Modelling he Dis ibu ion o Radionuclides
7 in Deep Ocean
Wa e Columns. Applica ion o 3H, 13 Cs and 239•246Pu
R. Pe iáñez
Op o. Física Aplicada, E.U. Ingenie ía Técnica Ag ícola, Uni e sidad de Se illa, C a.
U e a km 1, 41013- Se illa, Spain
ABSTRACT
A one-dimensional model o simula e he dispe sion o adionuclides down deep
wa e columns has been de eloped. The model includes he ans e s o adionuclides
be ween wa e , suspended ma e and bo om sedimen s. Such ans e s a e
o mula ed in e ms o kine ic ans e coe icien s. A suspended ma e sub-model has
also been de eloped o ob ain he suspended ma e concen a/ion p o ile. The
dependence o he se ling eloci y o suspended pa icles on he salini y p o ile and
he dependence o he e ical u bulen di usion coe icien on he ho izon al wa e
cu en p o ile a e included in he model. The mode/ has been alida ed by compa ing
measu ed and compu ed p o iles o 3 H, 137 Cs and 239'240 Pu in he A lan ic, he
Medi e anean and he Paci ic. So ne p edic i e s udies and sensi i i y es ha e a/so
been ca ied ou .
INTRODUCTION
The e has been an inc easing in e es in measu ing adionuclide p o iles in
wa e columns in he deep ocean o e he las ew yea s (Bowen e al.,
1980; Fukai e al., 1980; Li ings on e al., 1987; Mole o e al., 1995).
Howe e , ew one-dimensional ma hema ical models ha e been de eloped
o s udy such p o iles.
The model o Mon e e al. (1991) simula es he dispe sion o
conse a i e adionuclides (neglec ing in e ac ions wi h suspended ma e
and bo om sedimen s) in deep lakes. The wa e column is di ided in o
h ee laye s: epilimnion, he mocline and hypolimnion. This model
ep oduces he dep h dis ibu ion o adionuclide concen a ions in so ne
lakes, bu in o he cases, he e a e disc epancies due o he ac ha
in e ac ion wi h sedimen s 1s an impo an ac o in emo ing
adionuclides om he wa e .
The model o Ribbe e al. (1991) includes he in e ac ions o
adionuclides wi h suspended ma e and bo om sedimen s, and is applied
ín a shallow sea (wa e dep h is a ound 140m). A cons an suspended
ma e dis ibu ion in he wa e column is assumed, as well as a cons an
e ical u bulen di usion coe icien . These may be ealis ic assump ions
in shallow wa e s, bu no in he deep ocean (wa e dep hs o so ne
housands o me e s). Indeed, suspended ma e concen a ions dec ease
om he su ace o he bo om (B ewe e al., 1976; Eisma, 1993). Also,
since he ho izon al wa e eloci y is no cons an in he wa e column
(Pugh, 1987) and since u bulence is ela ed o he wa e eloci y, he
di usion coe icien will no be cons an along he wa e column. Because
o his, he model o Ribbe e al. (1991) <loes no adequa ely ep oduce he
adionuclide concen a ions in he deepes wa e laye s.
In his pape , a one-dimensional dispe sion model o bo h conse a i e
and non-conse a i e adionuclides is p esen ed and alida ed by compa ing
measu ed and compu ed e ical p o iles o 3H, 137Cs and 239•240Pu in he
deep ocean. Toe exchange o adionuclides be ween wa e , suspended ma e
and bo om sedimen s is desc ibed in e ms o kine ic ans e coe icien s.
Thus, a coe icien k1 go e ns he ans e om wa e o he solid phase, and
a coe icien k2 go e ns he in e se p ocess. The adso p ion o adionuclides
on suspended ma e , and he e o e he ans e coe icien k1, depend on he
suspended ma e concen a ion. Thus, a suspended ma e sub-model is
de eloped o ob ain he suspended ma e concen a ion p o ile. The e ical
di usion coe icien is w i en as a unc ion o he ho izon al wa e eloci y,
which also a íes along he wa e column. The model is o ally gene al and
can be applied o bo h s a i ied and non-s a i ied seas. The salini y along
he wa e column is in oduced in he model as inpu da a and so he salini y
p o ile may ea u e a halocline i necessa y.
