Effects of Water Flow Rates on Leaching - ACS Symposium Series

22 Effects of Water Flow Rates on Leaching 1

C. PESCATORE

University of Illinois at Urbana-Champaign, Urbana, IL 61801 A. J. MACHIELS

Downloaded by UNIV LAVAL on December 15, 2015 | http://pubs.acs.org Publication Date: March 8, 1984 | doi: 10.1021/bk-1984-0246.ch022

University of Illinois at Urbana-Champaign, Nuclear Engineering Program, Electric Power Research Institute, Palo Alto, CA 94303

Waste form leach rates in a geologic repository will be affected by unknown water flow rates and by extensive cracking of the waste form monolith. An understanding of these effects is important in predicting the geochemical behavior of disposed radioactive waste forms over the full range of possible scenarios. The dependence of the waste form source term on the rate of renewal of aqueous solution is first established for the simple but important case of solubility-limited network dissolution control. Next, the case of selective leaching control is investigated. Leaching in the presence of both mechanisms is then explored by using the mechanistic leaching code, LIX. The latter appears particularly well suited for deriving, from information obtained in static tests, the leach rates applicable to low-flow conditions which are difficult to simulate experimentally. It is suggested that, for glass waste forms, the leaching process is eventually controlled by selective leaching of modifier species at very low flow rates and by network dissolution of the glass structure at higher flow rates. In g l a s s l e a c h i n g experiments, the r a t e o f renewal o f the c o r r o s i o n s o l u t i o n i s an important system parameter, the e f f e c t of which has been i n v e s t i g a t e d i n a number of recent s t u d i e s focusi n g on complex, simulated n u c l e a r waste glasses (1-4). In p a r t i c u l a r , changes i n the leachant renewal frequency have been found to s t r o n g l y a f f e c t elemental r e l e a s e s of both network formers and modifers as w e l l as the pH of the s o l u t i o n . The r e s u l t s p a r a l l e l those f o r the effects, of the sample s u r f a c e area-tos o l u t i o n volume r a t i o (5,6). Namely, higher mass l o s s e s a r e obtained the more d i l u t e the c o n t a c t i n g aqueous s o l u t i o n ( i . e . , the higher the s o l u t i o n flow r a t e ) . 'Current address: Brookhaven National Laboratory, Upton, N.Y. 11973.

0097-6156/ 84/ 0246-0349$06.00/ 0 © 1984 American Chemical Society In Geochemical Behavior of Disposed Radioactive Waste; Barney, G., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1984.


350

GEOCHEMICAL BEHAVIOR O F RADIOACTIVE WASTE

In a geologic r e p o s i t o r y , waste form l e a c h i n g w i l l be a f f e c t e d by unknown flow r a t e s both under normal r e p o s i t o r y operation and a c c i d e n t a l c o n d i t i o n s . An understanding of these e f f e c t s i s then necessary i n order t o p r e d i c t the geochemical behavior of disposed r a d i o a c t i v e waste over the f u l l range of possible scenarios. In the present paper, flow r a t e e f f e c t s on l e a c h i n g are analyzed from a t h e o r e t i c a l p o i n t of view and are r a t i o n a l i z e d i n a c o n s i s t e n t , generic l e a c h i n g model i n c o r p o r a t i n g the dependence of the mechanisms of s e l e c t i v e l e a c h i n g and network d i s s o l u t i o n on s o l u t i o n feedback e f f e c t s . Flow r a t e e f f e c t s on the r a t e of d i s s o l u t i o n of the g l a s s network and on the r a t e of s e l e c t i v e l e a c h i n g o f glass m o d i f i e r s are discussed f i r s t s e p a r a t e l y , i n order to address expected l e a c h i n g behaviors under network d i s s o l u t i o n c o n t r o l and s e l e c t i v e l e a c h i n g c o n t r o l , r e s p e c t i v e l y . Flow r a t e e f f e c t s are then analyzed i n the presence of both l e a c h i n g mechanisms. I t i s concluded that the d i s t i n g u i s h i n g f e a t u r e of flow r a t e e f f e c t s on l e a c h i n g i s that they determine the long-term r a t e - c o n t r o l l i n g l e a c h i n g mechanisms. E f f e c t s on Network D i s s o l u t i o n A d i s t i n g u i s h i n g e f f e c t of flow r a t e i s that s a t u r a t i o n of the s o l u t i o n i s never achieved under dynamic l e a c h i n g c o n d i t i o n s . Thus, network d i s s o l u t i o n , a s o l u b i l i t y l i m i t e d process, i s never allowed to h a l t . A steady-state c o n d i t i o n i s e v e n t u a l l y establ i s h e d whereby leach r a t e s o f network formers e q u a l i z e the r a t e of removal o f species from the leachant due to the flowing s o l u tion. This can be i l l u s t r a t e d by formulating a network d i s s o l u t i o n model which i n c o r p o r a t e s the dependence of l e a c h i n g of network formers on s o l u b i l i t y l i m i t s and water flow r a t e s . With reference t o the s i l i c a d i s s o l u t i o n r e a c t i o n s : [ S i 0 ] ( g l ) + 2 [H 0](aq) = [ l ^ S i O ^ (aq) 2

