Modelling he physico-chemical specia ion o
plu onium in he eas e n I ish Sea
R. Pe iaH n8 ez
Depa amen o Fn&sica Aplicada, E.U. Ingenie &naTe&cnica Ag &ncola. Uni e sidad de Se illa.
C a U e a km 1, 41013-Se illa, Spain
Abs ac
A nume ical model o simula e he specia ion o 239,240Pu in he eas e n I ish Sea is
p esen ed. The model sol es he h ee dimensional hyd odynamic equa ions, using no malized
p coo dina es in he e ical di ec ion. Simul aneously, he equa ion o suspended ma e , ha
includes ad ec ion, di!usion, se ling, deposi ion and e osion o he sedimen , is sol ed oo.
Thus, he idal dispe sion o non-conse a i e adionuclides can be simula ed. Reduc ion and
oxida ion eac ions a e included in he model; hey a e desc ibed in e ms o eac ion eloci ies.
I is conside ed ha Pu can be p esen in solu ion, suspended ma e and bo om sedimen s.
Also, Pu can be in educed and oxidized o ms in each o hese h ee phases. Thus, six equa ions
a e sol ed, whose solu ions gi e he empo al e olu ion o Pu concen a ion in each phase o
bo h educed and oxidized o ms. The model has been applied o he eas e n I ish sea, whe e Pu
is eleased om he Sella"eld nuclea uel ep ocessing plan . Obse ed and compu ed Pu
dis ibu ions in wa e and bo om sedimen s ha e been compa ed. Also, he model gi es he
pe cen age o Pu ha is educed and oxidized in each phase. Finally, dis ibu ion coe$cien s o
o al Pu ( educed plus oxidized), oxidized and educed Pu ha e been calcula ed o e he sea.
Resul s a e, in gene al, in ag eemen wi h obse a ions.
Keywo ds: Plu onium; Specia ion; I ish Sea; Sella"eld; Modelling
1. In oduc ion
O e ecen yea s, he e has been an inc easing in e es in de eloping models o
simula e he dispe sion o non-conse a i e adionuclides in aqua ic en i onmen s since
hese models can be used as p edic i e ins umen s ha can be applied in he assessmen
o adioac i e con amina ion ollowing an acciden al elease o adionuclides.
The " s models o non-conse a i e adionuclides we e long- e m dispe sion
models, in which he ans e o adionuclides be ween he liquid and solid phases was
desc ibed in e ms o equilib ium dis ibu ion coe$cien s (Gu bu , Ke shaw & Du -
ance, 1987; Ab il & Ga cmHa-LeoHn, 1993a). Pe iaHn8ez, Ab il & Ga cmHa-LeoHn (1996a)
de eloped a model o simula e he dispe sion o non-conse a i e adionuclides in
idal wa e s based upon kine ic ans e coe$cien s and hus he model could be used
unde non-equilib ium condi ions. This model was applied o simula e he dispe sion
o 226Ra, 238U and 232Th in a Spanish es ua y (Pe iaHn8ez, Ab il & Ga cmHa-LeoHn, 1996b;
Pe iaHn8ez & Ma mHnez-Agui e, 1997a). Recen ly, Pe iaHn8ez (in p ess) de eloped a h ee
dimensional model o simula e he idal dispe sion o non-conse a i e adionuclides
in he ma ine en i onmen , also based upon kine ic ans e coe$cien s. A simila
model was also de eloped by Ma g elash ily, Made ich and Zheleznyak (1997).
