V NU JOURNAL OF SCIENCE, M athematics - Physics T.XVIII, N04 - 2002 D IF F U S IO N -S O R P T IO N E X P E R IM E N T F O R S T U D Y IN 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 iig T h i P h u o n g N a m D epartm ent o f Physics, College o f Science , VN U G e r a ld K ir c h n e r Faculty o f Physics, University o f Bremen, 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 assessments 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 he experimental data were evaluated by numerical analysis, incorporating lin ear and nonlinear sorption models (six sorption isotherm models) This procedure enables us to calculate the sorption parameters of different sorption isotherm models T he parameters determinated were the diffusion and sorption properties of cesium and strontium in an Orthic Podsol soil (Germany) I I n tr o d u c tio n It is w ell recognized th a t m a n y radionuclides, p articu larly th e ca tio n ic sp ecies m i gra te slow ly as a result o f in tera c tio n o f radionuclidevS w ith th e so il m a trix A m ong ra d ion u clid es, yẦ7C s and 90S r b elo n g to the m ost h azard ou s rad ion u clid es d u e to their lon g h alflives and th eir low m igration tes (o f th e order o f cm per year Ị1 ] ) T h is im p lies th a t after m any years, th ey still rem ain w ith in th e root zon e o f th e so il w here th ey can be tak en u p by p la n ts an d later co u ld reach th e ground w ater A s a co n seq u en ce, th ey tran s fer in to h u m an fo o d chains an d d rin k in g w ater T herefore, it is im p o rta n t to u n derstand th e tra n sp o rt p ro cess o f l37ơ s and 90S r in the so il m atrix T h ere are various la b o to ry m eth o d s for stu d y in g tra n sp o rt o f radionuclides in soil, such as th e b a tch m eth o d and th e colum n m eth o d T h e m a in a d v a n ta g e o f th e batch m eth o d is its sim p licity H ow ever, th ere are also several d isad van tages: n o t all hydrologie flow effects are co u n ted , th e tio o f the so lu tio n to the so lid is h igh er (d u e to exp erim en tal n ecessitie s), a n d h igh er so rp tio n ca p a cities m ay be available for tracer d u e to the sh aking p rocess Ilen ce, b eca u se o f th e ex p erim en ta l co 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 ccu te resu lt [2] T h e co lu m n m e th o d can elim in a te th ese d isad van tages Its m ajor d isa d v a n ta g e is its co m p lex ity an d th a t it is very tim e- sum ing [3-4]• T h e work p resented h ere appU es a d ifferent m eth o d for stu d y in g tra n sp o rt o f cesium and stro n tiu m in soil, the m od ified diffu sion -sorption ex p erim en t In th e present study, 90S r h a s b een su b stitu te d by S5S r w h ich is ch em ica lly id en tical, h as a sid era b ly shorter halflife an d can b e d etected m o re easily 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 a n g T h i P h u o n g N a m , G e r a ld K ir c h n e r 22 D eterm in e diffusion and so rp tio n p aram eters for 137C s an d 85 S r Sorp tion m o d els (linear, L angniuir, Freundlich) are te ste d by fittin g th e exp erim en tal d ata II E x p e r im e n ta l p r o c e d u r e T h e d iffu sion -sorp tion exp erim en t w a s perform ed u sin g O rth ic P o d so l soil sistin g o f 96.2% sand, 3.1% silt and 0.7% clay It is a typ ical soil in N o rth G erm an y [1] 37C s (cesiu m chloride in IN HC1) and 85S r (stro n tiu m chloride in aq u eou s so lu tio n ) were u sed as tracers T h e tracer so lu tio n w a s prepared by ad d in g som e sy n th e tic so lu tio n to the acid so lu tio n ta in in g the rad ion u clid es In itia l tracers co n cen tra tio n s, C o in the reservoir cell were a b ou t 70 k Bq/1 T h e arrangem ent for th e diffu sion -sorption exp erim en t is illu str a ted 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 ll '5 c/5 Fig l E x p erim en tal set-u p for th e diffu sion -sorption ex p erim en t T h e soil p e lle t w as a