waste Forms

WasteGeometry

Waste . Age (Yr)

Leaching Condition

Mass Flow RatOgOf Release (MPC-m /s )

cy linde r 1 1 9.73 E+2

cy linder TO 1 4.75 E+2cubes 1 1 5.84 E+3cubes TO ; i ■■ 2,85 E+3

cy linde r y-;T;2 ; 2.50 E+5 ’cy linder TO ' ' 2 - 3.97 E+3cubes 1 2 1.50 E+6cubes ’ ; ' ■' .V: 2 . 2.38 E+4cy linde r T 1 3 6.58 E+3cy linder TO 3 3.37 E+3cubes 1 3 3.97 E+4 -cubes 10 V 3 2.02 E+4cy linder TO 4 7.26 E+3cy linder TO 5 1.02 E+4

1 - vitreous waste, 1eachant a t 298k2 - d e v it r i f ie d waste, 1eachant a t 298K3 - v itreous waste, 1eachant a t 372k4 - modeled glass, 1eachant a t 298k, one day o f leaching5 - modeled glass, 1eachant a t 372k, one day o f leaching

29

Table VII. Majoc Radioisotopes Released from Ten Year Old Waste Forms . : /v:.;..--:/; ; : :

Waste Leaching Radio­ Mass Flow RateGeometry Condition isotope (MPC-m3/s)

c y lin d r ic a l 1 90Sr 236.3

137Cs 0.6

125Sb 0.4 ■

: ,54Eu : y , 0.3

cubic 1 90Sr 1417.8

137Cs 3.5

,25Sb 2.2

154Eu1.9

c y lin d r ic a l 2 , " s r 1699.0

154Eu 259.4

106Ru88.3

147Pm 62.1

14:4Ce 23.0

137Cs 7.5

cubic 2 90Sr 10194.0

154Eu1556.7

106Ru530.1

147Pm 372.4

144Ce 137.8

137Cs 45.0

30

Tab1e V I I9 Gbntinued

Waste Leaching Geometry Condition

Radio­isotope ;

Mass Flow Rate (MPC-m3/s )

c y lin d r ic a l 3 sv 16416

T37cs 35.5

134Cs ■ 8.6cubic 3 90Sr 9849,8

137c, 212.8

134Cs 51.3

106Ru 4.4c y lin d r ic a l 4 90Sr 6841.8

137Cs 149.6

1S4Eu 9.2

134Cs 3.2

;CfiRu 3.1cy lin d r ic a l 5 90Sr 9621.0

137Cs 210.4

154Eu 12.9

134Cs 4.6

106Ru 4.3

1 - vitreous waste, leachant a t 298K2 - d e v it r i f ie d waste, leachant a t 298K3 - vitreous waste, leachant a t 372K4 - modeled glass, leachant a t 298K, 1 day o f leaching5 - modeled glass, leachant a t 372K, 1 day o f leaching

. ;• ' . ' . ; 31 .

where m ^ mass flow rate o f radioisotopes

Vg = volumetric flow rate o f body o f water (V^-D)

The concentrations o f radionuclides calculated by th is equation

are contingent on the perfect mixing o f released radioisotopes w ith the

volume o f flow o f water. Thus, using equation (18)s and knowing the

mass flow .rate o f radioisotopes from the waste form, the amount o f

water necessary to achieve proper d ilu t io n o f radioisotopes may be de­

termined. • 1

Again re ca llin g equation (14), to demonstrate the use o f th is

equation, a sample ca lcu la tion has been done. The mass flow ra te o f

major radioisotopes from ten year old d e v it r i f ie d cubic p a rtic le s is

shown in Table V II. The ca lcu la tion assumes tha t these radioisotopes

are leached in 10"* m /s o f water, and are undiluted. The radioisotopes

are then transported through a typ ica l desert environment. The ion ex­

change holdup factors used fo r each o f these.radioisotopes are l is te d 29 1

in Table V I I I . F in a lly , the concentrations o f these radioisotopes

are lis te d against the time which the groundwater trave ls in the envi­

ronment in Table IX.

Values in Table IX and a l l other tables in th is work are lis te d

in System In te rn a tio n a l or SI un its . A l is t in g o f a few less common SI

units is found in Appendix I .