[H Si0 ](aq) = [ l ^ S i O ^ a q ) 4

(1)

2

4

+

+ [H ](aq)

pK=9.8 a t 25° C

(2)

the instantaneous s i l i c o n d i s s o l u t i o n leach r a t e per u n i t area of the s o l i d , L ( t ) , can be expressed as: (4,7) L(t) = L

o

(1 - C / C

s a t

)

(3)

where C denotes the concentration of o r t h o s i l i c i c a c i d i n s o l u t i o n . L i s a k i n e t i c parameter r e p r e s e n t i n g the r a t e of forward r e a c t i o n (1) when the s o l u t i o n i s uncontaminated w i t h silica. Gsat * s a t u r a t i o n value of o r t h o s i l i c i c a c i d i n s o l u t i o n . Both L and C t e x h i b i t an Arrhenius dependence on temperature, but n e g l i g i b l e dependence on pH i n water (7,8). 0

s t

n

Q

e

s a

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

22.

Effects of Water Flow Rates on Leaching

PESCATORE AND MACHIELS

351

Considering, then, an example of l e a c h i n g under moderate pH condi t i o n s (pH 9, s a y ) , such that i o n i z a t i o n of o r t h o s i l i c i c a c i d can be neglected, the balance of s i l i c o n species i n a well-mixed s o l u t i o n can be w r i t t e n as f o l l o w s :


| £ = 3 (9t) - Φ(0 -C*)

t>0

(4) 11

3

-

r a t i o between the sample " t r u e surface area, A, and the volume of the c o n t a c t i n g s o l u t i o n V;

Φ

-

r a t i o between the volumetric flow r a t e of the leachant, F, and the volume of the c o n t a c t i n g s o l u t i o n , V, i . e . , the leachant renewal frequency;

C*

-

s i l i c o n volumetric concentration i n the incoming s o l u tion;

t

-

time.

I n d i c a t i n g by C the i n i t i a l c o n c e n t r a t i o n of s i l i c o n i n s o l u t i o n , Equation (4) p r e d i c t s i t to evolve according to the expression : Q

th

C ( t ) = ( C - CJe~

+ C

(5)

m

0

where : g L

+

c

C = o * * " BL + » C

c

sat

(6)

C

0

( b > 8 a t

and τ = C

s a t

(6L + K

/

0

s

a

t

)

(7)

A c c o r d i n g l y , a flow-rate l i m i t e d steady-state c h a r a c t e r i z e d by a constant c o n c e n t r a t i o n of s i l i c o n i n s o l u t i o n , Coo, and a constant leach r a t e Κ-**

α

- C* / C

s a t

)

β

™ï

$

C

s

a

(8)

t

i s e v e n t u a l l y achieved. The time needed to reach 1% departure from steady-state, T, i s approximately:

T

=

5

T

=

BL

0

/ C

s a t

+ Φ

(

9

)

Therefore, i f l e a c h i n g i s network d i s s o l u t i o n c o n t r o l l e d , the higher the flow r a t e the sooner steady-state i s achieved and the higher the leach r a t e , which accords with the experiments1 evidence. In p a r t i c u l a r , because 3 = A/V and Φ - F/V, Equations (6)-(8) i n d i c a t e that the only parameter c h a r a c t e r i z i n g


352

GEOCHEMICAL BEHAVIOR OF RADIOACTIVE WASTE

the system a t steady s t a t e i s the r a t i o F/A, i . e . , i n a r e p o s i t o r y environment, the s p e c i f i c flow of groundwater past the waste form specimen.