I mus be no ed ha ho izon al ad ec ion and di usion o con aminan s
a e no incJuded in he model. This e ec can be neglec ed in he case, o
ins ance, o allou ha is cons an o e a la ge a ea. In he case o a poin
discha ge, ho izon al dispe sion will be impo an , and he ime ha he
model compu es o he emo al o adionuclides om he wa e column
will be longe han he eal ime, since such ho izon al dispe sion p oduces a
as e dec ease in concen a ion. Thus, a one-dimensional model mus be
applied in he case o uni o m sou ces o con amina ion.
In he nex sec ion, he suspended ma e and he adionuclide
dispe sion models a e p esen ed. In he hi d sec ion, he model is
alida ed and applied o so ne p edic i e s udies dealing wi h hypo he ical
acciden s. Finally, so ne sensi i i y es s ha e been pe o med o s udy he
model esponse o a ia ions in he pa ame e s in ol ed in he model.
MODEL DESCRIPTION
Suspended ma e sub-model
As men ioned in he In oduc ion, he e ical suspended ma e
dis ibu ion mus be known o compu e he ans e o adionuclides
om wa e o suspended pa icles.
l is assumed ha , in a s eady s a e si ua ion, he upwa d di usion a e
o suspended pa icles is equal o he downwa d se ling a e, which leads
o he ollowing equa ion (Nicholson and O'Conno , 1984; Eisma, 1993):
(1)
whe e Kz, m and Wz a e, espec i ely, he e ical di usion coe icien , he
suspended ma e concen a ion and he se ling eloci y o suspended
pa icles a le el z measu ed om he su ace o he bo om.
The se ling eloci y o pa icles is ob ained om S okes' law:
(2)
whe e g is g a i y, µ he iscosi y o wa e , d he mean diame e o suspended
pa icles, Ps he densi y o suspended pa icles and Pz is he wa e densi y a a
dep h z below he su ace. The se ling eloci y is conside ed o be independen
o m, ha is, he e ec s o agg ega ion and o hinde ed se ling a high alues
o m ha e been neglec ed. This is a easonable assump ion gi en he low
suspended ma e concen a ions ound in he ocean (Jones e al., 1994).
The e ical di usion coe icien , K2, is conside ed o be p opo ional o
he ho izon al wa e eloci y (Nicholson and O'Conno , 1984):
(3)
whe e U2 is he ho izon al wa e eloci y a dep h z. U2 can be ela ed o
he su ace wa e eloci y, Us, h ough he ela ionship (Pugh, 1987):
(4)
D is he o al wa e dep h and n is an in ege numbe ha anges be ween
5 and 7 (Pugh, 1987). The coe icien x. in Eq. (3) is ob ained om a
calib a ion exe cise.
Equa ion (1) is sol ed nume ically o ob ain he suspended ma e
concen a ion p o ile. The alues o he di e en pa ame e s will be
gi en la e .
Dispe sion o adionuclides
Radionuclides can be dissol ed o ixed o solid pa icles. Ionic exchanges
p oduce a ans e o adionuclides be ween wa e and suspended ma e .
This ans e is desc ibed by kine ic ans e coe icien s. Radionuclides in
he dissol ed phase a e subjec o u bulen mixing, and adionuclides in he
pa icula e phase ha e a alling eloci y equal o he se ling eloci y o
suspended pa icles. In he wa e laye ha is in con ac wi h he bo om
sedimen an ionic exchange be ween he wa e and he sedimen akes place.
Also, adionuclides in suspended ma e can be deposi ed on he sea bed.
Resuspension o ma e ial om he sea bed is ela ed o he p esence o
s ong bo om cu en s (Eisma, 1993). This e ec has been neglec ed; hus,
he model should be applied only in egions lacking such cu en s.
The wa e column is di ided in o a numbe o laye s o hickness �z.