32

Table VM I. Ion Exchange Holdup Factors fo r "Typica l" U.S. Desert Soil

Western

Element r1 Element r1t r i t iu m 1 iodine iberyl 1i urn 3x10‘ 3 cesium Ix lO "3

cerium 4x10"4carbon 1x10-1 promethium 4xT0"4sodium . 2x10"2 samarium 4x10” 4ch lorine " i '■: europium 4x10"4argon 1 holmium 4x10"4potassium 6x10” 3 tha llium Ix lO "1calcium 1x10” 2 lead 6x10"5iron 3x10"4 bismuth 2x10"2cobalt 3x10"3 polonium 9x10"3nickel 3x l0 "3 astatine 1selenium , 1x10"2 radon 1 -krypton ■ 1 francium Ix lO "3rubidium 2x10"3 radium 2x10"3strontium 1x10” 2 actinium 2x10” 4y ttr iu m Ix lO "4 thorium 2x10"5zirconium 1x10" 4 protactinium 6X10"5niobium 1x10"4 uranium 7x10"5molyodenum 4x10"2 neptunium Ix lO "2technetium 1 plutonium Ix lO "4rutheni um 3x10” 4palladium 9x1O” 4 americium Ix lO "4cadmium Ix lO "4 curium 3x10"4t in 9x10” 4 berkelium 3x1O"4antinomy Ix lO "2

33

tab le IX. Concentrations o f Radioisotopes Dissolved from D e v itr if ie d Reference Waste as The^ Are Transported through the Environ^ ment

90Sr V54Eu CT06^trat1H 7 p ; C) H 4Ce 137^ I % (Y r )

1.62E8 L56E7 B,30E6 3.72E6 T.3BE6 4,S0E5 09.95E7 5.28EB 4.90E-4 3.87:3 3.T7E-4 3.S7E5 0.019.71E7 1.79E6 ■ 3,55 = ,a 3 2.83E5 0.029.47E7 6.05E5 3i 46E-3 2,25E5 0.039.24E7 2.05E5 e» =» 1.79E5 0,049.02E7 6,94vE4 '="= 1,42E5 - - 0.058.62E7 2,35E4 ao=e 1.13E5 0.068.58E7 7,95E3 -b i- “ — 8.92E4 0.078.37E7 2.S9E3 •m=e 7,09E4 0.088.17E7 . 9,12E2 “ =» 5.S3E4 0.097.97E7 3.09E2 4.46E4 0.106.2317 6.11E-3 “ *° 4.43E3 0.204 .87E7 —— <«>.co 4.39E2 0.30.3.80E7 =oe” 4.36E1 0.402.97E7 . ‘= CD ' 4,33 0.502.32E7 • '«> «* 4,29E-1 0.601.81E7 — ” » => ™ == = *»=> onac 0.701V39E7 -*> —> . • = *=° == = == = bo CO 0.801.09E7 =* = CO CD coco 0,908.66E6 * =° esco ” — 1.007 . 35E5 CO.OD 2,00€»23E4 —— <=>«= 3.005.29E3 ' co’=D op = COCO = a 4.004.49E2 ” = 5.003, St El «=>” =° 6,003,23 ==™ ' c» « 7.002.74E-1 -------- ■=“ ** coco =° «= 8,00

CHAPTER 5

DISCUSSION A # CONCLUSIONS

A study has been performed to develop the importance o f the d is ­

so lu tion phenomenon to h igh-leve l nuclear waste management. Theory has

been presented describing the mechanisms o€ radioisotope release from

an a rb itra ry waste form.

Typical borosi11 cate glass waste forms made from PUREX-LWR

waste have been considered. The mass flow o f radioisotopes from these

waste forms has been calculated. F in a lly , expressions have been de­

veloped showi ng the re la tio n between the. so lu tion behavior o f waste

forms and the environmental transport o f radioisotopes, w ith numerical

examples displayed fo r the typ ica l waste form placed in possible envi­

ronments.

Several im portant observations may be made from the analysis.

