Faculty o f P hysics, U niversity o f Brem en, G erm any

D I F F U S I O N - S O R P T I O N E X P E R I M E N T F O R S T U D Y I N G T R A N S P O R T P I I O P E R T I E S O F

137C s

A N D

S5S r

I N S O I L

D a i i g T h i P h u o n g N a m

D epartm ent o f Physics, College o f Science

,

V N U

G e r a l d K i r c h n e r

Faculty o f P hysics, U niversity o f Brem en, G erm any

A b s t r a c t . T h e radionuclides released from nuclear weapon tests during the 1960’s and from nuclear industries may still endanger the terrestrial environment. Therefore, a diffusion-sorption experiment has been carried out t.0 study the behaviour of the radionu­

clides that are of interest in safety assessm ents in the environmental radioactivity field such as

vi7C s

and 90S r. T he system s studied were as close as possible to those encountered in the field. T h e experimental data were evaluated by numerical analysis, incorporating lin­

ear and nonlinear sorption m odels (six sorption isotherm m odels). T his procedure enables us to calculate the sorption parameters of different sorption isotherm models.

T h e parameters determinated were the diffusion and sorption properties of cesium and strontium in an Orthic Podsol soil (Germany).

I. I n t r o d u c t i o n

It is w ell reco g n ized th a t m a n y rad ion u clid es, p a rticu la rly th e c a tio n ic sp ecies m i­

g r a te slo w ly as a result o f in te r a c tio n o f radionuclidevS w ith th e so il m a trix . A m o n g ra­

d io n u clid e s,

yẦ7C s

and

90S r

b e lo n g to th e m o st h a za rd o u s ra d io n u clid es d u e to their lo n g h a lfliv es an d th eir low m ig ra tio n ra tes (o f th e order o f 1 cm p er year Ị1] ). T h is im p lies th a t after m an y y ea rs, th ey s till rem ain w ith in th e root zo n e o f th e so il w h ere th ey can be ta k en u p by p la n ts a n d la ter c o u ld reach th e grou n d w ater. A s a co n seq u en ce, th ey tra n s­

fer in to h u m a n fo o d chains a n d d rin k in g w ater. T h erefore, it is im p o rta n t to u n d erstan d th e tra n sp o r t p r o ce ss o f l37ơ s an d

90S r

in th e so il m a trix .

T h ere are various la b o ra to ry m eth o d s for s tu d y in g tr a n sp o r t o f rad ion u clid es in so il, su ch as th e b a tc h m e th o d an d th e co lu m n m e th o d . T h e m a in a d v a n ta g e o f th e b a tch m e th o d is its sim p licity . H ow ever, th e re are a lso several d isa d v a n ta g es: n o t all h yd rologie flow e ffe c ts are co u n ted , th e r a tio o f th e so lu tio n to th e so lid is h ig h er (d u e to ex p erim e n ta l n e c e s s itie s), a n d h ig h er so rp tio n c a p a c itie s m a y b e ava ila b le for tracer d u e t o the sh a k in g p ro cess. Ile n c e , b eca u se o f th e e x p er im e n ta l c o n d itio n s (w h ich differ from th o se in the field) th is m e th o d m ay give in a c c u r a te resu lt [2]. T h e co lu m n m e th o d ca n e lim in a te th ese d isa d v a n ta g e s. Its m ajor d isa d v a n ta g e is it s co m p lex ity a n d th a t it is v ery tim e- co n su m in g

[3-4] •

T h e w ork p resen ted h ere appU es a d ifferen t m e th o d for s tu d y in g tr a n sp o r t o f cesiu m an d str o n tiu m in soil, the m o d ified d iffu sio n -so rp tio n e x p erim en t. In th e present stu d y,

90S r

h a s b ee n s u b s titu te d by

S5S r

w h ich is ch em ic a lly id en tica l, h a s a co n sid era b ly sh orter halflife a n d can b e d e te c te d m o re ea sily . T h e a im s o f th e work are to:

T y p e s e t by .ẦẠ/ÍiS-T^X

21

D eterm in e d iffu sion an d so rp tio n p a ram eters for 137C s a n d 85

S r

S o rp tio n m o d els (linear, L angniuir, Freundlich) are te s te d by fittin g th e ex p erim en ­ tal d a ta .

I I. E x p e r im e n ta l p r o c e d u r e

T h e d iffu sio n -so rp tio n ex p er im en t w a s p erform ed u sin g O rth ic P o d s o l so il co n sistin g o f 96.2%

sand,

3.1% silt

and

0.7% clay. It

is

a ty p ica l soil in N o r th G e rm a n y [1].

