J. En i on. Radioac i i y, Vol. 35, No. 3, pp. 281-304, 1997
0 1997 Published by Else ie Science Limi ed
All igh s ese ed. P in ed in I eland
ELSEVIER PII: SO265-931X(96)00057-4 0265-931X/97 $17.00 + 0.00
U anium and Tho ium Concen a ions in an Es ua y
A ec ed by Phospha e Fe ilize P ocessing: Expe imen al
Resul s and a Modelling S udy
R. Pe ihiiez & A. Ma inez-Agui e
Dp o Fisica Aplicada, E.U. Ingenie ia Tkcnica Ag icola, Uni e sidad de Se illa, C a
U e a km 1, 41014 Se illa, Spain
(Recei ed 16 Feb ua y 1996; accep ed 25 June 1996)
ABSTRACT
The Odiel i e , in sou hwes Spain, o ms an es ua ine sys em which is
uj ec ed by was e disposal om a e ilize complex. U anium and ho ium
concen a ions in wa e s and suspended ma e , ac i i y a ios and dis ibu ion
coe icien s, kd, ha e been measu ed along he i e du ing wo di e en idal
s a es. The esul s ha e shown ha a adioac i e impac is being deli e ed o
he i e , as well as a sign jiican a iabili y depending on he sampling poin
and he idal s a e. Thus, a quan i a i e s udy o he dis ibu ion o adio-
nuclides can be ca ied ou bes bq’ means o a ma hema ical model. The model
includes he pa i ion o adio ace s be ween ou phases (wa e , suspended
ma e and wo sedimen ac ions) and has been designed o non-equilib ium
condi ions. Thus, adio ace ans e s a e desc ibed in e ms o kine ic
ans e coe icien s ins ead o kds. The model simul aneously sol es he
hyd odynamic equa ions, he suspended ma e equa ion (including depos ion
and esuspension p ocesses) and he equa ions which desc ibe he ime e olu-
ion o adionuclide concen a ions in each one o he ou phases. The model
has yielded good esul s in p edic ing U and Th concen a ions in wa e and
suspended ma e , dis ibu ion coe icien s and ThjU mass a ios. o 1997
Published by Else ie Science Limi ed. All igh s ese ed
1 INTRODUCTION
The Odiel i e is loca ed in he sou hwes o Spain. A i s lowes eaches,
i o ms a idal es ua ine sys em which discha ges in o he A lan ic Ocean.
281
282 R. Pe ici iez, A. Ma inez-Agui e
The es ua y is close o a la ge indus ial a ea in which a phospha e e i-
lize p ocessing complex ope a es. This complex p ocesses a ound 1.6 MT
o phospha e ock pe yea om Mo occo, Senegal and Togo. Pa o he
was e is eleased di ec ly in o he Odiel i e .
I is well known (Van de Heijde e al., 1988; Laiche & Sco , 1991) ha
such was es con ain signi ican amoun s o na u al adionuclides: U, Th,
Ra and hei daugh e s. The p esence o 226Ra and 224Ra in wa e and
suspended ma e samples collec ed om he Odiel i e has al eady been
in es iga ed (Pe ia iez & Ga cia-Leon, 1993; Pe iaiiez e al., 1994a). These
s udies ha e e ealed ha a adioac i e impac is being deli e ed o he
i e since, o ins ance, le els up o 670mBq 1-l o 226Ra ha e been
measu ed in a wa e sample collec ed close o he e ilize complex.
Al hough he e a e da a on he U- and Th-iso ope con en in he Odiel
i e wa e and suspended ma e (Ma inez-Agui e e al., 1994a), a mo e
de ailed s udy is epo ed in his pape . The objec i e o his wo k is o
unde s and he U and Th dispe sion mechanisms in dynamic aqua ic
sys ems, including he dis ibu ion be ween he solid and liquid phases as well
as he e ec o idal oscilla ions. Thus, wa e samples we e collec ed along he
Odiel i e a wo di e en idal s a es (high and low wa e ) and he U- and
Th-iso ope con en s in wa e and suspended ma e we e measu ed. The
dis ibu ion coe icien s kd we e also calcula ed. A quali a i e desc ip ion o
he esul s is no s aigh o wa d as he e is signi ican a iabili y in ac i i y
concen a ions and kd, depending upon he sampling poin and he idal
s a e. This is a logical esul since we a e dealing wi h an open sys em in
which some di e en e ec s a e aking place a he same ime: non-cons an
inpu om he sou ce, adso p ion o adionuclides on o suspended ma e
and bo om sedimens, deso p ion, and wa e and suspended ma e mo e-
men s due o ides. Thus, a quan i a i e unde s anding o he U and Th
dispe sion can be achie ed bes by means o ma hema ical models.
