Radionuclide Sorption Mechanisms and Rates on Granitic Rock

3 Radionuclide Sorption Mechanisms and Rates on Granitic Rock Determination by Selective Chemical Extraction Techniques F. B. WALTON, T. W. MELNYK, J. P. M. ROSS, and A. M. M. SKEET Atomic Energy of Canada Limited, Whiteshell Nuclear Research Establishment, Pinawa, Manitoba R0E 1L0 Canada

Downloaded by CORNELL UNIV on August 8, 2016 | http://pubs.acs.org Publication Date: March 8, 1984 | doi: 10.1021/bk-1984-0246.ch003

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The gamma-emitting radionuclides Cs, Ce, Se and Co were simultaneously contacted with granite from the Lac du Bonnet batholith using both static and dynamic methods. Selective chemical extraction was then used to differentiate between the amounts of sorbed radionuclides that are (a) readily ionexchangeable, (b) associated with amorphous oxyhydroxide deposits, and (c) "fixed" by other mineralogical or physical processes. Comparison of the experimental results from the dynamic tests with calculations from single sorption site kinetic models, using a variety of isotherms, showed that the models did not adequately describe the sorption reactions. Use of double sorption site models greatly improved the ability to describe solution concentrations and radionuclide surface inventories measured by extraction methods. Laboratory alteration of fresh granite surfaces was found to affect the sorption capacities and ratios of Co, Se and Ce. Granite alteration on a laboratory time scale had no effect on Cs sorption. Rate constants determined for the various processes indicate that under oxidizing conditions ionexchange processes are rapid, with equilibrium achieved within days. Reactions with oxyhydroxides or other mineralogical or physical processes take longer to achieve equilibrium, but, on time scales relevant to groundwater flow rates, will provide more significant retardation of the radionuclide migration than ion exchange. 60

60

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0097-6156/ 84/ 0246-0045S06.25/ 0 © 1984 American Chemical Society

Barney et al.; Geochemical Behavior of Disposed Radioactive Waste ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

46

GEOCHEMICAL BEHAVIOR O F RADIOACTIVE WASTE

The l o c a t i o n and p h y s i c a l complexity of hard-rock f r a c t u r e systems make i t d i f f i c u l t to determine the mechanisms a f f e c t i n g r a d i o n u c l i d e m i g r a t i o n under f i e l d c o n d i t i o n s . Techniques are needed that, under c l o s e l y c o n t r o l l e d c o n d i t i o n s , provide data r e l e v a n t to mass transport i n the f i e l d . Development of two such techniques i s described here. Knowledge of s o r p t i o n k i n e t i c s i s e s s e n t i a l f o r the design of l a b o r a t o r y or f i e l d r a d i o n u c l i d e m i g r a t i o n experiments. There are two requirements f o r the r e t a r d a t i o n of r a d i o n u c l i d e migration: f i r s t , an i n t e r a c t i o n between the r a d i o n u c l i d e and the g e o l o g i c m a t e r i a l , and second, s u f f i c i e n t time f o r the i n t e r a c t i o n to occur. C r i t e r i a f o r assessing the l a t t e r requirement have been developed (1) i n terms of a dimensionless s o r p t i o n rate parameter 3 kAt /V, where k i s the s o r p t i o n ( f i r s t order) r a t e constant, t i s tîîe water t r a n s i t time (the time taken f o r w groundwater to flow between two observation p o i n t s ) , and A/V i s the r a t i o of the g r a n i t e surface area to the groundwater volume. The degree of r e t a r d a t i o n provided by a given chemical mechanism i s r e l a t e d not only to the e q u i l i b r i u m d i s t r i b u t i o n parameter, k , but a l s o to the s o r p t i o n rate parameter, 3. For instance, a pulse i n j e c t i o n of a r a d i o n u c l i d e w i l l t r a v e l with the groundwater and d i s p l a y only t a i l i n g f o r 0.1 < β < 1. On the other hand, complete r e t a r d a t i o n , according to the value of k can be assumed f o r 3 > 100. For intermediate values of 3, k i n e t i c peak broadening w i l l occur. In these s t u d i e s a dynamic t e s t i n g method (the m i x i n g - c e l l ) has been used to measure the s o r p t i o n k i n e t i c s of 4 d i f f e r e n t r a d i o n u c l i d e s on Lac du Bonnet g r a n i t e from the Archean Superior Province of the Canadian S h i e l d . This method has been used p r e v i o u s l y (2) f o r measurement of s o r p t i o n k i n e t i c s without the i n t e r f e r e n c e of h y d r a u l i c d i s p e r s i o n common i n many other dynamic techniques· A v a r i e t y of chemical e x t r a c t i o n techniques has been developed by s o i l s c i e n t i s t s to determine q u a n t i t a t i v e l y the amount of trace metals bound to s o i l p a r t i c l e s by various mechan isms. Multimechanism s o r p t i o n has been suggested i n order to e x p l a i n p a r t i a l i r r e v e r s i b i l i t y of r a d i o n u c l i d e s o r p t i o n and i n creased s o r p t i o n with exposure time. The f i v e main s o r p t i o n mechanisms that have been reported a r e :