37C s

(cesiu m chloride in IN HC1) an d 85S r (stro n tiu m chloride in a q u eo u s so lu tio n ) were u se d as tracers. T h e tracer so lu tio n w a s p rep ared by a d d in g so m e s y n th e tic s o lu tio n to the a cid so lu tio n co n ta in in g the ra d io n u clid es. I n itia l tracers co n cen tra tio n s, C o in the reservoir cell were a b o u t 70 k Bq/1.

T h e arran gem ent for th e d iffu sio n -so rp tio n ex p erim en t is illu s tr a te d in F ig .l.

R e s e r v o i r c e ll

•wo

"3 c .

...

M e a s u r e m e n t c e l l '5c/5

Fig. l.

E x p erim en ta l se t-u p for th e d iffu sio n -so rp tio n ex p e r im e n t

T h e so il p e lle t w as a disk w ith a d ia m eter o f 1.78 cm an d a th ic k n e ss o f 0.4 cm . T h e d im en sio n s o f th e so il p e lle t w ere 2 .4 9 cm 2 x 0.4 cm . P o ro sity a n d d en sity o f the soil p e lle t w ere 36% and 1.70 ± 0.01 g cm""3, resp ectiv ely . T h e so il p e lle t w as fixed b etw een tw o cells, th e reservoir cell o f 4 9 0 m l co n ta in in g th e tracers a n d t h e m easu rem en t cell o f 230 m l co n ta in in g s y n th e tic so il so lu tio n . T h e co n cen tra tio n s C o ( t ) o f tracers in th e reservoir cell were a llow ed to d ecrease w ith tim e by th e a m o u n t d iffu sed in to soil p elle t, a lso by th e d ecay o f th e tracers. In th e m ea su rem en t cell sa m p le s w ere w ith d raw n a t certa in in tervals. T h e fluid o f th e m ea su rem en t cell w a s rep la ced b y th e sy n th e tic so il so lu tio n , m a in ta in in g a n ea r-zero co n cen tra tio n . A s y n th e tic s o lu tio n w as se lec ted co n ta in in g elem en t c o n cen tra tio n s w h ich are as clo se as p o ssib le t o th e v a lu e s ca lcu la ted from th e a n a ly se s o f the so il s o lu tio n sa m p le in th e field. T racers d iffu se from high to low co n cen tra tio n .

T h e ex p erim e n t w a s p erfo rm ed a t ro o m te m p era tu re o f 2 0 ° c . 137C s and 855 r con ­ cen tra tio n s in s o lu tio n s a m p le s w ere d e te c te d by h ig h p u rity g erm a n iu m - d etecto r. S ta ­ tistic a l c o u n tin g errors w ere in th e ran ge o f 14-5%.

I I I .

D a t a a n a ly s is

A ssu m in g a sin g le -p o r o sity m e d iu m , in w h ich th e d iffu sion co efficien t D is c o n sta n t in tim e a n d sp a ce, tra n sp o rt (d iffu sio n is a cco m p a n ied by so rp tio n ) in th e liquid phase can b e d escrib ed by a o n e-d im en sio n a l eq u a tio n

d ( x i t) d t

d 2C { x ) l) _ p d S ( X ) t )

d x2 € ỠÍ (tgeqO, 0 < X < L ), ₍1)

w h e r e

c

: c o n cen tr a tio n o f tra ce in so lu tio n ; 5 : c o n c e n tr a tio n o f tra ce sorbed;

p:

so il d en sity;

6 : so il p oro sity ;

D

: effectiv e d iffu sion coefficien t;

L

: le n g th o f s o il

pellet .

F o r o u r e x p e rim e n ta l a rra n g e m e h t, in itia l c o n d itio n s are given as

T h e s o rp tio n o f th e tra c e r to th e soil m a trix is m o d elled by a n o n -lin e a r first o rd e r k in e tic m o d el

w h e re

r

: k in e tic tim e c o n s ta n t;

F ( C ) : s o rp tio n iso th e rm .

N o a n a ly tic a l s o lu tio n is k n o w n for th is p ro b lem ; so lu tio n s a re o b ta in e d by n u m erical m e th o d . T h is is p e rfo rm e d by u sin g C ra n k -N ic o lso n m e th o d o f a fin ite difference a n d solving th e re s u ltin g s y s te m o f n o n lin e a r d ifference e q u a tio n s b y N e w to n -R a p h s o n m e th o d . T h is w as d e sc rib e d in m o re d e ta il by G . K irc h n e r, [3]. T h e n u m e ric a l a lg o rith m s were b u ilt in to th e n o n lin e a r c o d e P A R o f th e B M D P s ta tis tic a l co d e p ack ag e (B M D P s ta tis tic a l so ftw are w . J . D ixon, [5]).