disk w ith a diam eter o f 1.78 cm and a th ick n ess of 0.4 cm T h e d im en sion s o f th e so il p ellet w ere 2.4 cm x 0.4 cm P orosity an d d en sity o f the soil p ellet w ere 36% and 1.70 ± 0.01 g cm""3, resp ectively T h e soil p e lle t w as fixed b etw een tw o cells, th e reservoir cell o f 490 m l tain in g the tracers an d th e m easurem ent cell o f 230 m l co n ta in in g s y n th e tic so il solu tion T h e co n cen tra tio n s C o (t) o f tracers in the reservoir cell were allow ed to d ecrease w ith tim e by th e a m o u n t diffused in to soil p ellet, also by th e decay o f th e tracers In th e m easu rem en t cell sa m p les w ere w ithdraw n at certain in tervals T h e fluid o f th e m easu rem en t cell w a s rep laced b y th e sy n th etic soil solu tion , m a in ta in in g a n ear-zero cen tration A s y n th e tic so lu tio n w as selected tain in g elem en t co n cen tra tio n s w hich are as close as p o ssib le t o th e v a lu es calcu lated from th e a n a ly ses o f the so il so lu tio n sam p le in th e field Tracers diffuse from high to low cen tration T h e exp erim en t w a s perform ed at room tem p era tu re o f ° c 137C s and 855 r con cen tration s in so lu tio n sa m p les w ere d etected by h ig h p u rity germ an iu m - d etector S ta tistica l co u n tin g errors w ere in th e range o f 14-5% I I I D a ta a n a ly sis A ssu m in g a sin g le-p o ro sity m ed iu m , in w h ich th e diffusion coefficien t D is stan t in tim e an d sp ace, tran sp ort (d iffu sion is accom p an ied by sorp tion ) in th e liquid phase can b e d escrib ed by a on e-d im en sio n a l eq u ation D iffu s io n -S o r p tio n E x p e r im e n t fo r d ( x i t) dt 23 d 2C { x ) l) _ p d S ( X ) t ) dx2 € ( tgeqO , < X < L ), ỠÍ ( 1) w h ere c : co n cen tra tio n o f trace in so lu tion ; : co n cen tra tio n o f trace sorbed; p: soil density; : soil porosity; D : effectiv e diffusion coefficient; L : len 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 Co, 0, X = 0, X > (2) A n d th e b o u n d a ry co n d itio n s a re [3] (3) C ( L , t ) = (4) A ccording to P ic k ’s law eq (3) m ay be w ritte n as (5) 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 odelled by a n o n -lin e a r first o rd er k in etic m odel = r { F ( C ) - S }, (6) w h ere r : k in e tic tim e c o n sta n t; F ( C ) : s o rp tio n iso th erm N o a n a ly tic a l so lu tio n is k now n for th is problem ; so lu tio n s a re o b ta in e d by num erical m e th o d T h is is p e rfo rm ed by usin g C ran k -N ico lso n m e th o d o f a finite difference a n d solving th e re su ltin g sy ste m o f n o n lin e a r difference e q u a tio n s by N e w to n -R a p h so n m e th o d T h is w as d escrib ed in m ore d e ta il by G K irc h n e r, [3] T h e n u m erical a lg o rith m s were b u ilt into 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 code package (B M D P s ta tistic a l softw 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 so rp tio n m o d els to e x p e r im ental d a ta C r ite r ia b ased o n Akaike in fo rm a tio n c rite rio n A IC if m e asu re m e n t e rro rs are a d d itiv e a n d n o rm ally d is trib u te d w ith m ean zero it is given as c C obeli, [6] A I C = N in R s s +2p, w here N : n u m b e r o f d a ta p o in ts; IỈSS • re sid u al su m o f sq u ares of th e fit; D ang Thi Phuong N a m 24 G e r a ld K ir c h n e r , p : nu m ber o f p a m eters fitted A ccord in g to th e te s t, th e so rp tio n m o d el w ith th e low est v a lu e o f A I C is considered th e b e st, ta k in g in to a cco u n t th e g o o d n e ss o f th e fit as w ell as and num ber o f th e p aram eters fitted IV R e s u lts a n d d is c u s s io n T h e so rp tio n m o d e ls liste d in ta b w ere fitte d to th e ex p erim en ta l d ata for 85S r an d l37C s w ith th e linear, F reu n d lich , and L an gm u ir iso th erm a ssu m in g in sta n tan eou s and first order k in e tic so rp tio