The equa ion whose solu ion gi es he ime e olu ion o adionuclide
concen a ion in wa e , Cd (Bq m -3), a a gi en laye is:
JCd J ( JCd)
75 = az Kz az -k, Cd + k2mCs -J..Cd,(5)
whe e Cs is he adionuclide concen a ion in suspended ma e (Bq g-1)
and A is he adioac i e decay cons an . k1 and k2 a e he kine ic ans e
coe icien s. The ans e o adionuclides om wa e o suspended
ma e depends on he suspended ma e su ace pe uni wa e olume,
which is deno ed as he exchange su ace (Pe iáñez e al., 1996a).
Assuming sphe ical pa icles and a s ep unc ion o he g ain size
dis ibu ion o suspended ma e , he coe icien k1 can be w i en as
(Pe iáñez e al., 1996a):
3m
k, =x,R
Ps
(6)
whe e R is he mean adius o suspended pa icles and Xi is a pa ame e
ha depends on he wa e condi ions (salini y, pH, empe a u e). Since i
has dimensions o a eloci y, i is deno ed he exchange eloci y (Pe iáñez
e al., 1996a). The coe icien ha go e ns he ans e o adionuclides
om suspended pa icles o wa e , k2, is assumed o be cons an
(Pe iáñez e al., 1996a).
The equa ion ha gi es he ime e olu ion o adionuclide
concen a ion in suspended ma e is:
(7)
whe e k1 is gi en by Eq. (6). In hese equa ions, he se ling eloci y o
suspended pa icles and he e ical di usion coe icien a e aken as in
he suspended ma e sub-model.
The deepes wa e laye also in e ac s wi h he bo om sedimen s.
Neglec ing esuspension, he equa ion ha gi es he ime e olu ion o
sedimen ac i i y pe a ea uni , As (Bq m-2), is:
(8)
whe e '*' means ha he espec i e quan i y is e alua ed o he deepes
wa e laye . The equa ions o Cd and C., in his deepes laye a e also
co ec ed o ake in o accoun in e ac ions wi h he sedimen s.
In his equa ion, he ans e coe icien k� will depend on he exchange
su ace o he sedimen . This coe icien can be w i en as (Pe iáñez e al.,
1996a):
k* _ 3L l/J
1 -X1 Ró.z (9)
whe e L gi es he mean dep h o which he wa e pene a es he sedimen
due o i s po osi y, is he ac ion o ac i e sedimen , which is made up
o pa icles wi h a diame e < 62·5 µm (Benes e al., 1994), R is he mean
adius o he ac i e sedimen pa icles and 1/J is a geome ical accessibili y
ac o , which akes in o accoun ha , o geome ical easons, no all he
mass o he ac i e sedimen is in con ac wi h wa e . The mean adius o
he ac i e sedimen pa icles has been conside ed o be equal o he mean
adius o suspended pa icles (Pe iáñez e al., 1996a).
The concep s o exchange su ace and exchange eloci y and he
o mula ion o he ans e coe icien k1 ha e been success ully applied
o simula e he dispe sion o 226Ra, 238U, 232Th and 210Po in a idal
es ua y in sou h-wes Spain (Pe iáñez e al., 1996b; Pe iáñez and
Ma ínez-Agui e, 1997, in p ess).
MODEL RESULTS
Calib a ion and esul s
The model has been alida ed by compa ing adionuclide p o iles
measu ed in he A lan ic Ocean, he Paci ic Ocean and he
Medi e anean Sea wi h he compu ed p o iles.

Fi s , he suspended ma e concen a ion p o ile mus be ob ained by
sol ing Eq. (1). The wa e column is di ided in laye s o hickness
�z =lOOm. Wa e iscosi y is aken as µ=1·005x10-3Ns m-2 and he
mean densi y o suspended pa icles is selec ed as 2600 kgm-3, which is he
es ablished alue o he densi y o soil pa icles (Ba e e al., 1972) and has
been used in p e ious modelling wo k (Pe iáñez e al., 1996b; Pe iáñez and
Ma ínez-Agui e, 1997b). Wa e salini y, S, is conside ed o inc ease
linea ly wi h dep h om 30gl-1 a he su ace o 90gl-1 a he bo om.