A kaike in fo rm a tio n c rite rio n A IC c a n b e u sed to fit th e s o rp tio n m o d e ls to e x p e r­

im e n ta l d a ta . C r ite r ia b a se d o n A kaike in fo rm a tio n c rite rio n A IC if m e a s u re m e n t e rro rs are a d d itiv e a n d n o rm a lly d is tr ib u te d w ith m e a n zero it is given as c . C o b eli, [6].

Co,

X

= 0,

0,

X

> 0. (2)

A n d th e b o u n d a ry c o n d itio n s a re [3]

(3) C ( L , t ) = 0. (4)

A cco rd in g to P ic k ’s law eq. (3) m a y b e w ritte n as

(5)

= r { F ( C ) - S }, ₍6)

A I C =

N i n R s s

+ 2 p , w here

N

: n u m b e r o f d a ta p o in ts ;

I ỈSS

• re s id u a l su m o f sq u a re s o f th e fit;

p :

n u m b er o f p a r a m e te r s fitte d .

A c co rd in g t o th e te s t, th e s o r p tio n m o d e l w ith th e lo w est v a lu e o f

A I C

is con sid ered th e b e s t, ta k in g in to a c co u n t th e g o o d n e s s o f th e fit as w ell as an d nu m ber o f th e p a ram eters fitted .

IV . R e s u lts a n d d is c u s s io n

T h e so r p tio n m o d e ls lis te d in ta b . 1 w ere fitte d to th e e x p e r im e n ta l d a ta for 85S r a n d

l37C s

w ith th e lin ear, F r eu n d lich , an d L a n g m u ir iso th e r m a ssu m in g in sta n ta n e o u s an d first ord er k in e tic so r p tio n , resp ectiv e ly . T h e d ifferen tial e q u a tio n th u s o b ta in ed ca n b e a p p lied as a reg ressio n m o d e l w it h

D }r ) Kd) K f t ì Khai) K lq.

2

) N

as fit t in g param eters.

T h e ta b le 1 sh o w s so r p tio n m o d e ls fitte d to th e e x p e r im e n ta l d a ta o f 85ỐY,137C\s a n d th e o b ta in e d v a lu es o f

A I C

a n d

R s S '

T a b . l

T e s tin g th e fits o f th e s o r p tio n m o d e ls for

S5S r

and

l37C s

u sin g th e Akaike criterio n --- 85

No

1 2 3

4

5

6

Sorption model

S r ¹³⁷C s

a s dt

— ,

ÕỈ : ÔS

dt

^{= r}

Rss AIC R-ss AIC

II n 116571 678 38955 1050

= K F r C N

^{116572 6 8 0 37722 1049}

1

+ K La2C

^{116576 6 8 0 38954 1052}

- r{KdC - S }

_{116575 6 8 0 34353 1040}

r{K..rC N - s

_{116881 6 8 4 34388}

1042

f Ku£ J

+ 1

^{7 2 0 2 7 813 34353 1042}

A s ca n b e s e e n from ta b . 1, th e b e s t fit t o th e e x p e r im e n ta l d a ta for 85S r a n d 137Cs w ere o b ta in e d a ssu m in g a lin e a r iso th e r m a n d a k in e tic linear iso th erm , resp ectiv ely .

P a r a m e te r s r e su ltin g from fittin g th e so r p tio n m o d e ls for th e linear iso th e r m o f

S5S r

a n d for th e k in e tic lin ear is o th e r m o f

l37C s

are g iv e n in ta b . 2.

T a b .2 . P a ra m e te rs o b tain ed by fittin g th e ex p erim en tal d ata of 86S r a n d 137Cs, where th e u n c e rta in tie s of th e v alu es w ere deriv ed from th e asym ptotic s ta n d a rd deviations.

P a r a m e t e r N u m e r i c a l v a l u e

85S r 137C s

D ( 1 0 '3 c m 2 h ' 1) 1 0 .1 ± 0 .6 2 9 .6 ± 1.1

k ! ( c m - V ) 7 .4 ± 1.3 5 0 .7 ± 1 3 .3

r (1 0 "6 s ' 1) i n s t a n t a n e o u s 1 .3 6 ± 0 . 4 7

T he ex p erim en ta l d a ta o f s tr o n tiu m and c e siu m c o n c e n tr a tio n s d iffu sed in to the m ea su r e m e n t cell an d th e fitte d c u r v e s o b ta in e d from th e reg r essio n a n a ly s is are sh o w n in fig u r e 2 and 3, resp ectiv ely .