n , resp ectiv ely T h e d ifferential eq u a tio n th u s ob tain ed can b e a p p lied as a regression m o d e l w ith D }r ) Kd) K f t ì Khai) Klq ) N as fittin g param eters T h e ta b le sh o w s so rp tio n m o d e ls fitte d to th e ex p erim en ta l d a ta o f 85ỐY,137 C\s an d th e o b ta in e d v alu es o f A I C a n d R s S ' T a b l T e stin g th e fits o f th e so r p tio n m o d els for S5S r and l37C s u sin g th e Akaike criterion 137 - 85 Sr Cs Rss AIC R-ss AIC n Sorption model 116571 678 38955 1050 = K F rC N 116572 680 37722 1049 + K La2C 116576 680 38954 1052 116575 680 34353 1040 116881 684 34388 1042 72027 813 34353 1042 II No as - r{KdC dt — , ÕỈ : -S } r{K rC N - s ÔS = rf dt Ku£ + J A s can b e seen from ta b , th e b e s t fit to th e ex p erim en ta l d a ta for 85S r an d 137Cs w ere o b ta in e d a ssu m in g a lin ea r iso th erm a n d a k in etic linear iso th erm , resp ectively P a m e ters resu ltin g from fittin g th e so rp tio n m o d els for th e linear iso th erm o f S5S r an d for th e k in e tic linear iso th e r m o f l37C s are giv en in tab T a b P a m e te rs obtained by fittin g th e experim ental d ata of 86S r an d 137Cs, where th e u n c e rta in tie s of th e v alues w ere derived from th e asym ptotic sta n d a rd deviations P a m e te r N u m e r i c a l v a lu e 85S r D ( '3 c m h '1) 10.1 ± 137C s ± 1.1 k! (c m -V ) ± 1.3 ± 13.3 r (1 "6 s ' 1) in s ta n ta n e o u s ± D iffu s io n -S o r p tio n E x p e r im e n t fo r 25 The exp erim en ta l d a ta o f stro n tiu m and cesiu m co n c e n tr a tio n s diffused in to the m easu rem en t cell and th e fitted cu rv es o b ta in ed from th e reg ressio n a n a ly sis are sh ow n in fig u r e and 3, resp ectively Fig.2 C oncentrations of 85S r diffused into th e m easu rem en t cell in d ay-intervals d u rin g th e experim ent com pared to th e fit of a lin e a r so rp tio n model Fig.3 C oncentrations of 137Cs diffused into th e m e a su re m e n t cell in day-intervals d u rin g th e experim ent com pared to th e fit of a kinetic lin e a r sorption model As can be seen in figures 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 strontium d a ta have been corrected for its decay, since the hatf-life of 85S r is 65 days T he uncertainties of D a n g T h i P h u o n g N a m ,J G e r a l d K i r c h n e r 26 th e valu es o f th e effectiv e d iffu sio n co efficien ts are below % T h e h ig h u n certain ties o f o b ta in ed so rp tio n p a m eter m a y resu lt in large errors on in d iv id u a l d a ta p o in ts due t o th e variation o f th e co n cen tra tio n s o f cesiu m an d stro n tiu m diffused in to th e m easu rem en t cell T h e resu lts sh o w th a t th e so rp tio n iso th erm s for b o th stro n tiu m an d cesium are linear T h e in tera c tio n k in etic s for stro n tiu m to th e soil m atrix is a fast p ro cess w hile th e k in etic so rp tio n for cesiu m is slow From the v a lu e o f r (1.36 ± )* 10 “ s ” 1, the reaction tim e o f cesiu m T = In / r ca n b e c a lcu la ted to b e days T h is result, is in g o o d agreem ent w ith corresp on d in g v a lu es in th e litera tu re [7-11] T h e w id e n g e o f K d -v a lu es rep o rted in th e literatu re, up to th ree order o f m ag n itu d e an d m ore [ 12 ], is d u e to th e different geoch em ical factors o f th e v ariou s m a terials u sed H ow ever, our resu lts are sim ila r to th o se o f sim ilar soil and tracer co n cen tration s fou n d b y som e a u th o rs [7,12-14] In co n clu sio n , d iffu sio n -so rp tio n ex p erim en ts have a num ber o f a d v a n ta g es such as th eir ex p erim en ta l sim p lic ity a n d th e p o ssib ility to m o d el co n d itio n s th a t are close to th ose in th e field and th erefore g iv e a ccu 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 tio n rate o f stro n tiu m a n d cesiu m in soil w ill b e th e su b je c t o f a n o th er stu d y , w e can give a rough e stim