A wo-dimensional model, ha includes he ans e p ocesses be ween
ou phases (wa e , suspended ma e and wo g ain size ac ions o
bo om sedimen s), has been applied o he Odiel i e . The model simul-
aneously sol es he hyd odynamic equa ions, he suspended ma e
dynamic equa ion (including he esuspension and deposi ion p ocesses)
and he equa ions ha desc ibe he ime e olu ion o adionuclide
concen a ions in o each o he ou phases. Al hough he model has been
p e iously applied o s udy he dispe sion o 226Ra in he Odiel i e
(Pe iaiiez e al., 1996a), he e a e wo main objec i es in applying i o U
and Th: o achie e a quan i a i e unde s anding o he expe imen al
esul s and o p o ide ex a alida ion o he model, ha is, o alida e he
model o elemen s wi h e y di e en geochemical beha iou s, such as U
and Th.
U anium and ho ium in an es ua y 283
In he nex sec ion, he sampling and expe imen al me hods a e desc i-
bed. Nex , he expe imen al esul s a e discussed. The modelling wo k is
desc ibed in Sec ion 4.
2 EXPERIMENTAL
Wa e samples we e collec ed in plas ic bo les along he Odiel i e basin
(see Fig. 1) du ing July 1990. Two samples we e collec ed om each
sampling s a ion: one du ing high wa e and he o he du ing low wa e so
as o s udy he in luence o idal oscilla ions on he esul s. The wa e was
il e ed as soon as possible h ough p e iously weighed Nuclepo e il e s
(0.4pm po e size) o sepa a e he suspended ma e . The il e was hen
d ied and weighed o calcula e he mass o eco e ed ma e . Typical
suspended ma e concen a ions in he Odiel i e anged om 24 o
50ppm, depending on he sampling poin and he idal s a e du ing
sampling. The il e was hen co e ed wi h HCI and in oduced in o an
ul asonic ba h o hal an hou , du ing which, he suspended ma e was
sepa a ed om he il e and dissol ed. The il e was hen washed wi h
Fig, 1. Map o he Odiel i e showing he sampling poin s. The ec angula box is he g id
used in he model.
284 R. Pe ici iez, A. Ma inez-Agui e
HNOs which was added o he HCI o o m aqua egia. This solu ion was
slowly hea ed o dissol e all emaining pa icles.
U anium-232 and 229Th spikes and Fe ca ie we e added o he il e ed
wa e and o he solu ion ob ained a e he dissolu ion o suspended
ma e pa icles. P ecipi a ion o Fe wi h oxyhyd oxides wi h concen a ed
amonium hen ollowed.
U anium- and Th-iso opes we e ex ac ed om he p ecipi a es by using
anion exchange esins (DOWEX AGlX8, HCl o m) and elec opla ed on
o s ainless s eel planche s. Ac i i ies we e measu ed wi h Si ion-implan ed
de ec o alpha spec ome y. De ails o he adiochemical and measu e-
men me hods can be ound in Ma inez-Agui e (1991).
3 EXPERIMENTAL RESULTS
Wa e samples a e deno ed by ‘0’ and suspended ma e samples by ‘SO’.
The numbe s gi en o each sample iden i y he sampling s a ions (see
Fig. l), which a e dis ibu ed along he low eaches o he i e , close o
he e ilize complex. S a ion 1 is, howe e , a ups eam o his a ea. As
i is no belie ed o be a ec ed by idal oscilla ions, only one sample was
collec ed he e.