s

fl

1. 2. 3. 4. 5.

exchange with CaCl^ or M g C l , binding by carbonates, binding by organic compounds, s o r p t i o n by i r o n or manganese oxyhydroxides, and r e s i d u a l or " f i x e d " m a t e r i a l . 2

Since the m i x i n g - c e l l experiments were conducted with f r e s h or s l i g h t l y weathered g r a n i t e s u r f a c e s , techniques f o r determin ing s o r p t i o n by carbonates and organic compounds were omitted. Using e x t r a c t i o n techniques to determine r a d i o n u c l i d e sorbed by


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Radionuclide Sorption Mechanisms and Rates

47

mechanisms 1, 4 and 5 above on both m i x i n g - c e l l s and g r a n i t e coupons, i t was found that r a d i o n u c l i d e s o r p t i o n can be c o n s i d e r ed q u a n t i t a t i v e l y to i n v o l v e at l e a s t two mechanisms with varying rates of r e a c t i o n . In a d d i t i o n , rock a l t e r a t i o n k i n e t i c s p a r t i c u l a r l y when f r e s h rock i s used - were found to s t r o n g l y a f f e c t the s o r p t i o n of some r a d i o n u c l i d e s .


Theory and S o r p t i o n Models In order to assess the f e a s i b i l i t y of any nuclear waste d i s p o s a l concept, mathematical models of r a d i o n u c l i d e s o r p t i o n processes are r e q u i r e d . In a l a t e r s e c t i o n k i n e t i c d e s c r i p t i o n s of the three common s o r p t i o n isotherms (3) are compared with experiment a l data from the m i x i n g - c e l l t e s t s . For a r a d i o n u c l i d e of con c e n t r a t i o n C i n the groundwater and concentration S on the sur face of the g r a n i t e , the net r a t e of s o r p t i o n , by a f i r s t - o r d e r r e v e r s i b l e r e a c t i o n , i s given by dS/dt » k C - k S x

(1)

2

where k, and k~ are the s o r p t i o n and desorption r a t e constants r e s p e c t i v e l y , V i s the f l u i d volume and A i s the g r a n i t e surface area. For a F r e u n d l i c h isotherm the net r a t e of s o r p t i o n can be expressed as dS/dt = k.C (C/C ) l o o

n

- k S

(2)

0

I

where η i s a constant and C i s the i n i t i a l t r a c e r concentration i n the groundwater. ° For a Langmuir s o r p t i o n isotherm the net s o r p t i o n r a t e can be written dS/dt = k.C(S - S)/S - k S ι ο ο ζ 0

(3)

where S i s the maximum surface concentration of r a d i o n u c l i d e . As w i l l be shown l a t e r , s o r p t i o n of most r a d i o n u c l i d e s may be a f u n c t i o n of two or more mechanisms. The combination two f i r s t - o r d e r r e a c t i o n s has been s u c c e s s f u l l y a p p l i e d to Sr m i g r a t i o n over a twenty-year time period i n a sandy-aquifer ( 1 ) . The equations d e s c r i b i n g two p a r a l l e l f i r s t - o r d e r r e a c t i o n s are S = S, + S dS /ά\ = k*C - k ^ dS^/dt = k^C - k^S χ