This is a ealis ic assump ion (see o ins ance he measu emen s o Feely e
al., 1979). The densi y o wa e (kg m-3) inc eases linea ly wi h salini y
ollowing he ela ion gi en by Kowalick and Mu y (1993):
p = 998 · 91(1 + 7 · 5 X 10-4S). (10)
Such a salini y p o ile leads o s able s a i ica ion, which is cha ac e ized by
a Richa dson numbe g ea e han 1 (Eisma, 1993).
Only pa icles wi h a diame e less han 62 ·5 µm can be p esen in he
wa e column as suspended ma e ; la ge pa icles quickly sink o he
bo om (Gu bu e al., 1987). Thus, he mean diame e o suspended
pa icles is ixed as 30 µm. Using hese pa ame e s, he se ling eloci ies
o he suspended pa icles, Wz, a e in he o de o 10-3 m s-1, which is in
ag eemen wi h ha ound by Jones e al. (1994) and Nicholson and
O'Conno (1984). The a e age wa e eloci y a he su ace is aken as
Us=0·02ms-1 since his is a ypical alue o he esidual cu en in he
open sea (Ellio e al., 1992; P andle e al., 1993). To ob ain he cu en
p o ile, he mean alue 6 was aken o he in ege n.
Suspended ma e concen a ions in su ace wa e s in he sea can ange
om 0·005mg l-1 o he lOO mg l-1 measu ed in coas al wa e s (Eisma,
1993). In his wo k, a su ace concen a ion o 2 mg 1-1 is aken as he
bounda y condi ion o nume ically sol e Eq. (I).
In he ocean, he e is a mo e u bid su ace laye and a dec easing
concen a ion o suspended pa icles wi h dep h (B ewe e al., 1976).
Thís e ec is obse ed in he solu ion o Eq. (I). Indeed, a suspended
ma e concen a ion o 0· 13 mg 1-1 is ob ained o he deepes wa e
laye (i he o al wa e dep h is 4000m), which ep esen s 6·5% o he
concen a ion in he su ace. This suspended ma e p o ile has been used
as inpu da a o he adionuclide dispe sion model.
A deep nepheloid laye (wa e close o he sea bo om wi h a la ge
suspended load) may exis [see, o ins ance, Biscaye and Ei eim
(197 7)). Deep nepheloid laye s in he deep ocean a e ela ed o he
p esence o s ong bo om cu en s (Eisma, 1993) ha p oduce
esuspension o pa icles om he sedimen . Since esuspension has been
neglec ed, he deep nepheloid laye <loes no appea .
O cou se, he suspended ma e dis ibu ion along he wa e column
will no be he same o he Medi e anean, he A lan ic and he Paci ic,
bu he compu ed dis ibu ion can be conside ed as ep esen a i e o he
eal si ua ion in he sea. Indeed, such a p o ile will be mo e ealis ic han
assuming a cons an suspended ma e concen a ion as in Ribbe e al.
(1991). This is con i med by he ac ha esul s in ag eemen wi h
measu emen s a e ob ained when using his suspended ma e p o ile in
modelling he dispe sion o non-conse a i e adionuclides along he
wa e column.
The mixing dep h in he sedimen has been aken as L = 0-1 m ollowing
p e ious modelling wo k (Ab il and Ga cía-León, 1993; Pe iáñez e al.,
1996b ). The ac ion o ac i e sedimen s was aken as
= O· 30, which is a
common alue (Pe iáñez and Ma ínez-Agui e, 1997b), and he
geome ical ac o is selec ed as 1/1=0-001 (Pe iáñez and Ma ínez
Agui e, 1997b ).
The model has been applied o simula e he dispe sion o 137Cs,
239•24ºPu and 3H. Thus, he exchange eloci y XI and he ans e
coe icien k2 mus be known o hese adionuclides. In he case o 137
Cs
hey ha e been ob ained om labo a o y expe imen s ca ied ou by
Ny ele e al. (1984): XI =2-10x10-8ms-1 and k2= l-16x10-5s-1.