The esul s o low and high wa e suspended ma e samples a e
p esen ed in Tables 1 and 2, espec i ely. In he case o he low wa e
samples, he e is a high concen a ion peak a s a ion S04, o bo h U and
Th, e ealing he p esence o a local sou ce o ac i i y. Up o 86 and
116 pg g- o U and Th, espec i ely, ha e been measu ed in his sample,
alues which a e much highe han hose p e iously ound o suspended
ma e samples collec ed om o he i e s. Indeed, U concen a ions
anging om 1.8 o 2.4 pg gg’ ha e been de ec ed in he Amazon and
Mississippi i e s (Moo e, 1967). On he o he hand, Th concen a ions in
hese i e s ange om some 8 o lOpgg_’ (Moo e, 1967). In some Japa-
nese i e s, Th concen a ions ange om some 2.2 o 6.7 pg g-’ (Miyake
e al., 1973). Thus, i seems clea ha samples SO4 and S05, collec ed
close o he e ilize complex, a e a ec ed by he was e disposal om he
complex.
In he case o he high wa e suspended ma e samples, he dis ibu ion
o Th and U is di e en . The maximum Th concen a ion is 0.7pgg-‘,
and he e is a gene al homogeniza ion o concen a ion le els. This could
be due o idal mixing, inpu o non-con amina ed suspended ma e om
he sea and a non-cons an inpu o con aminan s om he sou ce ( he
e ilize complex). On he o he hand, U concen a ions a e also lowe
han du ing low wa e , al hough he e is s ill an impo an peak in sample
U anium and ho ium in an es ua y 285
TABLE 1
Concen a ions o U and Th (pgg-‘) o he Suspended Ma e Samples Collec ed Du ing
Low Wa e , and Ac i i y Ra ios
Sample U1 [Th/ 234 Ui23R U 230Th/232Th ThjU
so1 l.lOz O.24 1.2 I 0.3
so2 1.08 0.13 0.07 I 0.04 1.27 0.14 7*4 0.06 i 0.04
so3 2.03 i 0.24 0.11 0.05 1.39z o.17 9 4 0.05 x 0.03
so4 86 I 10 116&6 0.98 0.05 5.28 z!z 0.13 1.35 0.17
so5 25.3 z 1.3 31 3 1 .OO 0.07 6.1 0.7 1.22z o.13
SO6 13.4 1.5 0.052 z 0.024 1.07 0.17 2.4 & 1.4 (3.9 + 1.8) x 1O-3
so7 19.1 I 1.7 1.06 z 0.06
E o s a e la.
TABLE 2
Concen a ions o U and Th (pg g-‘) o he Suspended Ma e Samples Collec ed Du ing
High Wa e , and Ac i i y Ra ios
Sample
so1
so2
so3
so4
so5
SO6
so7
l.lOz O.24
3.9 * 0.5
2.8 0.3
9.oz 1.0
69 i 3
1.6 IIZ 0.4
2.4 zk 0.4
F”hl
0.12 0.07
0.19 z 0.07
0.27 0.13
0.06 0.04
0.7 * 0.2
234u1238u
230Th/232Th ThjU
1.2zlco.3
1.12 0.16 13 8 0.031 0.018
1.09 0.10 3.2 1.4 0.07 * 0.03
1.24 0.10 1719 0.030 z 0.015
1.04 * 0.07
0.9 k 0.3 8 5 0.04 0.03
0.91 0.17 5.1 * 1.9 0.29 k 0.10
E o s a e la.
S05, which is close o he e ilize complex. This e ec has al eady been
obse ed o 226Ra (Pe ia iez e al., 1994a).
In gene al, 234U/238U ac i i y a ios a e compa ible wi h he exis ence o
secula equilib ium in samples in which high U concen a ions ha e been
de ec ed. This is no a ypical ea u e o i e s, bu i is ypical o he
mine als used o e ilize p oduc ion (Ma inez-Agui e e al., 1994a).
The secula equilib ium ound sugges s an ex e nal o igin o he suspen-
ded ma e pa icles, which mus be he e ilize complex.
The 230Th/232Th ac i i y a ios a e highe han 1 all along he i e o
bo h high and low wa e suspended ma e samples. This e eals he high
con amina ion by membe s o he 238U adioac i e chain.