2

[ ,

(4)

The theory and v e r i f i c a t i o n of the m i x i n g - c e l l mass balance equation has been reported p r e v i o u s l y ( 2 ) . For a c e l l with i n i t i a l concentration of t r a c e r , C . flushed with t r a c e r - f r e e ο water at a volumetric r a t e , W, the mass balance i s given by

American Chemical Society Library 1155 16th St., N.W.

Barney et al.; Geochemical Behavior of Disposed Radioactive Waste Washington, D.C. 20036 ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

48

GEOCHEMICAL BEHAVIOR OF RADIOACTIVE WASTE

VdC/dt - -WC

- A(dS/dt)

For the s p e c i a l case of a non-reactive Equation 5 gives C(t)/C

Q

(5) t r a c e r , i n t e g r a t i o n of

» exp(-tW/V)

(6)


Experimental A c t i v e Coupon Experiments* Coupons (19.8 χ 19.8 χ 4.00 mm) of Lac du Bonnet g r a n i t e , obtained from the Cold Spring Quarry near the W h i t e s h e l l Nuclear Research Establishment (WNRE), Pinawa, Manitoba, were exposed to g r a n i t e groundwater anji brings ço^taining^ghe gamma-emitting n u c l i d e s Cs, Ce, Se, Sb, Sn and Co. Pétrographie and chemical analyses of the g r a n i t e are given i n Table I ( 4 ) . Radionuclides were obtained c a r r i e r - f r e e from New England Nuclear. Groundwater compositions and r a d i o n u c l i d e s t a r t i n g concentrations are given i n Tables I I am} I I I . A rock surface area to s o l u t i o n volume r a t i o of ^ 1 cm /mL, approximately the same as the r a t i o i n the m i x i n g - c e l l experiments, was used i n these t e s t s . The f o l l o w i n g procedures, i n order of a p p l i c a t i o n , were used to determine the l o c a t i o n s and q u a n t i t i e s of r a d i o n u c l i d e s a s s o c i a t e d with v a r i o u s s o r p t i o n mechanisms: 1.

2.

3. 4.

5.

6.

7.

The coupons were contacted with g r a n i t e groundwater or b r i n e c o n t a i n i n g s i x r a d i o n u c l i d e s f o r 28 d. The coupons were removed and the s o l u t i o n s assayed to determine the amount of sorbed r a d i o n u c l i d e s . The coupons were contacted with t r a c e r - f r e e groundwater s o l u t i o n s , which were assayed a f t e r 28 d to determine the amount of a c t i v i t y that i s r e v e r s i b l y bound to the g r a n i t e under normal groundwater c o n d i t i o n s . The coupons were contacted with 0.5 mol/L CaCl« s o l u t i o n f o r 72 h to d i s p l a c e a l l remaining exchangeable r a d i o n u c l i d e s . The coupons were contacted f o r 24 h with a s o l u t i o n (termed KTOX) c o n t a i n i n g 0.1 mol/L potassium t e t r a o x a l a t e and 0.1 mol/L hydroxylamine hydrochloride to remove r a d i o n u c l i d e s a s s o c i a t e d with i r o n and manganese oxyhydroxides. The coupons were contacted with b o i l i n g Na^CO^ s o l u t i o n (5 wt%) f o r 15 min to remove r a d i o n u c l i d e s a s s o c i a t e d with hydrated s i l i c a t e s . The coupons were contacted f o r a second 48 h period with KTOX s o l u t i o n to remove some of the r a d i o n u c l i d e s a s s o c i a t e d with l a t t i c e s u b s t i t u t i o n into iron-bearing minerals. The coupons were gamma counted to determine r e s i d u a l or f i x e d activity.

I n a c t i v e Coupon Experiments. A f r e s h cut surface of Lac du Bonnet g r a n i t e contains both a l t e r e d and unaltered ferromagnesian



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WALTON ET AL.