Ny ele e al. (1984) ound a e y small a iabili y in k2 (less han an
o de o magni ude) when hey measu ed his pa ame e o a wide se o
elemen s (Th, Sn, Hg, Pa, Zn, Sb, Cs, Se, Cd, Ba) wi h e y di e en
chemical beha iou s. This small a ia ion makes i possible (Ny ele e
al., 1984) o es ima e XI wi hou labo a o y expe imen s. Thus, he k2 o
Pu can be aken o be equal o ha o Cs. F om he coe icien k2 and
he mean alue o he dis ibu ion coe icien , kd, o Pu in he sea, he
exchange eloci y o Pu can be es ima ed ollowing he me hod p esen ed
in de ail in Pe iáñez and Ma ínez-Agui e (1997a). Indeed, he ollowing
ela ionship be ween Xi, k2 and kd (Pe iáñez e al., 1996b) holds:
kd = �_2__ (11)
k2PsR
This me hod has yielded good esul s in p e ious modelling wo k
(Pe iáñez and Ma ínez-Agui e, 1997a, b). The exchange eloci y
ob ained is x1=1-51x10-5ms-I. The exchange eloci y o Pu is h ee
o de s o magni ude g ea e han ha o Cs, due o he la ge a ini y o
Pu o solid pa icles. In he case o 3H, in e ac ions wi h he solid phases
a e neglec ed: XI= k2 = O.
Once all he pa ame e s in ol ed in he model ha e been de ined, he
dispe sion equa ions a e sol ed using a ini e di e ence explici scheme
wi h a ime s ep b. = 100 s and aking b.z = 100 m. The ac ual
con amina ion o he ocean is caused by he allou esul ing om nuclea
weapon es s, he Chemobyl acciden , eleases om nuclea acilli ies, e c.
This allou has been aking place o e se e a! decades, and so he model
should un o e long ime scales. To sa e CPU ime, simula ions o e
2 yea s a e ca ied ou . A = O, he wa e column is has no adioac i i y,
and he allou s a s. The allou magni ude is ampli ied in such a way
ha a e 2 yea s, he ac ual le els o con amina ion a e eached. O
cou se, he magni ude o he allou is no cons an in ime, bu a
cons an deposi ion a e o adionulides on he sea su ace is conside ed,
which can be aken as a mean deposi ion. This echnique o ampli ing
he sou ce e ms has been used success ully in p e ious modelling wo k
(Pe iáñez and Ma ínez-Agui e, 1997b). The magni udes o he
deposi ion a es (used o ob ain he ac ual con amina ion le els a e jus
2 yea s o each adionuclide and o each loca ion whe e he model is
applied) we e selec ed by ial-and-e o exe cises. Un o una ely, he
deposi ion a es could no be compa ed wi h measu emen s owing o he
lack o da a a he places in which he model is applied.
Measu ed and compu ed 137Cs p o iles in he Paci ic ocean a e shown
in Fig. lA (Tahi i) and B (Tuamo o A chipelago). Expe imen al da a
we e aken om Bou la e al. (1996) and Hamil on e al. (1996),
espec i ely. Uni s and scales used by he au ho s o he expe imen al
wo ks ha e been ollowed in d awing he igu es p esen ed in his pape .
As men ioned abo e, he pa ame e a in he di usion coe icien is
ob ained om a calib a ion exe cise o each loca ion whe e he model is
applied. This calib a ion consis s o selec ing, by ial and e o , he
alues o a ha p oduce he esul s in he bes possible ag eemen wi h
he measu emen s. l was aken as O· l in Tahi i and 0-08 in Tuamo o
A chipelago. Thus, di usion coe icien s simila , by o de o magni ude,
o hose used by Ribbe e al. (1991) and Mon e e al. (1991) a e
ob ained. As can be seen in Fig. 1, model esul s a e in good ag eemen
wi h he expe imen al measu emen s.
In Fig. 2A and B, measu ed and compu ed p o iles o 137 Cs in he
Medi e anean Sea and 3H in he A lan ic Ocean, espec i ely, a e
shown. The Cs p o ile was aken om Papucci e al. (1996) and he
i ium one om Ny ele e al. (1996). a was aken as 0-8 in he A lan ic
and 0-08 in he Medi e anean sea. Again, he model gi es good esul s
o bo h adionuclides.
