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 expe
Trang 1D 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
Trang 2D 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
•w o
"3
c
M e a s u r e m e n t c e l l
'5 c/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
Trang 3d ( x i t)
d t
d 2C { x ) l) _ p d S ( X ) t )
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,
A n d th e b o u n d a ry c o n d itio n s a re [3]
(3) (4)
C ( L , t ) = 0
A cco rd in g to P ic k ’s law eq (3) m a y b e w ritte n as
(5)
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;
Trang 4p : 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
a s
dt
ÕỈ : ÔS
dt = r
1042
f Ku£ J
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
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
Trang 5T 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 oncentrations of 85S r diffused into th e m easu rem en t cell in 1 day-intervals during
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 oncentrations of 137Cs diffused into th e m ea su re m e n t cell in 1 day-intervals
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
Trang 6th 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.
References
1 G K irch n er, D B a u m g a r tn e r , M ig ra tio n R a te s o f R a d io n u c lid es D e p o site d A fter
th e C h ern o b y l A c c id e n t in V ariou s N o r th G erm an S oils, A n a lyst 1 1 7 (1 9 9 2 ) p p 175-
4 7 9
2 K B u iiz l, H B a ch h u b e r a n d w S ch im n iack , D istr ib u tio n C o effic ien ts o f o f 137C s,
85S r ,141 C e ,103 / ỉu ,131 J ,95rnT c in the Various of C ultivated soils in Germany, Pro ceedings o f the In te rn a tio n a l Sym p o siu m on Recent Investigation s in the Zone o f AeratÀon o f the Soil, M un ich , O c t 1984, p p 567-568.
3 c D S h ack elford , L a b o r a to r y D iffu sio n T e stin g for W a ste D is p o sa l, A R ev iew , J
C ontam Hydrol. 7 ( 1 9 9 1 ) p p 177-217.
Trang 74 G K irchner, D B a u m g a rtn er, V D elitzsch , G S ch a b l, R W elln er, L a b o ra to ry
S tu d ie s on th e S o rp tio n B eh a v io u r o f F a llo u t R a d io n u c lid e s in A g ric u ltu ra l U sed
S oils, M odel Geo-biosphere Process 2, (1 9 9 3 ) p p 115-125.
5 w J D ix o n , Ỉ Ỉ MDP Statistical Sofwarc 1990, e d , U n iv e r s ity o f C a liforn ia P ress.,
B erk eley 1990.
6 C C o b elli, A R ugger, E v a lu a tio n o f A lte r n a tiv e M o d e l S tr u c tu r e s M e ta b o lic S y s
te m s, Med A n d Biol Eng A n d Com put, 2 0 ( 1 9 8 2 ) p p 4 4 4 -4 5 0
7 B T o resten felt, K A d ersson , B A llard , S o rp tio n o f S tr o n tiu m a n d C e siu m s o n rocks
an d m in erals, Chemical Geology (1 9 8 2 ) pp 12 3 -1 3 7
8 G K irchner, G N a g eld in g er, R W ellner, M o d if ie d D iffu sio n T e ch iq u e for S tu d y
in g N o n lin ear and K in e tic S o rp tio n a n d D e so r p tio n P r o c e s se s, Radoichim A c ta,
7 4 (1 9 9 6 ) pp 189- 192.
9 F B rü n jes, H B ra n ew itz, G K irchner, D iffu sion a n d D iffu sio n -C o n v e c tio n E x p e r
im e n ts for stu d y in g th e so r p tio n o f R a d io n u c lid es in S o il, C zechoslovak Journal o f
P hysics, V ol 4 9 (1 9 9 9 ) p p 175-180.
10 P A S in ith , M o d elin g a D iffu sio n -S o rp tio n E x p e r im e n t b y L in ea r a n d N o n lin ea r
S o rp tio n Iso th erm s, N ucl.TechnoL, 9 2 (1 9 9 0 ) p p 3 6 3 -3 7 3
11 J H o ry n a , z D louhy, S tu d y on S o r p tio n P r o p e r tie s o f S le e te d clay, Jad Energie
3 4 (1 9 8 8 ) p p 300-302.
12 H B ach h u b er, K B u n zl an d w S ch im m ack , T h e m ig r a tio n o f 137Cj and 9 0 5r in
m u ltila y ered so il, Nuclear technology, Vol 5 9 ( N o v 1982) p p 2 9 1 -3 0 1
13 J A D eld eb b io , S o rp tio n o f S tro n tiu m , S ele n iu m , C a d m iu m , a n d M ercu ry in S oil,
Radoichirn A d a , 5 2 / 5 3 ( 1 9 9 1 ) p p 181-186.
14 K A kiba, H H a sh im o to , T K a n n o , D is tr ib u tio n C o efficien t o f C e s iu m an d C a tio n
E x c h a n g e C a p a c ity o f M in erals a n d R ocks, J N u c le a r S c ie n c e a n d T ech n o lo g y,
2 6 ( 1 2 ) ( 1 9 8 9 ) p p 1130-1135.