49

minerals ( 4 ) . Exposing the unaltered or p a r t i a l l y a l t e r e d phases to groundwater s o l u t i o n s during an experiment w i l l produce f u r t h e r phase a l t e r a t i o n . Since KTOX s o l u t i o n s e l e c t i v e l y d i s s o l v e s oxyhydroxide phases, i t can be used to monitor t h e i r production d u r i n g a l t e r a t i o n . A second s e r i e s of i n a c t i v e e x p e r i ments was performed to study a l t e r a t i o n r a t e s of f r e s h g r a n i t e coupon s u r f a c e s . The coupons were u l t r a s o n i c a l l y cleaned and placed i n a s o l u t i o n of GGW f o r 101 d. They were then leached with KTOX s o l u t i o n f o r incremental times of 1,2,3,6,12,24,24 and 48 h, with the s o l u t i o n being renewed at each time i n t e r v a l . The same e x t r a c t i o n procedure was a p p l i e d to f r e s h l y cut coupons. The KTOX s o l u t i o n s were analyzed by i n d u c t i v e l y coupled plasma (ICP) spectrophotometry f o r i r o n i n order to c a l c u l a t e oxyhydroxide e x t r a c t i o n r a t e s as a f u n c t i o n of cumulative exposure to KTOX s o l u t i o n . 2 A g r a n i t e surface area to e x t r a c t i o n s o l u t i o n volume of * 1 cm /mL was used i n a l l e x t r a c t i o n procedures.

Table I .

M i n e r a l and Chemical Composition of Lac du Bonnet G r a n i t e (4)

Mineral

Modal Percent

Oxide

Weight Percent

Quartz

25.8

sio

K-feldspar

28.1

A1 0

Plagioclase

33.9

FeO

0.81

F e

0.76

73.1

2

2

3

14.2

Biotite

5.2

Muscovite

2.5

2°3 CaO

Opaques

0.7

MgO

Epidote

1.5

Na 0

4.23

Chlorite

2.3

κο

4.88

0.46 2

2

Tio

2

0.03

H0

n.d.

co 100.0

0.22

MnO 2

Total

1.43

2

Total

n.d. 100.09

n.d. - below l e v e l of d e t e c t i o n


50

GEOCHEMICAL BEHAVIOR O F RADIOACTIVE WASTE

Table I I . Groundwater Compositions (mg/L) *1

Brine

GGW +

Na K

Mg

2 +

Ca

2 +

Sr

2 +

F


+

8.3

5,050

3.5

50

3.9

200 15,000

13

-*2

e

t Si

HCO; Cl~ 2

20

15 10

5.0

34,260

so " 4 NO^

8.6

790

0.62

50

F~

0.19

-

pH

6.5±0.5

7±0.5

*1 ^2 GGW g r a n i t e groundwater In e q u i l i b r i u m with C0^ i n atmosphere s

Table I I I .

C a r r i e r - F r e e Radionuclide S t a r t i n g Concentrations Isotope

Starting,concentration (10 Bq/mL)

*Jco

26.9

t~ Ce ti'cs

53.3 27.7

7

n

*

Specific U 4

Ce

5.2Ί0

2.05 1.37 0.347

a c t i v i t i e s of isotopes i n Bq/g are:

- 1.2Ί0 1 4

*ÎSb ^Se Sn

;

1 1 3

1 4

;

1 3 7

Cs

- 3.2Ί0

Sn - 3.7Ί0

1 2

;

1 2 5

60 13 Co - 4.2·10 ;

Sb - 3.9Ί0

1 3

;

7 5

Se -

1 4

M i x i n g - C e l l Experiments. A schematic diagram o f a t y p i c a l c e l l used i n these experiments i s shown i n Figure 1. The c e l l s are