F irs t , regarding sp e c ific radioisotope release, i t is apparent tha t the

m ajority o f the radioisotopes $ which may be p o te n tia lly released are

composed o f a few sp e c ific f is s io n products, not the actin ides. The

data in Table V II ind ica te tha t fo r ten year old waste forms, ^ S r ,

^ C s , ^ R u , ^ C e , ^ P m , and ^ % u are the radioisotopes o f major

release. These radioisotopes have h a lf- l iv e s such th a t a fte r several

hundred years, they w i l l have nearly decayed. On the other hand, on

34

th is time scale the summation o f a i l actin ides released is a t r i v ia l

fra c tio n o f the to ta l radioisotope concentration released by th is mech­

anism to the environment.

From the analysis comparing vitreous and d e v it r i f ie d products,

i t is cohcluded tha t d e v it r i f ic a t io n is a detrim ental phenomenon based

on the higher so lu tion rates o f d e v it r i f ie d glass forms. Calculations

showed tha t the in i t ia l mass flow ra ta o f radioisotopes from a d e v it r i ­

f ie d waste form is greater than 10® MPC-m^/s, while a vitreous waste

form in the same condition is about 200 times less so luble.

The statement th a t a d e v it r i f ie d product is worse than a v i t ­

reous form must be made w ith a note o f caution. This analysis is based

on the d isso lu tion o f waste form sf In the case o f the dropping o f the

waste form, i t may be advantageous fo r the product to be d e v it r i f ie d .

Some evidence ex is ts tha t a d e v it r i f ie d product has a higher impact

strength than the vitreous product. However, th is work does not address

th is subject, ra ther i t is noted as a p o s s ib ility .

On the basis o f ca lcu la tion , i t is concluded th a t i t might be

advantageous to have waste forms in small shapes ra ther than in large

ones. Data presented tha t d e v it r i f ic a t io n or a b o ro s ilica te glass

could re su lt in a 200-fo ld increase in the so lu tion ra te over a v itreous

form. From a heat tra n s fe r po int o f view, lower temperatures might be

expected w ith smaller waste forms thus the rate o f d e v it r i f ic a t io n

would be slower. I f the Smaller waste form did not cause a surface

area increase o f greater than 200 times, then from a rad io iso top ic

release po in t o f view, i t would become advantageous to have such forms.

Before such a decision could be made, an assessment o f the overa ll envi­

ronmental impact o f such a decision would have to be done to ensure th a t

the overa ll r is k to man would not be increased.

Regarding the release o f radioisotopes in some transporta tion

accident scenario placing the waste form in to some r iv e r type environ­

ment, co rre la tions have been developed showing the type o f environment

flow rate necessary to ensure proper d ilu t io n o f radioisotopes as a

function o f radioisotope release rate from waste forms. In terms o f the

reference b o ro s ilio a te waste form, i t is concluded th a t the best waste

form to ship would be a vitreous form, o f a t least ten years o f age.

This statement is made on the basis tha t th is form has the lowest re­

lease ra te o f radioisotope o f those considered in the analysis.

Several s im p lify in g assumptions were made in the course o f the

above mentioned ca lcu la tions. Of primary importance, i t was assumed*

fo r the c y lin d r ic a lly shaped waste form, tha t the e n tire surface area

o f the form was exposed to some leaching environment. In a c tu a lity , i t

is l ik e ly tha t in any transporta tion type scenario, th is condition w i l l

not e x is t. Rather more l ik e ly , several decades o f reduction o f the ex­

posed surface area wpuld e x is t. This fa c t alone would g rea tly reduce

the quan tities o f water which would be necessary to ensure proper d i­

lu tio n o f radioisotopes.

In regard to the release o f radioisotopes in some disposal

scenario, i t was shown th a t re la tiv e ly high flow rates o f ground water

carrying radioisotopes would be s u ff ic ie n t to ensure proper hold-up o f

rad io isotopes;in a desert type environment. Ca1cu1 atidns showed th a t■90fo r the quan tities o f Sr released from a ten year old d e v it r i f ie d

waste form9 i f the ground water took about e ight years to transport

from the nuclear waste disposal s ite to man's environment, then concen- 90tra tionS o f Sr reaching man would be a t permissible, le ve ls . I t was

also shown tha t i f the ^ S r was con tro lled through i t s environmental

transport, then a ll other radioisotopes would be s im ila r ly con tro lled .