Ab il and Ga cmHa-LeoHn (1993b) and Pe iaHn8ez (in p ess) applied hei espec i e
models o simula e he dispe sion in he I ish Sea o plu onium eleased om he
nuclea uel ep ocessing plan a Sella"eld. Howe e , he beha iou o Pu in aqua ic
sys ems is o conside able complexi y due o he ac ha i can simul aneously exis in
di!e en oxida ion s a es. Thus, Pu (III) and Pu (IV) p edomina e as he educed and
Pu (V) and Pu (VI) as he oxidized o ms. The educed Pu is highly pa icle- eac i e
and has been shown o possess a dis ibu ion coe$cien ha is wo o de s o
magni ude highe han ha o he mo e soluble oxidized Pu (McKay & Pa enden,
1993; Mi chell, Vi es i Ba lle, Downes, Cond en, LeoHn-Vin oH& Sanchez-Cabeza,
1995). Hence he alues obse ed in "eld measu emen s ep esen he p ope ies o
he mix u e o oxida ion s a es ha is p esen in he pa icula sample. To o e come
his p oblem, Ab il and Ga cmHa-LeoHn (1993b) and Pe iaHn8ez (in p ess) used a mean
dis ibu ion coe$cien and mean kine ic ans e coe$cien s, espec i ely, in hei
models. Ne e heless, he main di$cul y is ha he oxida ion s a e o Pu changes wi h
ime: Pu is eleased in a educed o m and a e some days an equilib ium in he
pa i ion o Pu be ween he educed and oxidized species is achie ed (Pen ea h,
Ha ey & Lo e , 1986).
The objec i e o his pape is o p esen he " s esul s on a Pu dispe sion model
ha includes educ ion and oxida ion ( edox) eac ions in a simple way. Thus, mean
kine ic ans e coe$cien s a e no used ( educed and oxidized Pu ha e hei co e-
sponding speci"c coe$cien s) and he model can also gi e in o ma ion on he
specia ion s a e o Pu in wa e , suspended ma e and bo om sedimen s. Mo eo e ,
he model calcula es o al dis ibu ion coe$cien s and dis ibu ion coe$cien s o he
educed and oxidized Pu sepa a ely.
The model sol es he h ee dimensional hyd odynamic equa ions using no malized
pcoo dina es in he e ical, so ha e ical esolu ion is no educed in he shallowe
egions, he equa ion o suspended ma e , which is also w i en in pcoo dina es and
includes ad ec ion, di!usion, se ling, deposi ion and e osion o he sedimen , and he
equa ions whose solu ions gi e he ime e olu ion o educed and oxidized Pu in
wa e , suspended ma e and bo om sedimen s. In his way, he idal dispe sion o
educed and oxidized Pu is ob ained.
The model is p esen ed in he nex sec ion. The ea e , he model esul s a e
p esen ed and discussed.
Fig. 1. Pe cen age o oxidized Pu as a unc ion o ime om he expe imen s o Bous e al. (1996) (poin s)
and he esul om nume ical " ing o Eq. (3) (line).
2. The model
2.1. Redox eac ions
Redox eac ions will be desc ibed in e ms o eac ion eloci ies. Thus, he a e a
which Pu is oxidized is conside ed o be p opo ional o he concen a ion o educed
Pu a each pa icula poin . The p opo ionali y ac o is he oxida ion eloci y b1.
Simila ly, he a e a which Pu is educed is conside ed o be p opo ional o he
concen a ion o oxidized Pu. The p opo ionali y ac o will now be he educ ion
eloci y, deno ed as b2.
An es ima ion o he alues o b1and b2can be ob ained om he labo a o y
expe imen s ca ied ou by Bous , Mi chell, Ga cia, Cond en, LeoHn-Vin oHand
Lecle c (1996). Fil e ed sea wa e was spiked wi h Pu(IV) a a well known concen a-
ion and he oxida ion eac ion was ollowed du ing some 30 d (de ails can be seen in
Bous e al., 1996). The % o oxidized Pu, as a unc ion o ime, is gi en by he poin s in
Fig. 1. In ou model, he equa ions ha gi e he empo al e olu ion o he concen a-
ion o oxidized and educed Pu, C09 and C3%$ espec i ely, a e:
LC3%$
L "!b1C3%$#b2C09 (1)
LC09
L "b1C3%$!b2C09 (2)
I hese equa ions a e sol ed, knowing ha a "0, C09"0 and C3%$"C3%$(0), i
ollows ha
C09"b1
b1#b2
C3%$(0)(1!e~(b
1
`b
2
) ). (3)
b1and b2can be ob ained om nume ical " ing o Eq. (3) o he expe imen al poin s
p esen ed in Fig. 1. I nume ical " ing is ca ied ou , he ollowing eac ion eloci ies
a e ob ained:
b1"1.85]10~6 s~1,
b2"4.48]10~7 s~1.