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51

c i r c u l a r i n c r o s s - s e c t i o n and are f a b r i c a t e d by a double diamondd r i l l c o r i n g operation on a s l a b of Lac du Bonnet g r a n i t e . Two sets of experiments were conducted using s i x r a d i o a c t i v e t r a c e r s simultaneously. S t a r t i n g concentrations are given i n Table I I I . Radionuclides were e l u t e d from the c e l l s with groundwater s o l u t i o n s using a p e r i s t a l t i c pump. E f f l u e n t was c o l l e c t e d at 90-min i n t e r v a l s by means of a f r a c t i o n c o l l e c t o r connected to the c e l l with small-bore T e f l o n tubing. Concentrations of the various isotopes i n the e f f l u e n t were measured by gamma spectrometry. In the f i r s t set of experiments, s i x c e l l s were u l t r a s o n i c a l l y cleaned to remove rock powder produced during c o r i n g , and then f l u s h e d before t r a c e r i n j e c t i o n . Three were f l u s h e d with GGW and three with b r i n e . A second set of experiments was designed to determine whether mineral a l t e r a t i o n ratés and/or s o l u t i o n temperature a f f e c t the r a t e of r a d i o n u c l i d e i n t e r a c t i o n w i t h g r a n i t e . (Test c o n d i t i o n s a r e given i n Table VI o f the Results S e c t i o n ) . The 60°C temperature was maintained by submerging the c e l l s i n a water bath. Two c e l l s were f l u s h e d with GGW f o r s e v e r a l weeks and then allowed t o s i t , f i l l e d with GGW, f o r approximately f i v e months before the experiment was s t a r t e d . A f t e r both sets of experiments were completed, the groundwater was drained from the c e l l s and s e l e c t i v e chemical e x t r a c t ions of the g r a n i t e c e l l walls were performed. The c e l l s were f i l l e d with 0.5 mol/L CaCl- s o l u t i o n and s t i r r e d continuously f o r 72 h t o d i s p l a c e exchangeable r a d i o n u c l i d e s . A f t e r a r i n s e with demineralized water to remove r e s i d u a l C a C l s o l u t i o n , the c e l l s were f i l l e d with KTOX s o l u t i o n and s t i r r e d f o r 24 h t o remove r a d i o n u c l i d e s a s s o c i a t e d with oxyhydroxides. A l l s o l u t i o n s were analyzed by gamma spectrometry t o determine the amounts of r a d i o n u c l i d e s e x t r a c t e d . Residual a c t i v i t y was measured by d i r e c t gamma counting of the c e l l s . 9

Results E x t r a c t i o n of I n a c t i v e Coupons with KTOX S o l u t i o n . Average i r o n e x t r a c t i o n rates are p l o t t e d as a f u n c t i o n o f cumulative e x t r a c t ion time i n Figure 2. Where r a t e s f o r the a l t e r e d and unaltered g r a n i t e d i f f e r , the confidence l e v e l a t which the d i f f e r e n c e i s s i g n i f i c a n t i s i n d i c a t e d i n brackets. During the f i r s t s i x hours of e x t r a c t i o n , more i r o n i s r e moved from the a l t e r e d g r a n i t e than from the f r e s h g r a n i t e . The extra i r o n from the a l t e r e d g r a n i t e i s b e l i e v e d t o be that associ a t e d with the production o f i r o n oxyhydroxides during the 101-d exposure of the g r a n i t e to GGW. The i r o n e x t r a c t i o n r a t e s f o r both f r e s h and a l t e r e d g r a n i t e decrease f o r the f i r s t 24 h and become the same constant r a t e f o r the remaining 24 t o 120 h . Thus the i r o n a s s o c i a t e d with oxyhydroxides (formed during recent exposure to GGW or during hydrothermal a l t e r a t i o n ) i s removed during the f i r s t 24-h exposure to




Figure 1.

C r o s s - s e c t i o n a l view of c y l i n d r i c a l m i x i n g - c e l l .

2 7 (90%) Ε 6

I

I FRESH GRANITE

HI GRANITE ALTERED 101 d IN GRANITE GROUNDWATER

^ 5 (95%)

< cr

4

( ) CONFIDENCE LEVEL OXYHYDROXIDES FORMED DURING 101 d "EXPOSURE TO GRANITE GROUNDWATER

3

cr hx

IRON OXYHYDROXIDES

LU

-z. Ο cr

2 3 4 5 6 12 24 48 72 120 CUMULATIVE EXPOSURE TIME (h) TO KTOX

F i g u r e 2. Average i r o n e x t r a c t i o n rates f o r f r e s h and a l t e r e d Lac Du Bonnet g r a n i t e as a f u n c t i o n of cumulative e x t r a c t i o n time.