The exis ence o an ex e nal sou ce o ac i i y is con i med om he Th/
U mass a ios. Since U is conside ably mo e soluble han Th, i is o en
ound in de ici wi h espec o Th in he solid su ace en i onmen . Thus,
suspended ma e in unpe u bed i e s usually has ThjU mass a ios

286 R. Pe i&ez, A. Ma inez-Agui e
abo e 1. This is no he case wi h he Odiel i e . I can be seen, in Tables
1 and 2, ha , wi h he excep ion o samples SO4 and SO5 in low wa e ,
he Th/U mass a ios a e below 1. This con i ms he exis ence o an
ex e nal sou ce o U con amina ed pa icles o he i e . The excep ions
men ioned abo e show a ios abo e 1, alues which a e ypical o unpe -
u bed i e s’ suspended pa icles (al hough hey a e he mos con ami-
na ed samples). These esul s will be discussed u he , wi h he help o he
ma hema ical model.
The esul s o he wa e samples a e p esen ed in Table 3. Un o u-
na ely, only he low wa e samples could be measu ed (due o echnical
p oblems in he labo a o y). Sample 01 shows an anomalously high U
concen a ion wi h espec o he es o he da a. The e y low pH o he
wa e , 2.86 (Pe iaiiez & Ga cia-Leon, 1993) due o local geology condi-
ions (Ma inez-Agui e e al., 1994b), accoun s o he enhanced U
concen a ion. The acid wa e s a ound s a ion 1 p o oke a dissolu ion o
U om he solid phase (suspended ma e and bo om sedimen s) o he
liquid phase. This e ec has also been obse ed o Ra-iso opes (Pe iaiiez
& Ga cia-Leon, 1993). The pH o wa e s downs eam om s a ion 01
anges om 6.3 o 7.6; hus, his e ec does no ake place (Pe iaiiez &
Ga cia-Leon, 1993). High U concen a ions a e also obse ed all along he
s udied a ea wi h a peak a ound sample 04, close o he complex. Indeed,
U concen a ions in i e wa e ange om some 0.02 pgll’ in he
Amazon i e (Be ine e al., 1970) o some 3.5 pgll’ in he Nahe i e
(Mangini e al., 1979). Simila alues we e ound in some Indian i e s
(Bha & K ishnaswamy, 1969). Thus, i seems ha an inpu o U-
con amina ed wa e is aking place a ound he sampling s a ion 04. This
inpu is again p obably ela ed o he ope a ion o he e ilize complex.
In he case o Th, concen a ions a leas one o de o magni ude highe
TABLE 3
Concen a ions o U and Th in Wa e Samples (pgl-‘) Collec ed Du ing Low Wa e , and
Ac i i y Ra ios
Sample [VI [Th/ 234 38 u 230 Th/232 Th Thl U
01 7.5 0.3 1.89 0.03
02 2.85 0.16 0.102 0.018 1.09 & 0.05 7.9 1.4 0.014 0.003
03 3.09 0.18 0.147 0.020 1.02 0.04 7.5 1 .o 0.048 & 0.007
04 6.9 & 0.4 8.4 . 1.0 1 .oo 0.05 5.4 * 0.02 1.22 0.16
05 5.3 0.3 0.58 0.19 1.06 0.09 11 z 4 0.11 0.04
06 4.5 0.3 0.29 0.05 1.09 &O.ll 5.8 1.1 0.064 0.012
07 4.98 z 0.24 0.14 0.02 1.08 z 0.04 7.4 1.2 0.028 0.004
E o s a e la.
U anium and ho ium in an es ua y 287
han in o he non-pe u bed wo ld i e s (Moo e, 1967; Miyake e al.,
1973) ha e been de ec ed. A high concen a ion peak (8.4pgl-‘) has been
ound in sample 04, p obably ela ed o he ope a ion o he complex.