As previously discussed, s im p lify ing assumptions were made en

route to these conclusions. The exposed surface area s im p lif ic a tio n

would force calculated values to be lower. In add ition , th is analysis

assumed very T i t t le radioisotope d ilu t io n . In r e a l i ty , i t is a n t ic i­

pated tha t as some 1 eachant moved through the environment, i t would be

greatly d ilu ted . Thus, calculated values would again be lowered in

re a lity .

On the basis o f the theory and numerical examples, i t is con­

cluded th a t two factors dominate the concentrations o f radioisotopes

which may reach man from s o lid if ie d HLW. The f i r s t is the temperature

o f the waste form. This is o f importance because o f the arrhenius re ­

la tio n describing the d isso lu tion o f a waste form. As the temperature

fo r d isso lu tion increases, the d isso lu tion ra te is seen to increase a t

an exponential ra te .

The second fa c to r o f importance is the waste form iso la tio n

distance from man and the ion exchange holdup encountered in tha t d is ­

tance allow ing rad ioactive decay to reduce the isotope concentration.

The in i t ia l concentration o f radionuclides has very l i t t l e e ffe c t on

. : ; : ; : - 3:8

the tsoTation distance required. As a s e n s it iv ity ana lys is9 the volume

flow rate o f ground water used in the calcuTation o f Table IX was in -4

creased by a fa c to r o f 10 . As th is g rea tly reduced the I n i t ia l con­

centra tion o f the radioisotopes, i t was believed th a t the iso la tio n

distance from man would also be g rea tly reduced. However, the decrease

was found to be only a fa c to r o f ten. This is reasonabie sihoe the

is o la tio n distance is a function o f the natural logarithm o f the in i t ia l

concentration9 and the natural log Of 10 is about 10.

The proper is o la tio n o f a waste form may then:be described as

both the temperature contro l o f the waste form to ensure lower disso­

lu tio n ra tes , and geometric is o la tio n o f the waste form in a ca re funy

seTected environment w ith favorable sorption c h a ra c te r is tic s . Thus» i t

is concluded tha t w ith the temporary storage o f a s o lid if ie d waste fo r

several years to lower heat generation rates and w ith carefu l s ite

se lection fo r the waste repos ito ry , h igh-leve l nuclear waste disposal

may be ca rried out ensuring minimum exposure o f man to radionuclides.

APPENDIX A

LISTING OF MAJOR RADIOISOTOPE COMPOSITION IN PUREX WASTES

Iso tope...■ .... ' ... v . .. • . . . .. ... .............. ; „ ...