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53

KTOX. Iron extracted during the subsequent 24 to 120 h i s probably a s s o c i a t e d with the i r o n - b e a r i n g minerals (e.g. magnetite). This hypothesis i s c o n s i s t e n t with autoradiographic s t u d i e s des c r i b e d i n the f o l l o w i n g s e c t i o n . S e l e c t i v e Chemical E x t r a c t i o n of A c t i v e Coupons. Using gamma spectrometric a n a l y s i s of the groundwaters i n the s o r p t i o n and desorption steps, d i s t r i b u t i g n coe||^cienÇj^(k )ytjave f f f c a l c u l a t e d f o r the isotopes Co, Cs, Cef Se, Sb and Sn. Values of k f o r these isotopes i n GGW and b r i n e have been reported elsewhere ( 2 ) . Figure 3(A) shows a photograph of a t y p i c a l g r a n i t e coupon that was exposed to the GGW s o l u t i o n . Autoradiographs of t h i s coupon a f t e r a 28-d GGW d e s o r p t i o n , a 72-h C a C U e x t r a c t i o n and a 24-h KTOX e x t r a c t i o n ( F i g u r e s 3(B), (C) and (D)) i n d i c a t e that the areas of most h i g h l y concentrated a c t i v i t y ( l i g h t areas i n the autoradiographs) correspond to ferromagnesian and/or other dark, i r o n - b e a r i n g minerals i n the photograph. However, Figure 3(B) shows that there i s some s o r p t i o n on a l l mineral phases. F i g u r e 3(C) shows a darkening of a l l areas a f t e r CaCl^ e x t r a c t i o n , i n d i c a t i n g the removal of exchangeable a c t i v i t y from a l l areas. Figure 3(D), taken a f t e r the 24-h KTOX e x t r a c t i o n , shows a decrease i n a c t i v i t y i n the l o c a t ion of the i r o n - b e a r i n g minerals and v i r t u a l e l i m i n a t i o n of a c t i v i t y i n a l l other areas. I t i s not p o s s i b l e to d i s c e r n the behaviour of any i n d i v i d u a l n u g l i d e ^ y o m t^g^e auj^radio^çaphs; £j>yever, sgççific studies of Sr, Cs, Ce, Pu, Se, Pm and Am, using a combination of autoradiographic and pétrographie techniques, i n d i c a t e a c l e a r preference f o r s o r p t i o n on ferromagnesians, opaques and t h e i r a l t e r a t i o n products (4,5). The amount of r a d i o n u c l i d e removed from the g r a n i t e i n the groundwater desorption and s e l e c t i v e e x t r a c t i o n procedures wgg measured,by gammayspectrometry. The data i s summarized f o r Co, Cs, Ce and Se i n Figure 4. In t h i s f i g u r e the percentage of the i n i t i a l r a d i o n u c l i d e inventory sorbed during contact with the two groundwaters i s i n d i c a t e d n u m e r i c a l l y . In the bar chart the t o t a l amount of sorbed a c t i v i t y has been normalized i n order to compare the r e l a t i v e amounts of s o r b e ^ 2 § y^Ç ^ by the d i f f e r e n t reagents. A c t i v i t i e s f o r Sb and Sn were below background d e t e c t i o n l i m i t s . The a c t i v i t y on the surface of the g r a n i t e a f t e r the 28-d s o r p t i o n has been d i v i d e d i n t o four c a t e g o r i e s : exchangeable, a s s o c i a t e d with oxyhydroxides, associ a t e d with hydrated s i l i c a t e s , and " f i x e d " to ferromagnesians, t h e i r a l t e r a t i o n products and/or other opaque mineral phases. There are three s i g n i f i c a n t features i n Figure 4. F i r s t , the various s o r p t i o n mechanisms a f f e c t each n u c l i d e d i f f e r e n t l y . Second, the amount of each r a d i o n u c l i d e that i s exchangeable or r e v e r s i b l y sorbed i s l e s s than 50% f o r a l l n u c l i d e s t e s t e d . In 28 days, more than 50% of the sorbed r a d i o n u c l i d e s have undergone phase transformation or reacted with oxyhydroxides to form nonexchangeable phases. T h i r d , f o r a given r a d i o n u c l i d e , the n