The 234U/238U ac i i y a ios a e, in gene al, compa ible wi h he exis-
ence o secula equilib ium. This is no he ypical disequilib ium
obse ed in i e wa e s (Sco , 1982) bu is ypical o he mine als used
o e ilize p oduc ion. The high a io obse ed in sample 01 mus be
due o he highe end o 234U o be dissol ed. The 230Th/232Th ac i i y
a io is abo e uni y all along he i e , indica ing g ea e con amina ion
by adionuclides o he 238U adioac i e chain. Finally, he ThjU mass
a io is, wi h he excep ion o sample 04, below uni y. This is consis en
wi h he end o Th being associa ed wi h he solid phases in i e s. The
excep ion mus be, as in he case o suspended ma e , ela ed o he
con aminan s. This will be discussed la e , wi h he help o modelling.
kd dis ibu ion coe icien s be ween suspended ma e and wa e o
238~ 232Th and 230Th a e p esen ed in Table 4. In he case o 238U, ou
esul s a e in ag eemen wi h he alues ound in li e a u e. Indeed, kd o
U in coas al wa e can ange om 0.2 o 5 lg-‘, he mean alue being
1 lg-’ (IAEA, 1985). The kds a e e y simila o bo h Th-iso opes, indi-
ca ing ha hey a e dis ibu ed be ween wa e and suspended ma e in he
same way. Howe e , alues below he ange o a ia ion which can be
ound in he li e a u e (IAEA, 1985) ha e been ob ained. Ne e heless, a
clea conclusion o hese esul s is he la ge kd a ia ion be ween di e en
sampling poin s (up o wo o de s o magni ude). This a ia ion comes
om he kd de ini ion i sel : i assumes an equilib ium si ua ion o he
exchanges be ween he solid and liquid phases. This si ua ion is no always
achie ed when an in-si u measu emen o kd is pe o med, especially in
si es whe e he inpu in o he sys em is changing wi h ime (man-made
pollu ion). Thus, when a kd measu emen is ca ied ou , an ex ensi e
TABLE 4
Dis ibu ion Coe icien s (1 g-‘) o he Low-wa e Samples
Sample 238 I/ 232Th 230Th
01 0.15 z 0.3
02 0.38 z 0.05 0.7 I 0.4 0.59 IO.17
03 0.91 * 0.12 0.7 4 0.3 0.91 0.17
04 12.5 z 1.6 13.8 1.8 13.3 S 1.6
0.5 4.8 IIZ 0.4 531 18 30 4
06 3.0 0.4 0.2 * 0.1 0.07 x 0.02
07 3.8 z 0.4
E o s a e lo
288 R. Pe i i iez, A. Ma inez-Agui e
desc ip ion o he sampling condi ions (pH, empe a u e and salini y)
should be made in o de o in e p e he esul . In open dynamic sys ems,
such as in an es ua y, equilib ium condi ions will p obably ne e be
eached. Thus, ma hema ical models designed o non-equlib ium condi-
ions a e impo an ools o s udy he dispe sion o adionuclides in
dynamic aqua ic sys ems.
4 THE MODELLING STUDY
4.1 Model desc ip ion
The i s models which we e de eloped o s udy he dispe sion o non-
conse a i e adionuclides in aqua ic sys ems we e a e aged box models
in which he exchanges o adionuclides be ween he liquid and solid
phases we e desc ibed in e ms o kd, assuming comple e equilib ium in
he sys em (Howo h and Eggle on, 1988; Ab il & Ga cia-Leon, 1993).
Howe e , in open sys ems whe e he inpu is changing wi h ime (as in he
case o man-made pollu ion) and when s udying he dispe sion o adio-
nuclides in small coas al egions (such as es ua ies), he equilib ium
app oach will no hold. This is due o he ac ha , because o he high
spa ial and empo al esolu ions ha a e imposed by he nume ical
scheme, he equilib ium will no be eached in each ime s ep (Pe ia iez e
al., 19966). In hese cases, a kine ic app oach is mo e app op ia e. Thus,
he equilib ium will be he dynamic balance be ween wo opposi e chemi-
cal eac ions (Ny ele e al., 1984). The model de eloped o s udy he
dspe sion o adionuclides in he Odiel i e es ua y (which, o cou se,
could be applied o any o he si e) makes use o his kine ic app oach. The
model is p esen ed in de ail in Pe iaiiez e al. (1996b); hus, only a b ie
desc ip ion o he p ocesses ha a e included will be gi en he e.