' m wt%

FISSION PRODUCTS

V 8.97E-3 1.54E -3

129I : 6»49E-7 ; 6.39E-6

: 131, 3.07E-5 ' 4 .25E-6

89Sr 1.76 1.03E-1

■ : > ; 90s r 1.74 2.10E+1

90y 1.74 5.50E-3

: 91 y 3.63 2.55E-1

■ 95z , 6.36 5.13E-1

95raNb 1.35E-1 6.28E-4

95Nb 1.19E+1 5.21E-1

: 103Ru 2.25 1.216-1

103mRh 2.24 1.196-4

T06Ru 1 ,06E+1 5.35

106Rh 1.066+1 5.106-6

110mAg 5.91Et2 2.126-2

119mSn 6.29E-4 2.456-2

123mSn 4.57E-2 1.00E-2

39

Isotope wt%

125Sb : 1v52E-1 2.45E-1

1'25mTe 4.78E-2 4 .54E-3

127mte 7.61E-2 1.33E-2

Te : 7.49E-2 . 4 .84E-5

Te 1.T3E-1 6 .28E-3

129Ie T.13E-1 1 o08E-5

Cs 4 ,22 . 5.68

136Cs : 7 ,13E-4 1 . 65E-5

■ 137Cs 2.45 4 . 82E+1

137mBa 2.26 7 . 3TE-6

l40Ba 7 . 22E-3 1 . 69E-4

140La 8 . 30E-3 2 . 55E-5

141Ce 1.49 8 . 94E-2

144Ce 1 . 62E+1 8 .70

143Pr 1 . 278-2 3 . 26E-4

144Pr 1 . 62E+1 3 . 67E-4

Nd T.02E-3 2 . 17E-5

147Pm 2 .94 5.56

148Pm 4 . 71E-3 4 . 91E-5

151Sm 7 . 57E-3 . 4 . 91E-1

154Eu 1 . 805-1 2.12

155Eu 7 . 75E-2 9 . 75E-2

,uTb 3 . HE- 3 4 . 76E-4

41

■Isotope C i l : V Wt%

ACTINIDES

235U 4.00E-8 2.47E-1

238U 7, JOE-7 3.06E+1

238Np : 2.43E-3 1.23E-7

238Pu 1.69 1.28

239Pu 1.63E-1 3.52E+1

240Pu 3.06E-1 1.78E+1

241Pu ; ; ' 7.70E+1 J / 9.10

242Pu 1.46E-3 4.94

241 Am- 1.31E-1 - 5.34E-1

242Ara 2.43E-3 3.97E-8

242Cm 1.9TE+1 7.66E-2

243Cm : 1.171-2 3 .35E-3

244Cm 2.25 2.56E-1

APPENDIX B

WEIGHT FRACTIONS OF MAJOR FISSION PRODUCT RADIOISOTOPES

The absolute so lu tion in BorosiTicate Glass ra te o f each iso ­

tope from b o ro s ilica te g lass, unless otherwise determined, is the

product o f the bulk waste s o lid 1 each rate times the fra c tio n a l mass

which th a t isotope constitu tes o f the waste.

In th is ana lys is j the waste oxides constitu te about 22 wt% o f

the to ta l glass mass. In the waste oxides, the actual waste isotopes

are about 80 wt% o f the to ta l while the oxide is about 20 wt%. This

means tha t the actual waste radioisotope content is 17.6 wt%.

Appendix A presents the weight fra c tio n o f major fis s io n prod­

uct isotopes in wastes» The product o f the weight fra c tio n o f each

isotope o f a l l radioisotopes times the 0.176 mentioned above is the

weight fra c tio n o f each isotope in g la ss ifie d wastes. These frac tions

are presented in Table B - l .

42

43

Table B -L Weight Fractions o f Major Fission Product Radioisotopes in B o ros ilica te Glass

Isotope Weight Fraction Isotope Weight Fraction

89Sr 1.8IE-4 129mTe . I.ITEkS

90$r 3.70E-2 129fe 1,901-8

90y 9.68E-6134Cs . 1.001-2

91Y . 4.49E-4 ,36Cs 2.901-8

91mNb lv iiE -6,37Cs 8.501-2 V

95Nb 9.17E-4 137mBa I . 291-8

103Ru 2.13E-4 140Ba 2.971-7

103mRh 2.09E-7 UOla 4.491-8

106Ru9,42E*3

141Ce 1.571-4

106Rh 8.98E-9 144Ce T. 501-2

110mAg 3.73E-5 ' 144pr 6.461-7

119mSn 4.31E-5 147Nd 3.821-8

123mSn 1.7SE-5 147Pm 9.791-3

1253b 4.31E-4 148Pm • 8,641-6

125niTe 7,99E-6 151Sm 8.641-4

127mTe 2 .34E-5. 154Eu 3.731-3

127Te 8.52E-8155Eu

1.722-4

160Tb 8.382-7

APPENDIX C

WEIGHT FRACTION/OF ACTINIDES IN BOROSILICATE GLASS

Table I I shows the ra tio o f actin ides to f is s io n products in

POREX liq u id waste to be 0.190. In Appendix B, i t is Stated tha t the

fis s io n product isotopes constitu te 17.6 wt% o f the b o ro s i l lc a te glass

sol id . . This means actin ides are (0.176) x (0.190) or 3.36 wt% o f the

boros H i cate wastes. I f th is fig u re i s m u ltip lie d by the values o f

Weight each actin ide constitu tes o f a l1 actin ideS: the weight fra c tio n

o f the b o ro s ilica te waste each a c tin ide represents is determined.

These figures are shown in Table C - l.