Fig.2 C o n cen tratio n s of 85S r diffused in to th e m e a su re m e n t cell in 1 d ay -in terv als d u rin g th e experim ent co m p ared to th e fit of a lin e a r so rp tio n m odel

Fig.3 C o n cen tratio n s of 137Cs diffused in to th e m e a su re m e n t cell in 1 d ay -in terv als d u rin g th e experim ent com pared to th e fit of a k in etic lin e a r so rp tio n model

As can be seen in figures 2 and 3, the calculated curves are in satisfactorily agree­

ment w ith the experim ental d a ta for b o th strontium and cesium. T he stro n tiu m d a ta have

been corrected for its decay, since th e hatf-life of 85S r is 65 days. T he uncertainties of

th e v a lu es o f th e e ffectiv e d iffu sio n co efficien ts are b elow 6%. T h e h ig h u n certa in ties o f o b ta in e d so r p tio n p a r a m eter m a y r e su lt in la rg e errors o n in d iv id u a l d a ta p o in ts due t o th e v a ria tio n o f th e c o n c e n tr a tio n s o f cesiu m a n d stro n tiu m d iffu sed in to th e m ea su rem en t cell.

T h e r e s u lts sh o w t h a t t h e so r p tio n iso th erm s for b o th s tr o n tiu m a n d cesium are

linear.

T h e in te r a c tio n k in e tic s for str o n tiu m t o th e so il m atrix is a fa st p r o c e ss w hile th e k in etic so r p tio n for cesiu m is slo w . F rom the v a lu e o f r (1 .3 6 ± 0 .4 7 )* 10“ 6 s ” 1, th e rea ctio n tim e o f c e s iu m

T

= In 2 / r c a n b e c a lc u la te d to b e 6 days. T h is result, is in g o o d agreem en t w ith co r r esp o n d in g v a lu es in th e lite r a tu r e [7-11].

T h e w id e ra n g e o f K d -v a lu e s rep o rte d in th e litera tu re, u p to th ree order o f m a g ­ n itu d e a n d m o re [12], is d u e to th e different g eo ch em ica l fa cto rs o f th e v a rio u s m a teria ls u sed . H ow ever, ou r r e su lts a re sim ila r to th o se o f sim ilar soil an d tracer c o n cen tra tio n s fo u n d b y so m e a u th o r s [7,12-14].

In c o n c lu sio n , d iffu sio n -so r p tio n e x p e r im e n ts h ave a n u m ber o f a d v a n ta g es such a s th eir e x p e r im e n ta l s im p lic ity a n d th e p o s sib ility to m o d e l co n d itio n s th a t are clo se to th o se in th e field an d th erefo re g iv e a c c u r a te resu lts.

A lth o u g h th e d e te r m in a tio n o f th e m ig r a tio n ra te o f stro n tiu m a n d cesiu m in so il w ill b e th e s u b je c t o f a n o th e r stu d y , w e ca n g ive a rough e s tim a te o f th e m igration o f ra d io n u clid es in so il. D iffu sio n is d o m in a n t w h e n th e fluid v e lo c ity is o f th e order o f 5 cm p er year. In th e c a se o f lin e a r so r p tio n , th e d istrib u tio n coefficien t ca n b e used a s rough e s tim a te t o p r e d ic t th e m ig r a tio n o f ra d io n u clid es in so il w h ich can b e d escr ib e d as:

z =

y /2 e .D t/R d

w here:

R d =

1 +

- K d.

e

U s in g th e resu lts o f o u r e x p e r im e n t, th e m ig ra tio n o f 1 m o f e ith e r stro n tiu m or c esiu m in P o d s o l so il can b e e s t im a t e d to tak e a b o u t 100 (m ore or le ss) yea rs durin g w h ic h th e a c tiv ity w o u ld b e r ed u ce d b y a fa ctor o f 10. T h erefore, it is o f in ter e st to g et in fo rm a tio n o n th e m ig r a tio n a n d so r p tio n o f stro n tiu m an d cesiu m in v a r io u s m a teria ls (so il, ro c k ...) in ord er to a llo w a s a fe ty a n a ly sis in th e e n v iro n m en ta l r a d io a c tiv ity Geld.

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