The sys em unde s udy is di ided in o a numbe o g id cells o
‘compa men s’. Fou phases o subcompa men s a e p esen in each
g id cell, which a e wa e , suspended ma e and wo sedimen g ain
size ac ions. In Fig. 2, a g id cell is shown. Radionuclides can be
dissol ed o associa ed wi h suspended ma e . As ides p oduce a
con inuous mo emen o wa e , adionuclides in bo h phases will be
anspo ed om one g id cell o ano he by ad ec i e and di usi e
p ocesses. Only pa icles wi h a diame e 4 < 62.5 pm a e conside ed o
be p esen in he wa e column as suspended ma e (Gu bu e al.,
1987): la ge pa icles will apidly sink o he bo om. In sedimen s, we
will conside wo g ain size ac ions: pa icles wi h diame e
4 < 62.5 ,um (small g ain size ac ion) and pa icles wi h 4 > 62.5 pm
U anium and ho ium in an es ua y 289
ad ec ion
and
di usion
0
0
Fig. 2. G id
.#
ce lame ac ions
cell in which he adionuclide ans e p ocesses be ween he ou phases a e
ep esen ed.
(la ge g ain size ac ion). Only he small g ain size ac ion can be
esuspended in he wa e column and inco po a ed in o suspended
ma e . On he o he hand, when suspended ma e is desposi ed on he
es ua y bed, i will be inco po a ed in o he small g ain size ac ion o
he sedimen s. Thus, he deposi ion and esuspension p ocesses p oduce
an exchange o adionuclides be ween he suspended ma e and he
small g ain size ac ion o he sedimen . The wa e is in con ac wi h
he o he h ee phases; hus, adso p ion and deso p ion eac ions ake
place. These eac ions a e desc ibed in e ms o kine ic ans e coe i-
cien s. Finally, ex e nal sou ces o adionuclides (in dissol ed and
suspended phases) may exis in each g id cell.
We will conside ha he adso p ion p ocess ( ans e om wa e o he
solid phases) is go e ned by a coe icien kl and he in e se p ocess
(deso p ion owa ds he liquid phase) by a coe icien k2.
The adso p ion p ocess is a su ace phenomenon and will depend on he
su ace o pa icles pe wa e olume uni in o he g id cell. This quan i y
will be deno ed he exchange su ace. I we now conside only suspended
ma e as he solid phase (neglec ing sedimen s), we ha e:
kl = xl &> (1)
296 R. Pe ihiez, A. Ma inez-Agui e
12 - ,' 1
: :
I'
10 - ,' :
,jl :
8
2 ,'
8-
s /'
,'
,/
6- /
,/:: :
IL
4- '!
I'
I ,I :
,' '
,' '-_
2- --.__.________,,.---_
,I' L_
,'
NC
__________________- m
0 I 1 I I I I I 0
0 5 10 15 20 25 30 35 40
Fig. 5, Compu ed (line) and measu ed (poin s) dis ibu ion coe kien (I g-‘) o U du ing
low wa e .
gene al beha iou o he Th/U mass a ios is well ep oduced by he
model in all cases. I was men ioned in Sec ion 3 ha he U excess wi h
espec o Th in suspended ma e indica es he exis ence o an ex e nal
sou ce o U con amina ed pa icles o he i e . The e was, howe e , an
E
, I I I I 1 1 I
1.4 - exp. 8"s. - -
A model susp. ----
model disc --
1.2 -
,I'
l- ,
,' :
/' :
: .
'
0.8 - I'
: I
: :
: :
0.6 - : (1
:
:
I'
0.4 - : '._
I'
:
__--__________ 1'
0.2 - ' '
'
L__/ __.-.
I I I
0 5 IO 15 20 25 30 35 40
Fig. 6. Model esul s o Th dispe sion. (A) Wa e and suspended ma e du ing high
wa e . (B) Suspended ma e du ing low wa e . (C) Wa e du ing low wa e . Concen a-
ions a e gi en in pg 1-l and pg g-’ o wa e and suspended ma e samples, espec i ely.