E f f e c t s on S e l e c t i v e Leaching S e l e c t i v e l e a c h i n g of the g l a s s matrix takes place by i o n ex change of m o d i f i e r ions ( a l k a l i s or a l k a l i n e e a r t h s , e s s e n t i a l l y ) from the g l a s s f o r hydronium ions i n s o l u t i o n . T h i s process r e s u l t s i n d e a l k a l i n i z a t i o n of the o r i g i n a l g l a s s . Glass modi f i e r s e x h i b i t high s o l u b i l i t i e s i n water i n d i c a t i n g that s e l e c t i v e l e a c h i n g i s not s o l u b i l i t y l i m i t e d and that flow rates are not expected to i n f l u e n c e t h i s mechanism unless i n the extreme case of a stagnant s o l u t i o n . This can be i l l u s t r a t e d by formulating a s e l e c t i v e l e a c h i n g model which incorporates i o n exchange pro cesses t a k i n g p l a c e w i t h i n the glass bulk and a t the g l a s s - s o l u t i o n i n t e r f a c e as w e l l as the flow c o n d i t i o n of the s o l u t i o n . With reference to sodium species and to Figure 1, the i o n exchange r e a c t i o n [Na ](gl) + [H 0 ](aq)5Ê[Na ](aq) + +

+

+

3

(10)

+

[H 0 ](gl) 3

can be modeled s e p a r a t e l y f o r the g l a s s bulk and surface phases (4). Ion exchange i n the bulk phase r e s u l t s i n an i o n i c c o u n t e r d i f f u s i o n process c h a r a c t e r i z e d by a c o n c e n t r a t i o n dependent d i f f u s i o n c o e f f i c i e n t , D (4,9). Ion exchange at the g l a s s - s o l u t i o n i n t e r f a c e can be modeled i n terms of the phenomenological constants k and k"* y i e l d i n g the f o l l o w i n g expression f o r the leach r a t e of sodium species per u n i t area of the s o l i d : +

+

L ( t ) = k n = k" C

sol

where η represents the s u r f a c e concentration of sodium s p e c i e s ; sol concentration of sodium species i n s o l u t i o n ; k n the r a t e of sodium r e l e a s e i n t o s o l u t i o n ; k " " C i the r a t e of sodium r e s o r p t i o n on the g l a s s s u r f a c e . The parameters k and k~ depend i n general on temperature, and may depend on the physico-chemical p r o p e r t i e s of the s o l u t i o n and the glass s u r f a c e . Considering an example of l e a c h i n g under moderate pH excur s i o n , such that the a u t o p r o t o l y s i s of water can be neglected and k and k~ are approximately constant, the balance of sodium species i n the system obeys the f o l l o w i n g set of equations: (4) c

t

n

e

+

so

+

+

1

3x

J

3t

3x

dn dt

- L ( t ) + (D

5Jr )

x=0+

x,t>0

(12)

t>0

(13)

t>0

(14)

8x dC dt

sol

= 3 L ( t ) - (Csol-C*)


22.

Effects of Water Flow Rates on Leaching 353

PESCATORE A N D MACHIELS

where C * represents the sodium c o n c e n t r a t i o n i n the incoming l e a c h a n t henceforth assumed equal to zero. The two parameters 3 and Φ are the u s u a l s u r f a c e a r e a - t o - s o l u t i o n volume r a t i o and the leachant renewal frequency, r e s p e c t i v e l y . The c o e f f i c i e n t D can be expressed i n terms of the molar f r a c t i o n of sodium i n the g l a s s , XNa> * the s e l f - d i f f u s i o n c o e f f i c i e n t s of N a and H30 species: }

a n (

+

D D

D

Na

m

D

" -Na

Na

+

+

Η

(1

(15)

^Na>

D

H

In p r a c t i c e Djg >> D H , (10) and c o u n t e r d i f f u s i o n i s c o n t r o l l e d by the slower hydronium i o n . This suggests assuming t h a t :


a

which l i n e a r i z e s the system of Equations (12)-(14). Assuming f u r t h e r chemical e q u i l i b r i u m between sodium species on the g l a s s s u r f a c e and sodium species immediately adjacent i n the bulk phase, the law of mass a c t i o n r e q u i r e s t h a t : =K

n(t)

t>0 —

(16)

where Κ i s a true e q u i l i b r i u m constant. W i t h i n the context of the above approximations, the o r i g i n a l system of Equations (12)-(14) can be solved w i t h the u s u a l boun dary and i n i t i a l c o n d i t i o n s : C(«,t) - C C(x,0) = C n(0) C

s o l

=

(0)

C

(17)

Q

(18)

Q

/ K

(19)

= 0

(20)

Q

The p r e d i c t e d asymptotic behaviors f o r the leach r a t e are follows: (4,11)

L.(t)

- Οο,β H-nt

.