The nume ical " ing o Eq. (3) is also ep esen ed in Fig. 1 as he solid line. I can be
seen ha he oxida ion eac ion is almos comple ed wi hin 15}20 d: 80% o Pu has
been con e ed o he oxidized o m.
I mus be poin ed ou ha edox eac ions occu in he h ee phases conside ed in
he model: wa e , suspended ma e and bo om sedimen s. I is assumed ha eac ion
eloci ies in suspended ma e and sedimen s a e he same as in wa e , which is
a simpli"ca ion since educ ion/oxida ion condi ions may be di!e en in he h ee
phases. O cou se, his can lead o disc epancies be ween model p edic ions and
obse a ions, as will be seen. Howe e , ou main objec i e is o p esen he model
o mula ion and some p elimina y esul s. The model can be u he e"ned as b1and
b2a e be e known in he o he phases om obse a ions and labo a o y expe i-
men s. On he o he hand, en i onmen al condi ions such as ligh and empe a u e
a!ec he eac ion eloci ies, which is no conside ed in he model. Thus, he model
sensi i i y o changes in b1and b2has o be s udied (see Sec ion 4) due o he
unce ain y in hei alues.
2.2. Hyd odynamics
The h ee dimensional hyd odynamic equa ions a e ans o med o pcoo dina es;
hus a cons an numbe o laye s is used in he e ical a each ho izon al g id poin
and e ical esolu ion is no educed in he shallowe a eas. The ans o ma ion o
pcoo dina es is (see Da ies, 1985a, o ins ance):
p"(z# )
(h# )(4)
whe e his he undis u bed dep h o wa e , is he sea su ace displacemen om he
mean le el due o idal oscilla ions measu ed upwa ds om he undis u bed le el and
he zcoo dina e is measu ed om mean sea le el o he bo om. The o m o he
equa ions, o a homogeneous sea, in pcoo dina es has been gi en p e iously (Da ies,
1985a) and will no be epea ed he e. De ails o he bounda y condi ions applied a he
sea su ace and he sea bo om can be seen in Pe iaHn8ez (1998a): no wind e!ec s a e
conside ed since we a e mainly in e es ed in es ing and uning he o mula ion o
he h ee dimensional dispe sion model including edox eac ions and ealis ic esul s
a e ob ained al hough wind is no included, as will be seen. A linea law o bo om
ic ion has been adop ed. Al hough a quad a ic o mula ion o bo om ic ion is now
mo e ex ensi ely used han he linea law, he la e has been adop ed since he idal
egime becomes es ablished as e . Also, he e a e no app eciable di!e ences in he
dispe sion pa e ns ( o dissol ed adionuclides) ob ained when he hyd odynamic
model is calib a ed using linea o quad a ic ic ion (Pe iaHn8ez, 1998a).
A#ow-dependen eddy iscosi y has been used in he model. This o mula ion gi es
good esul s o idal #ow s udies (Jones & Da ies, 1996; Da ies & Law ence, 1994;
Da ies, Kwong & Fla he , 1997):
N"CNJu62# 62h(5)
whe e CN"0.0025 is a dimensionless expe imen ally ob ained coe$cien and u6and
6a e dep h mean cu en s along he xand yaxis espec i ely.