U anium and ho ium in an es ua y 297
F
140 1 I 1 I , I b
=P. w
B model ----
120 -
100 I : - I
: /
/ :
80 - : )
:
: : ,
/j
,' :
60 - ,'
,'
,I'
,'
40 - ;p ,/' I
20 - ,' I' :
,'
I' I
,/ : . .
0 5 10 15 20 25 30 35 40
I
9 c
8
exp. -
model ----
10 15 20 25 30 35 40
Fig. 6. Con inued.
excep ion (samples SO4 and SO5 which we e he mos con amina ed).
Indeed, mo e Th han U is discha ged in o he i e , in bo h dissol ed and
suspended o ms. F om he second inpu a es ( he i s a e no indica i e
because hey a e used jus o c ea e he backg ound), i can be shown ha ,
in solu ion, ThjU = 2.4, and in suspended ma e , Th/U = 1.5. Thus,
mo e Th han U is discha ged and, as a consequence, he e is an excess o
Th in wa e and suspended ma e nea he sou ce. Howe e , he e is an
298 R. Pe ibiez, A. Ma inez-Agui e
100
80
20
1 I I I I I I
exp. -
model ..~_
,,--
>’ I ‘.
,/- Y_
I’ -._
_______.-._____-I --._________.----.-_
ok ” I I I I I I IA & 1
0 5 10 15 20 25 30 35 40
Fig. 7. Compu ed (line) and measu ed (poin s) dis ibu ion coe icien (1 g-‘) o Th du ing
low wa e .
excess o W in he es o he i e in bo h liquid and suspended phases. I
seems clea ha he dissol ed Th ha is eleased o he i e is quickly
ixed o solid pa icles, and hese pa icles ( oge he wi h he pa icles ha
a e eleased om he sou ce and a e ich in Th) a e deposi ed on he i e
0.25
0.2
3
E 0.15
0.1
5.000000e-02
0
I -
_‘..
.__________-.. ,,. ,--’ Y
,’ ,,’ ,,--
‘ _‘ I’
-*_- ._,_‘-
$I ,I’
1, , , , ‘,
: I’ i :
.-. ,’
----.__________--- ** i i
( ,
0 5 10 15 20 25 30 35 40
Fig. 8. Compu ed (lines) and measu ed (poin s) ThjU mass a ios o suspended ma e
samples du ing high wa e (A), wa e samples du ing low wa e (B), and suspended ma e
samples du ing low wa e (C).
U anium and ho ium in an es ua y 299
1.4 I I !
exP. 1-41
model ----
l.2- 0
0.6 - I'
,,'
/'
I'
0.4 - I'
I'
/' I
,'
0.2 - I' ,' :
:
,,=
,' I :
* /__-' .I_
0. ________- ____---- I I ---___ _-----__-- _io___
0 5 10 15 20 25 30 35 40
1.4- c ,’
__-- 4 cup. w
model ----
____-- ,
,/--
1.2 - ,'
I
'
,' '
l- ,'
I
I'
0.6 - :
0.6 - ,' ,
I ‘ '
I'
: ),
: >/
0.4 - : :
: II
#' :
0.2 - : j
_____----..___I
'.
'..
o- e 1 I I I I ---___________T---g
I I
0 5 10 15 20 25 30 35 40
Fig. 8. Con inued.
bed nea he sou ce. In his way, a U excess would exis in he es o he
i e , as con i med by he expe imen al and he model esul s. This
hypo hesis is also suppo ed by he ac ha an excess o Th has been
measu ed in sedimen s collec ed close o he e ilize complex (Ma inez-
Agui e e al., 19946).
The sensi i i y o he model o he di e en pa ame e s, he way o
c ea ing he backg ound and he magni ude o he sou ce e m ha e
al eady been s udied (Pe ia iez e al., 19943, 1996a,c).
300 R. Pe icinez, A. Ma inez-Agui e
5 CONCLUSIONS
U anium and Th concen a ions ha e been measu ed in wa e and
suspended ma e samples in an es ua ine sys em a ec ed by was e dispo-
sal om a e ilize p ocessing complex. Dis ibu ion coe icien s ha e also
been calcula ed. The esul s ha e shown a adioac i e impac and a
signi ican kd a iabili y. In o de o pe o m a quan i a i e s udy on he
dis ibu ion o U and Th, as well as on he kd a iabili y, a modelling
s udy has been ca ied ou .