In Fig. 3, model and expe imen al esul s o 239•24ºPu in Tahi i and he
Tuamo o A chipelago a e shown. Expe imen al esul s a e aken om
Bou la e al. (1996) and Hamil on e al. (1996). Model esul s a e in
ag eemen wi h measu emen s in bo h p o iles. The model shows wo
in e es ing ea u es ha ha e been obse ed: he subsu ace maximum
2.5 (a) "model" -
"exp• 1-+-l
2
1.5
�
Ji
0.5
m lll 111 111
o o 500 1000 1500 2000 2500
dep h (m)
10
(b) "model" -
"exp • i-+---,
?'"
Ji
0.1
0.01 .___���..__�......_�...__�.....__�......___�_._______.
O 500 1000 1500 2000 2500 3000 3500 4000
dep h (m)
Fig. l. Compu ed and measu ed 137Cs p o iles in wa e samples (dissol ed phase)
collec ed a Tahi i (A) and Tuamo o A chipelago (B). E o s a e 2<T in (B).
de ec ed a ound 600 m below he su ace and he 'high Pu deep laye '
desc ibed in Li ings on e al. (1987) and Bowen e al. (1980). Indeed, in
Fig. 3, a sligh inc ease o dissol ed Pu om 1500 m o he bo om can
be obse ed. Thus, in deep wa e , Pu is eleased o he dissol ed phase by
M'
M'
0.6 .---"""T""-- -----.----,---,-------.--....-----,
0.5
0.4
0.3
0.2
0.1
o
o
90
80
70
60
50
40
30
20
10
o o
(a)
(b)
" ime-1" -
" ime-2" ----·
" ime-3" ----
" ime-4"
500 1000 1500 2000 2500 3000 3500 4000
dep h (m)
" ime-1" -
" ime-2' ----·
" ime-3" ----
' ime-4" ····· ·
500 1000 1500 2000 2500 3000 3500 4000
dep h (m)
Fig. 7. To al con en s o 137Cs (A) and 239·240Pu (B) 5, 10, 15 and 20days ( ime!, ime 2,
ime 3 and ime 4, espec i ely) a e he deposi ion.
SENSITIVITY TESTS
So ne pa ame e s, such as he su ace suspended ma e concen a ion, he
su ace wa e eloci y and :i in he di usion coe icien , a e no known o
he places whe e he model is applied. Thus, alues ha a e simila o

3000 ------------...---.--�-�---.
"model" -
2500
2000
l1500
1000
500
oL...._.L.__.L-...:::...L--...L--.J--...L--....L.--'----'---'
o10 20 30 40 50 60 70 80 90 100
ime (days)
Fig. 8. Time e olu ion o 239·240Pu ac i i y in he bo om sedimen
0.6 ---------------�------.
0.5
' ime-1' -
' ime-2' ---
' ime-3' .....
' ime-4'
¿;, 0.4
1
0.3
0.2
0.1
o500 1000 1500 2000 2500 3000 3500 4000
dep h (m)
Fig. 9. To al con en s o 137Cs 5, 10, 15 and 20days ( ime 1, ime 2, ime 3 and ime 4.
espec i ely) a e he deposi ion when a halocline is p esen .
hose ound in cu en li e a u e ha e been selec ed. So ne sensi i i y es s
ha e been pe o med o s udy he model esponse o changes in hese
pa ame e s. The es s ha e been ca ied ou wi h he 239·24ºPu p o ile
measu ed a Tuamo o A chipelago.
Fi s , he sensi i i y o he model o changes in he wa e laye hickness
was s udied. The model esul s do no show any app eciable di e ence i
he hickness o he wa e laye s is aken as �z = 50 m.
In a second es , he model esponse o changes o he su ace suspended
ma e concen a ion was s udied. The esul is p esen ed in Fig. 10, whe e
'1' ep esen s he model esul when he su ace suspended ma e
concen a ion is aken as 1 mg 1- 1 and '2' is he model esul when such a
concen a ion is aken as 4 mg 1-1• I should be no ed ha changing he
su ace suspended ma e concen a ion implies ha suspended ma e
concen a ions along he wa e column also change, since he suspended
ma e equa ion is sol ed again wi h he new bounda y condi ion. A
dec ease in suspended ma e concen a ions leads o an inc ease in
dissol ed Pu concen a ions (' l' in Fig. 1 O) since he exchange su ace is
educed. Howe e , an inc ease in suspended ma e concen a ion ('2' in
Fig. 1 O) p oduces a dec ease in dissol ed Pu concen a ions since he
exchange su ace inc eases. I can be seen ha good esul s a e ob ained
wi h a su ace-suspended ma e concen a ion o 2 mg 1-1 ('model').