Table C - l. Weight Fractions o f Actihides in B o ros ilica te Glass

Isotope Weight Fraction Isotope Weight Fraction

235u 8 .30E-5 241 Pu 3.06E-3

238u 1.03E-2 242PU 1.661-3

238Np 4.13E-11 24lAm 1.801-4238pu 4,30Er4' 242Am 1.331-11

239PU 1.181-2 242Cm 2.571-5

240Pu . 5.98E-3 243Cm 1.131-6

244Cm 8.61E-5

44

APPENDIX D

TABULATION OF MAXIMUM PERMISSIBLE OONCENTBATIONS (MPC) OF VARIOUS ISOTOPES IN WATER

Isotope MPC (Bq/m3) Isoltope MPC (Bq/m3)

3H 1.81E8 . 110mAg 1.11£6

85Kr N/A 119mSn ' 1.1TE6

131mXe N/A 123mSn 1.11E6

,29I 2.22E3 V 125Sb 3.70E6131, T.TLE4 125mTe - 7.40E6

89Sr T.1TE5 127mTe 2.22E6

90Sr 1.11E4 127Te 1.1TE790y 7.40E5 129mTe 1..11E591y 1.11E6 129Te : 2.96E7

95Zr 2 .22E6 134Cs 3.70E6

95mi!b 3.70E6 136Cs 3.33E6

95Nb 3.70E6 137Cs 7.70E5

,03Ru 2,96E6 137mBa 7.40E5

' 03mRh 3.70E8 140Ba T.TIE6

1G6Ru ‘ - 3 .70E5 140La 7.40E5

,06Rh 3 .70E5 l41Ce 3.33E6

144Ce 3.70E5 238u 1.48E7

45

46

Isotope MFC (Bq/m3) Isotope : MFC (Bq/m3)

143Pr 1.85E6 ' 238Np 1.11E3

W p r 3.70E5 238Fu 1,8525

147Nd. 2.22E6 239Pu 1.8525

,47Pm 7V40E6 240Pu 1.8525

"* 43Pm ■ 1.85E6 : 241Pu 7 . 4026 :

i6 ism : 1-48E7 . 242Pu 1.8525

,54EU 7.40E5 241Am 1.4825

: 155eu 7.70E6 242Am . 1.4825

160ib 1.48E6, 242Cm 7.4025235.J 1.1127 243Cm 1.8525

' 244Cm 2.59E5

APPESlX E

M0IO1SOWIG.RELEASES FROM WASTE FORMS VITREOUS: , FORM» LEACHANT AT 2!98K :

Mass Flow Rate fromi . f6\/1 4 %n v*

Waste Formpit (MR0-m3/s )

Isotopev jiin u e r1 Year

Wjf 1 lilUGI10 Years

UUucd1 Year

Cubes■ 10 Years

89Sr 28.9 171.3

90Sr : 294.7 236.3 T 1767.9 1417,8

90y 294.7 216,3. 1767,9 1417.8

91Y 61.9 37T.4

95Zr 5.4 32.2

98mNb 0.1 0.4

95Nb 6.1 36.6

103Ru1.4 8.6

1(33mRh 0.01 0.1

1Q6Ru53,9 0.1 323,2 0.6

106Rh 51.9 0.1 321,2 . 0,6

118% 0.1 ” *= 0,6

1l9mSn 0.1 0.6

123mSn 0.1 0.5

125Sb 3.7 0.4 22,3 2.2

48

linder '■ Cylinder CubesIsotope 1 Year 10 Years 1 Year

Te

Te

Te

Ba

0.1 - 0.4

127je 0.01 — 0.1

0.02 - - 0.1

0.01 ** 0.1

134q 2.6 : 0.1 : 16.5

136cs —- ” ™

T3?Gs 0.7 ; ' 0.6 4.3

0.7 0.6 4.3

140ga 0.01 — 0.1

!40ta 0.02 — 0.1

141c 0.8 — 5.1

144Ce 80.7 0.03 484.5

143pr 0.01 — 0.1

144pr 80.7 0.03 484.5

MdWpm 0.7 0.07 4.5

0.5 * - 2.9Pm

151Sm .