Î 2 Κ

2

k +

D

3

2

_

(k 3)

t 2

t

l a r

*

e

e n o U

*

h

as

( 2 1 )

Φ = 0

and Loo(t) - co * / ^ H

t l a r g e enough Φ + 0


(22)

354

GEOCHEMICAL BEHAVIOR O F RADIOACTIVE WASTE

Equations (21) and (22) both suggest that l e a c h i n g w i l l e v e n t u a l l y slow down t o zero under s e l e c t i v e leaching c o n t r o l . Under the c o n d i t i o n s of Equation (21), l e a c h i n g tends t o zero as a build-up of g l a s s m o d i f i e r s i n s o l u t i o n allows the s o l i d s u r f a c e t o come to e q u i l i b r i u m with the leachant. Under the c o n d i t i o n s of Equation (22), species build-up e f f e c t s do not p l a y a r o l e , r e g a r d l e s s of how s m a l l the flow r a t e , and l e a c h i n g tends t o zero as the g l a s s matrix gets depleted of network m o d i f i e r s . This accords w i t h p h y s i c a l i n t u i t i o n . Equation (22) i s the c l a s s i c a l expression f o r the leach r a t e per u n i t area under d i f f u s i o n c o n t r o l l e d c o n d i t i o n s .


The General Case While i t proved convenient to consider flow r a t e e f f e c t s on l e a c h i n g under network d i s s o l u t i o n c o n t r o l and s e l e c t i v e l e a c h i n g c o n t r o l s e p a r a t e l y f o r i l l u s t r a t i o n purposes, these mechanisms are not independent of each other. Indeed, as i o n exchange r e a c t i o n s of the kind (10) deplete the s o l u t i o n of hydronium i o n s , the s o l u t i o n becomes more a l k a l i n e causing o r t h o s i l i c i c a c i d to i o n i z e and, consequently, a d d i t i o n a l d i s s o l u t i o n of the g l a s s matrix according to r e a c t i o n s of the kind (1). I t i s , however, the flow c o n d i t i o n of the s o l u t i o n that determines the long-term r a t e - c o n t r o l l i n g l e a c h i n g mechanisms. I f the s o l u t i o n i s stagnant, s a t u r a t i o n of the s o l u t i o n i s reached much sooner with respect to the network formers than the a l k a l i s ; thus l e a c h i n g w i l l e v e n t u a l l y take place a t a r a t e c o n t r o l l e d by s e l e c t i v e l e a c h i n g o f the a l k a l i s . I f the s o l u t i o n i s flowing, s a t u r a t i o n i s never achieved, and s e l e c t i v e l e a c h i n g , a process which otherwise would slow down to zero, i s c o n t r o l l e d e v e n t u a l l y by the constant network d i s s o l u t i o n r a t e of the g l a s s matrix. In t h i s case, a l l elements e v e n t u a l l y leach out a t the same r a t e d i c t a t e d by the d i s s o l u t i o n k i n e t i c s of the network forming element with highest s o l u b i l i t y i n s o l u t i o n and by the flow c o n d i t i o n s of the s o l u t i o n . This can be i l l u s t r a t e d f o r the case of sodium and s i l i c o n l e a c h i n g from nuclear waste glasses by combining together to the modeling approach o u t l i n e d e a r l i e r f o r network d i s s o l u t i o n and s e l e c t i v e l e a c h i n g c o n t r o l s , and by t a k i n g i n t o account the d i s s o c i a t i o n of the o r t h o s i l i c i c a c i d , Reaction (2), and the a u t o p r o t o l y s i s of water: H 0^±OH" + H

+

2

(23)

The mathematical formulation of the model complicates somewhat (4), and i t i s not reported here f o r the sake of s i m p l i c i t y . In p a r t i c u l a r , the model r e s u l t s i n a system of coupled, nonl i n e a r ordinary and p a r t i a l d i f f e r e n t i a l equations which have been f u l l y implemented i n a computer code, named LIX, t o p r e d i c t elemental r e l e a s e s of s i l i c o n and sodium from b o r o s i l i c a t e glass.


22.