The model includes he pa i ion o adio ace s be ween ou phases,
and his pa i ion is based on a kine ic app oach. The model sol es he
hyd odynamic equa ions, he suspended ma e equa ions and he ou
equa ions ha go e n he ime e olu ion o he adio ace concen a ions
in each one o he ou phases.
The model esul s a e in good ag eemen wi h he expe imen al da a o
bo h U and Th, and o bo h wa e and suspended ma e samples. The kd
a iabili y is ep oduced by he model, as well as he ThjU mass a ios.
This shows he goodness o he desc ip ion o he ans e p ocesses, since
good esul s a e ob ained o elemen s wi h a e y di e en chemical
beha iou (Ra, U, Th) by simply changing he alue o a pa ame e : he
exchange eloci y.
ACKNOWLEDGEMENTS
This wo k was pa ially suppo ed by ENRESA. The au ho is indeb ed o
J. M. Ab il o help in he modelling wo k.
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APPENDIX
Dissol ed phase
acL4
---Z
a -ki Cd j!$ + k2 C,m g + k2 (sed, + sedi) + (ad + di ), (Al)
whe e Cd and C, a e he adionuclide concen a ions in wa e (mgmh3)
and suspended ma e (mgg-‘), espec i ely, m is he suspended ma e
concen a ion (mgl-‘) and H is he wa e column heigh . The ime de i-
a i e mus be in e p e ed as in a o wa d ini e di e ences scheme. The *
means ha he co esponding quan i y mus be e alua ed in he new ime
s ep. The i s e m ep esen s he ans e o adionuclides om wa e o
he h ee solid phases. Thus, kl is gi en by eqn (3). ad + di ep esen s
ad ec i e plus di usi e anspo o dissol ed adionuclides om one g id
cell o ano he . The hi d e m is he ans e o adionuclides om he
wo ac ions o sedimen s o wa e :
sed s H*
sed I
(A21
(A3)
whe e a, and aI a e he adionuclide concen a ions in he small and he
la ge g ain size ac ion o he sedimen s, espec i ely (mgg-*). The bulk
densi y o he sedimen , pm, is gi en in kgme3.
U anium and ho ium in an es ua y
Suspended ma e
303
acs
a = m*H*
kl x - k2Cs s + ( es - dep) + (ad + di ). (-44)
As he i s e m is he ans e o adionuclides om wa e o jus
suspended ma e , kl is gi en by he i s e m o eqn (3). ad + di is he
ad ec i e plus di usi e anspo o adionuclides in suspended ma e .
The second e m is he ans e o adionuclides om suspended ma e o
wa e , and es and dep ep esen he esuspension and deposi ion p oces-
ses:
d C,m
dep = -
m*H*
iws 9
es = ___
m*H’ ( >
-- I 103,
VC,
(A%
whe e d and , a e he mean deposi ion and esuspension eloci ies, Cd
and ,, a e he c i ical deposi ion and esuspension eloci ies and q is he
wa e lux eloci y.
Bo h in he dissol ed phase and in he suspended ma e equa ions, he
ex e nal sou ces o adionuclides mus be included in he g id cells in
which hey exis .
Sedimen s
The equa ion o he small g ain size ac ion is:
&I, CdH
a =
kl -
P& lo3 - kza, ,b + (dep - es). (A7)
The i s e m is he ans e om wa e o he small ac ion o he sedi-
men . Thus, kl is gi en by he second e m o eqn (3). The second e m is
he ans e o adionuclides om he sedimen o wa e and dep - es
ep esen s he ans e s be ween he sedimen and suspended ma e
( h ough deposi ion and esuspension):
dep = (A@
a, ( >
z-1
es = 7 ,, . (A9)
304 R. Pe ici ?ez, A. Ma inez-Agui e
The equa ion o he la ge g ain size ac ion o he sedimen is:
8 al
a = (AlO)
whe e he i s e m is he ans e o adionuclides om wa e o he
sedimen [kl is gi en by he hi d e m o eqn (3)], and he second e m
ep esen s he in e se p ocess.