In he hi d es , he model sensi i i y o changes in he su ace wa e
eloci y was s udied. The esul is p esen ed in Fig. 11, whe e 'l'
ep esen s he model esul when he su ace wa e eloci y is aken as
0·08 m s- 1, and '2' ep esen s he model esul when i is aken as
0-005 m s-1• A la ge sub-su ace maximum is ob ained when he wa e
20
18
16
M' 14
12
.§.
� 10
� 8
6
Q.
4
2
o
o 500
'model' -
'exp' �
·1 • ----.
·2·
... 1 _________________
. ..
---· ····
1000
1500
dep h (m)
2000 2500
Fig. 10. Model esponse o changes in he su ace suspended ma e concen a ion. See
ex o explana ion o '1' and '2'.
¿;,
.s
12
10
8
6
4
2
500
1000
1500
dep h (m)
'model' -
'exp' -+--1
'1'
·2· .
2000 2500
Fig. 11. Model esponse o changes in he su ace wa e eloci y. See ex o
explana ion o 'I' and '2'.
eloci y dec eases since he di usion coe icien dec eases oo. The model
is no sensi i e om 1500 m o he bo om since wa e eloci ies a such
dep hs a e e y small in all cases (Eq. (4)).
Finally, he sensi i i y o he model o he pa ame e IX in he di usion
coe icien is p esen ed in Fig. 12. 'l' ep esen s he model esul aking
IX= 0-04 and '2' he model esul aking IX= O· 16. Again, a dec ease in he
di usion coe icien leads o a la ge sub-su ace maximum. The model is
no sensi i e om 1500 o he bo om o he men ioned abo e.
The o mula ion on which he ans e o adionuclides be ween he
dissol ed and solid phase is based, is p esen ed in Pe iáñez e al. (1996a).
In Pe iáñez e al. (1996b), he sensi i i y o such o mula ion o Xi, k2
and he geome ical accessibili y ac o 1/¡ is s udied.
CONCLUSIONS
A one-dimensional model has been de eloped o simula e he dispe sion o
adionuclides along deep wa e columns. The model includes he ans e
o adionuclides be ween wa e , suspended ma e and bo om sedimen s.
Such ans e s a e desc ibed by means o kine ic ans e coe icien s. A
suspended ma e sub-model is also de eloped o ob ain he suspended
ma e concen a ion p o ile along he wa e column. The u bulen
14
'model' -
12 'exp' 1-+-----,
'1' ...
·2·
(') 10
i 8
s
6
4
2
500 1000 1500 2000 2500
dep h (m)
Fig. 12. Model esponse o changes in he pa ame e C< in he di usion coe icien . See
ex o explana ion o 'I' and '2'.
di usion coe icien and he se ling eloci y o suspended pa icles
depend on he wa e dep h, which has imp o ed he model esul s wi h
espec o p e ious modelling wo k. Also, he model can be applied o
s a i ied seas since he salini y p o ile is used as inpu da a.
Model esul s a e in good ag eemen wi h measu ed concen a ion
p o iles o 137Cs, 3H and 239•240Pu in he A lan ic, he Paci ic and he
Medi e anean, which show he adequacy o he desc ip ion o he
p ocesses. Once he model has been alida ed, i has been applied o
so ne p edic i e s udies conce ning hypo he ical nuclea inciden s. The
esul s o hese nume ical expe imen s ha e, o ins ance, suppo ed
p e ious hypo hesis abou he mechanisms o emo al o di e en
adionuclides om he wa e column.
I should be no ed ha so ne e ec s ha e been neglec ed. Fo ins ance,
he exchange eloci y X depends on he wa e salini y and empe a u e.
This dependence is no included in he model because i is no known
quan i a i ely, bu could be easily implemen ed as expe imen al
knowledge inc eases.
ACKNOWLEDGEMENTS
This wo k was pa ially suppo ed by ENRESA.
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