a te o f th e m igration o f rad ion u clid es in so il D iffu sion is d o m in a n t w h en th e fluid v elo city is o f th e order o f cm per year In th e ca se o f lin e a r so rp tio n , th e d istrib u tio n coefficient can b e used as rough e s tim a te to p red ict th e m ig r a tio n o f rad ion u clid es in so il w hich can b e d escrib ed as: z = y /2 e D t/R d where: R d = + - K d e U sin g th e resu lts o f ou r ex p erim en t, th e m igration o f m o f e ith e r stron tiu m or cesiu m in P o d so l so il can b e e s tim a te d to take a b o u t 100 (m ore or less) years during w h ich th e a c tiv ity w o u ld b e red u ced b y a factor o f 10 T herefore, it is o f in terest to get in fo rm a tio n o n th e m ig tio n an d so rp tio n o f stro n tiu m and cesiu m in v a rio u s m aterials (soil, ro ck ) in ord er to a llo w a sa fe ty a n a ly sis in th e en viron m en tal d io a c tiv ity Geld References G K irch n er, D B a u m g a rtn er, M ig tio n R a tes o f R a d io n u clid es D e p o site d A fter th e C h ern o b y l A ccid en t in V ariou s N o rth G erm an Soils, A nalyst 1 (1 9 ) pp 175479 K B u iizl, H B a ch h u b er a n d w Schim niack, D istrib u tio n C o efficien 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 posium on Recent Investigations in the Zone o f AeratÀon o f the Soil , M unich, O ct 1984, pp 567-568 c D S hackelford, L a b o to ry D iffu sion T estin g for W a ste D isp o sa l, A R eview , J C ontam Hydrol (1 9 ) p p 177-217 D iffu s io n - S o r p tio n E x p e r im e n t fo r 27 G K irchner, D B au m gartn er, V D elitzsch , G S ch ab l, R W elln er, L ab oratory S tu d ies on the Sorp tion B eh aviou r o f F allou t R a d io n u clid es in A gricu ltu l U sed Soils, M odel Geo-biosphere Process , (1993) pp 115-125 w J D ixon , Ỉ Ỉ MDP Statistical Sofwarc 1990, ed , U n iv e r sity o f C alifornia P ress., B erkeley 1990 C C ob elli, A R ugger, E v a lu a tio n o f A ltern a tiv e M o d el S tru ctu res M eta b o lic S y s tem s, Med A n d Biol Eng A nd Com put, (1 ) pp 4 -4 B T oresten felt, K A dersson , B A llard, S orp tion o f S tr o n tiu m a n d C esiu m s o n rocks and m inerals, Chemical Geology (1982) pp 123-137 G K irchner, G N ageld in ger, R W ellner, M o d ifie d D iffu sion T ech iq u e for S tu d y in g N onlinear and K in etic S o rp tion an d D eso rp tio n P r o c e sse s, Radoichim A cta , (1 9 ) pp 189- 192 F B rünjes, H B ran ew itz, G K irchner, D iffusion an d D iffu sio n -C o n v ectio n E x p er im en ts for stu d y in g th e so rp tio n o f R a d io n u clid es in S o il, Czechoslovak Journal o f P hysics , Vol (1 9 ) p p 175-180 10 P A S in ith , M od elin g a D iffu sion -S orp tion E x p erim en t b y L in ear an d N on lin ear S orp tion Isoth erm s, Nucl.TechnoL, (1 9 ) pp -3 11 J.H oryn a, z D louhy, S tu d y on S o rp tio n P ro p er ties o f S le e te d clay, Jad Energie (1 8 ) pp 300-302 12 H B achhuber, K B u n zl and w S ch im m ack, T h e m ig tio n o f 137Cj and 5r in m u ltilayered soil, Nuclear technology, Vol (N o v 1982) p p 29 -3 13 J A D eld eb b io, S orp tion o f S tro n tiu m , S elen iu m , C a d m iu m , a n d M ercury in Soil, Radoichirn A d a , /5 ( 9 ) pp 181-186 14 K A kiba, H H a sh im o to , T K an n o, D istrib u tio n C o efficien t o f C esiu m and C ation E x ch an g e C ap a c ity of 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 echnology, ( ) ( 9 ) p p 1130-1135 ... v a lu es calcu lated from th e a n a ly ses o f the so il so lu tio n sam p le in th e field Tracers diffuse from high to low cen tration T h e exp erim en t w a s perform ed at room tem p era... e fit of a kinetic lin e a r sorption model As can be seen in figures 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... ultivated soils in Germany, Pro ceedings o f the In te rn a tio n a l Sym posium on Recent Investigations in the Zone o f AeratÀon o f the Soil , M unich, O ct 1984, pp 567-568 c D S hackelford,