154Eu 0.5 0.3 2.7

1B5Eu 0.02 0.1

160jb — - - 0.02

Cubes 10 Years

0.8

3.5

3.5

0.2

0.2

0.4

1.9

49

Cylinder Cylinder Cubes CubesIsotope 1 Year 10 Yeans I Year 10 Years

238^p ™- .0.02 “ “

Z3Spu 0.01 0.01 0.07 0.07

239pu 1.2E-3 1.2E-3 7.0E-3 7.0E-3

24QpiJ . ; >' 2 .2E -3- 2.2E-3 0.01 0.01

241.pu . 0.01 8.6E-3 0 .0 8 . 0.05

242pu 1.QE-5 1.0E-5 6.3E-5 6.3E-3

241Am 1.2E-3 1 .2E-3 7.0E-3 6.9E-3

242Am 2.2E-5 — 1.3E-4

242q^ 0.03 0 .2

2 4 3 ^ 8.3E-5 6.8E-5 5.0E-4 4.1E-4

244r 8.2E-3 5.8E-3 0.05 0.03

APPENDIX F

RADIOISOTOPIC RELEASES FROM WASTE FORMS OEVITRIFTED FORM, LEACHANT AT 298K .

Mass Flow Rate from Waste Form (MPC-m /s ) Cylinder Cylinder Cubes Cubes

Isotope 1 Year TO Years 1 Year 10 Years

89Sr 207.2 — 1243.3

90Sr 2118.1 / ; 1699.0 12710 . 10194

90Y 2118.1 1699.0 12710 10194

91Y 5183.2 — 31099

95Zr 4500.2 27000

95mNb 58.0 — 347.8

95Nb 5120.1 — 30720

108Ru 1193.9 — 7163.5 r - ' ■

103mRh 1193.9 — 7163.5

106Ru 45230 88.3 271400 530.1

106Eh 45230 88.3 271400 530.1

110mAg 83.8 0.01 502.8 0,05

119mSn 89 0 0.01 533.8 0.06

123rnSn 64.9 — 389.2 - -

125Sb 64.3 6.4 385.7 38.2

125mTe 10.2 — 61.0 —

127raTe 54.1 — 324.8

50

51

Cylinder Cylinder Cubes CubesIsotope 1 Year 10 Years 1 Year 10 Years

U /Te 10.7 64.1

127mTe 160.7 -oo» 964.3

129le 7.3 44.1

134Cs 35.3 1.8 211.8 10.9

136Cs

137Cs : 9.2 ; 7.5 55.4 45.0

137mBa ■ ; 9.2 7.5 55.4 45.0

140Ba 10.2 61.3

143U 6.3 37.5

l41Ce 740.5 4442.8

144Ce 67730 23.0 406400 137.8

143Pr 10.8 65.1

144Pr 67730 23.0 606400 137.8

147Nd 0.7 . 4,3

147Pm 625.7 62.1 3754.0 , 382,4

148Pm 398.4 2390,1

151Sm 0.8 0.8 4.8 4.5

154Eu 383.4 259.4 2300.6 1556.7

155Eu 16.6 0,4 99.5 2,5

160Tb 3.3 20.0

235U •

238u

52

IsotopeCylinder

1 YearCylinder 10 Years

Cufees . 1 Year

Cubes 10 Years

238Np 9.01*4 5.4E-3

238PU 3 .7E-3 3.5E*3 0.02 0.02

239Pu 3.6E*4 3.6E-4 . 2.2E-3 2.2E-3

2M?u 6.8E*4 6.8E-4 4 .1|*3 . 4.1E*3

245 ?u 4.2E-3 2.6E-3 . 0.03 0,02 .;

242PU 3.2E*6 3.2E-6 1.91^5 1.9E--5

2MAm 3.6E*4 : v 3.6E*4 : ' 2.2E-3 /y .;-'-2.2 i»3 ;-:

242a« 6.7E-6 , 4.31*5

242Cm 0.01 0.06

243Cm 2.6£*5 ■ 2.1E-5 1 .5E*4 1.3E*4

244Cm 2.5E-3 1.8E-3 0.02 0.01

APPENDIX 6

RADIOISOTOPE RELEASE FROM WASTE FORMS VITREOUS . FORM, LEACHANT AT 372K

Mass Flow Rate from Waste Form (MPC-m^/s) lin d e r Cylinder Cubes .Cubes

Ru

Ag

Isotope : 1 Year TO Years 1 Year 10 Years

S9Sr 199.8 — 1198.5 -

90Sr 2049.2 ; 1641.6 12295 9849.8

90y 2049.2 1641.6 12295 9849.8

91y 43.2 - . 259.0

95Zr 37.5 — 224.9 -

OSm 0.5 2=9

9 5 ^ 42.5 254.9

T03ru 10.0 59.9 “ “

103m^ 0.08 — 0.5

374.8 0.7 2248.9 4.4

106Rh 374.8 0.7 2248.9 4.4

0.7 — 4 .2

n9mSn 0.7 - 4.5

123nign 0.5 3.2

Sb 0.5 0.05 3.2 0.3

53

54

Cylinder Cylinder Cubes CubesIsotope 1 Year TO Years 1 Year TO Years

e

Te

te

0» 8 =- 5.1

127niT6 0,4 — ; 2.7

0.09 0.5

1.3 8.0

12 9^ 0.06 — 0.4. -

134Cs 166.5 8.6 998.8 ■ 51.3

136cs “ “ Q.02 —-

137€s 43.7 35.5 262.1 212.8

137% 43.7 35.5 262.1 212.8

140gg 0.08 _ ■ 0.5 - -

140^a 0,1 0.9 , - -

14Tce 5.9 35.1 ■“ t

T44Cg 561.9 0 .2 3371.7 : 1.1

143pr 0.09 — 0.5

144pr 561.9 0.2 . 3371.7 1.1

347Nd 0,04 - -

147ps 5.2 0.5 31.3 3.1

T48pm 3.3 - 19.9

T5Tsm ” = 0.04 0,04

154Eu 0.3 . 0.2 1.9 1.3

155Eu 0.1 — 0.8 0.02

160 j b 0.3 — 1.7

Cylinder Cylinder Cubes CubesIsotope 1 Year 10 Years 1 Year 10 Years

£ ODy

238u c4““

238np 0.04 0.3

238Pu 0.2 0.2 1.1 1.0

239Pu 0.02 0.02 0,1 0.1

240Pu ■ 0.03 : 0.03 ; 0.2 0.2

241Pu 0.2 0.1 1.2 0.8

242?u 1.5E-4 1.5E-4 ' • 9..21-4 9.2

24' ari0.02 0.02 0.1 0.1

CM 3.2E-4 1.9E-3 •=”

242Cm 0.5 3,0

243Cm 1.2E-3 1.0E-3 7.31=3 6.0

244Cm 0.1 0.08 0.7 0.5

APPENDIX H

RADIOlSOfGPlC RELEASES FROM WASTE FORMS, MODELED FORM AT ONE DAY OF LEACHING, WASTE AGE — TO YEARS

Mass Flow Rate from Waste From (MPC-m^/s)Isotope Cyfinder - - HgO a t 298K Cylinder — HgO at

90Sr ‘ 6841.8 9621.0

90Y. . 1 0 5 . 4 148.1

1Q6Ru / ; ' 8 . ( 1 9 : .4.35 :

106Rh 0.0117 0.0165

125Sb 0.266 0.318

Cs 3.25 4.6

Cs 149.6 210.4

137mBa 137.9 194.0

147Pm 2.66 3.74

l51Sm 0.0265 0.0372

154Eu 9.2 12.9

155Eu 0.0172 0.0242

235U 2.95E-10 4.15E-10

238U 4.28E-9 6.03E-9

■Pu 0.676 0.949

239Pu 0.0723 0.102

240Pu 0.131 0.185

56

57

Isotope Cylinder --HgO a t 298K Cylinder - - HgO a t 372K

241Pu 0.539 0,756

Pu 6,46E-4 9 .1 0 W

Am 0.0726 0.102

242Am 1.61E-8 2.34E-8

243Cm . 4.28E-3 6.03E-3

244Cm 0.351 0.494

APPENDIX I

; ' : NUMERICAL UNITS

Calculations performed in th is work are carried out in the Sys­

tems Internationa 1 or SI un its . This section 11ists some o f these un its

w ith the conventi onal engineering counterparts. In a dd ition , a m u lti-

p ly ing fa c to r to convert the SI u n it to the commntional u n it is in -

eluded.

Conventional M u ltip ly ingSI Unit Unit Factor

Mg/(m2s) g/(cm2day;) 8 .640E-6

W/mK B tu / f th r0F 1.872

kg/m3 g/cm3 1.0E-3

J/kgK B tu /lh m0F 7.755E-4

TJ/kgU MWD/MTU 2.778E5

EBq/m3 Ci/1 2.703E4 '

PBq/ffl3 Ci/1 2.703E1

53

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