Effects


of

Water

Flow

Rates

on Leaching

355

Figure 2 shows the p r e d i c t e d , normalized cumulative mass l o s s e s based on the behaviors o f s i l i c o n and sodium f o r three d i f f e r e n t values of the leachant renewal frequency. The p h y s i c a l parameters used r e f e r t o the l e a c h i n g of PNL 76-68 b o r o s i l i c a t e g l a s s i n d e i o n i z e d water a t 90°C, (4) and r e f e r e n c e i s made t o the geometric s u r f a c e area, SA, of the sample. In p a r t i c u l a r , the curves corresponding t o s i l i c o n and sodium tend t o have the same, constant slope with i n c r e a s i n g flow r a t e . In p a r t i c u l a r , the curves corresponding t o Φ = 1 day" p r a c t i c a l l y coincide, i n d i c a t i v e o f network d i s s o l u t i o n c o n t r o l .


1

Figure 3 shows the p r e d i c t e d behavior of the pH of the s o l u t i o n as a f u n c t i o n of leachant renewal frequency f o r the same system parameters. As can be seen, the higher the flow r a t e , the sooner steady s t a t e i s achieved, and the c l o s e r the leachant composition t o that of the o r i g i n a l s o l u t i o n . In p a r t i c u l a r , the pH curve f o r the s t a t i c case (Φ= 0) shows that the s o l u t i o n pH has not reached steady s t a t e yet a f t e r 28-days l e a c h i n g . Approach to steady s t a t e under the s t a t i c l e a c h i n g c o n d i t i o n s can be a very lengthy process. However, an e q u i l i b r i u m pH value can be estimated by use of the s o l u t i o n e l e c t r o n e u t r a l i t y c o n d i t i o n as a p p l i e d t o the r e a c t i o n s modeled. Indeed, a t a l l times: +

+

[H ]

+

+ [Na ] +

I [H ]

- [0H ] +

+ [Na ]

- [H Si0 -] =

- [0H~]

3

4

_

- [H Si0 ] } 3

4

t

=

Q

(24)

which y i e l d s an e q u i l i b r i u m pH of -12 a t 90°C based on the e q u i l i b r i u m r e l a t i o n between sodium s o l u t i o n and s u r f a c e s p e c i e s : k+C

iFi and

( 2 5 )

on values o f the p h y s i c a l parameters from Reference 4. Figure 4 shows a p l o t of the long term, normalized l e a c h r a t e , L * ( t ) = L o o ( t ) / L s i ( t = 0 ) , based on the behaviors of sodium and s i l i c o n as a f u n c t i o n of Φ, where l e a c h i n g f o l l o w s a law of the type (21). T h i s lower range of Φ values may encompass flow r a t e s i n a nuclear waste r e p o s i t o r y under normal o p e r a t i o n a l conditions. Network d i s s o l u t i o n c o n t r o l operates i n the higher ranges o f Φ according to a law of the type (8). Higher ranges of Φ values may encompass flow r a t e s i n a nuclear waste r e p o s i t o r y under accident c o n d i t i o n s . I f species are r e l e a s e d , whose s a t u r a t i o n c o n c e n t r a t i o n i s lower than the o r t h o s i l i c i c a c i d s a t u r a t i o n c o n c e n t r a t i o n , new s o l i d phases may form both i n s o l u t i o n and a t the s o l u t i o n - g l a s s i n t e r f a c e (12). Formation of new phases i n s o l u t i o n may a c c e l e r a t e l e a c h i n g ; new phases a t the s o l u t i o n - g l a s s i n t e r f a c e may s t a b i l i z e the d e a l k a l i z e d l a y e r and slow down both l e a c h i n g mechanisms.



356

GEOCHEMICAL BEHAVIOR OF RADIOACTIVE WASTE

Figure 1.

G r a p h i c a l Representation of the Waste Form-Leachant System.

DAYS

Figure 2.

P r e d i c t e d , Normalized Mass Loss v s . Time f o r Various Values of Φ. [φ] = [ d a y " ] ; Q* - grams of Glass Leached A f t e r 28 Days Assuming Congruent D i s s o l u t i o n at the I n i t i a l S i l i c o n Leach Rate. 1


22.

Effects


1

of

Water

Flow

1

_ SA/V= 10, m T = 90 °C

Rates

on Leaching

357

1

_l

1

φ = 0 day" —

—

^

s s s s s

—•

0.1

pH 8


-

10

-

-

1

0

Figure 3.

1

7

14 DAYS

21

28

P r e d i c t e d Behavior of S o l u t i o n pH v s . Time f o r Various Values of Φ.

I0

Effects of Water Flow Rates on Leaching - ACS Symposium Series

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