a

c t i v i t

x t r a c t e
Μ ιΗ

Φ

Ο

αΙ δ Φ c ο

•ρ to 3

U

•H Ρ Cd Pu f-l CM Pu Pu h J Q


3.


WALTON ET AL. G S -

57

Granite Groundwater Saline Groundwater

Groundwater

G

% Sorbed

59 9

S

2 8 - day Desorption 43

81 4 8

CaCL

55 18 I

100

1

80

I

First 2 4 - h Hot N a C 0 2

Exchangeable

KTOX-Oxyhydroxides

3

-

Hydrated Silicates

Second 4 8 - h K T O X 60

h

"Fixed"

Residual

i Is*

40


20

0 60,

137,

Co

Cs

144,

75

Ce

Se

F i g u r e 4. Percentage of sorbed r a d i o n u c l i d e s as a f u n c t i o n of v a r i o u s s o r p t i o n mechanisms f o r 28-cli contact with 60ç _ 1 3 7 _ , 144 e- and ^Se-doped g r a n i t e and s a l i n e groundwaters. o

Cs

C

χ

6 0

CO

ο

EXPERIMENTAL DATA NO SORPTION LINE

rr

SINGLE FIRST ORDER MODEL

LJJ

ο ζ ο ο

DOUBLE FIRST ORDER MODEL

Lu > Lu

5

10

15

20

25

RELATIVE TIME (CELL VOLUMES) F i g u r e 5. Comparison of s i n g l e f i r s t - o r d e r and f i r s t - o r d e r models to 6 0 ç m i x i n g - c e l l data.

double

o



58

Table V.

Double F i r s t - O r d e r Model Parameters and F i t Variance

Isotope Reference Variance


60

Co

137

Cs

144 Ce

75

Se

Rate Constants χ 10

3 37 34 33 4 35

0.010 0.010 0.025 0.056 0.020 0.007

η «cm 21.0 1.87 3.59 265. 3.27 0.500

6.96 11.6 5.52 33.2 9.87 7.17

η «cm 17.0 1.61 17.2 67.6 2.19 0.763

0.374 1.67 3.11 0.189 0.496 0.629

3 37 34 33 4 35

0.016 0.020 0.004 0.007 0.006 0.013

3.35 17.2 6.86 2.90 0.622 0.482

9.97 33.2 17.0 16.6 9.69 10.0

2.34 2.08 1.27 0.952 0.213 0.102

0.687 2.48 2.07 2.09 0.300 1.75

3 37 34 33 4 35

0.037 0.050 0.069 0.218 0.034 0.017

3 37 34 33 4 35

0.036 0.034 0.046 0.069 0.019 0.030

113. 1130. 6.19 227. 25.1 2.31 1.72 1.90 1.20 0.602 0.518 0.856

9.28 58.8 3.09 142. 9.20 9.89 13.8 15.6 10.1 9.73 8.59 13.2

83.1 46.9 12-8 30.1 17.0 1.18 0.447 0.703 0.887 1.66 0.789 0.994


0.475 0.211 0.054 0.671 0.225 1.36 0.383 1.19 0.487 0.225 0.158 0.309

3.

Radionuclide

WALTON ET AL.

Sorption

Mechanisms

and

Rates

59

e q u i l i b r i u m d i s t r i b u t i o n c o e f f i c i e n t s ( k ) which can be c a l c u l a t ed by assuming dS^/dt and dS2/dt are zero i n Equation 4 as time becomes l a r g e * k

k

al " a2

=

( S

( S

1

2

/ C )

/ C )

=

Radionuclide Sorption Mechanisms and Rates on Granitic Rock

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