2.3. Suspended ma e dynamics
The h ee dimensional equa ion o suspended ma e has been ob ained by ans-
o ming he equa ion p oposed by Nicholson and O'Conno (1986) in o pcoo di-
na es. De ails can be seen in Pe iaHn8ez (in p ess). Such an equa ion includes ad ec i e-
di!usi e anspo plus e ical all (se ling) o pa icles. E osion and sedimen a ion
a e inco po a ed in o he sea-bed bounda y condi ion o he equa ion. E osion and
deposi ion ha e been o mula ed in e ms o h eshold eloci ies in such a way ha
he e is e osion only i he sea-bed wa e eloci y is la ge ha he e osion h eshold.
O he wise he e osion e m is se o ze o. Simila ly, he e is deposi ion only i he
sea-bed wa e eloci y is smalle han he deposi ion h eshold eloci y. O he wise he
deposi ion e m is se o ze o.
As usual in suspended ma e s udies, i is conside ed ha only pa icles wi h
a diame e (62.5 lm can emain in he wa e column as suspended ma e , since
la ge pa icles will sink apidly o he bo om and, as a consequence, hei ho izon al
mo emen is negligible (Belde son, 1964; Cla ke, 1995; Pe iaHn8ez, Ab il, & Ga cmHa-
LeoHn, 1996c). Indeed, Eisma (1981) has poin ed ou ha o all p ac ical pu poses
muds can be ega ded as synonymous wi h suspended ma e .
A s anda d o mula o ep esen he inc ease in he se ling eloci y as he sus-
pended ma e concen a ion inc eases has been used in he model (Pej up, 1988;
Meh a, 1989; Cla ke, 1995; Pe iaHn8ez, in p ess). Also, a sou ce- e m is included in he
suspended ma e equa ion in hose g id cells loca ed along he coas line. This e m
ep esen s he inpu o pa icles om uno!o con inen al wa e s. All de ails can be
seen in Pe iaHn8ez (in p ess).
2.4. Radionuclide dispe sion
The model conside s ha adionuclides can be p esen in h ee phases: solu ion,
suspended ma e and ac i e bo om sedimen s (as deno ed by Benes, Ce nik
& Sla ik, 1994), ha consis o pa icles wi h a diame e (62.5 lm. In each phase, Pu
can exis in wo oxida ion s a es: educed and oxidized Pu. Reduc ion and oxida ion
p ocesses ( ha occu in each o he h ee phases) a e go e ned by he eac ion
eloci ies, ha we e p esen ed abo e. The ans e o Pu om he solid phase o
solu ion is go e ned by a kine ic ans e coe$cien k2and he in e se p ocess by

a kine ic ans e coe$cien k1. Howe e , hese coe$cien s will be di!e en o
oxidized and educed Pu. Thus, he model sol es six equa ions whose solu ion gi es
he ime e olu ion o he concen a ion o educed and oxidized Pu in wa e , sus-
pended ma e and bo om sedimen s.
I is known ha ac inide adso p ion ends o be a su ace phenomenon (Ramsay
& Raw, 1987) and will depend on he su ace o pa icles pe wa e olume uni in o
each g id cell. This quan i y has been deno ed as he exchange su ace (Pe iaHn8ez e al.,
1996a; Pe iaHn8ez & Ma mHnez-Agui e, 1997a). Thus (Pe iaHn8ez e al., 1996a):
k1"s1(Sm#Ss)"k11#k12 (6)
whe e Smand Ssa e he exchange su aces o suspended ma e and bo om sedimen s
espec i ely and s1is a pa ame e wi h he dimensions o a eloci y. I is deno ed as
he exchange eloci y (Pe iaHn8ez e al., 1996a). As a " s app oach, assuming sphe ical
pa icles and a s ep unc ion o he g ain size dis ibu ion o pa icles, i can be
ob ained (Pe iaHn8ez e al., 1996a) ha
Sm"3m/oR(7)
Ss"3¸//R*p H(8)
whe e mis he suspended ma e concen a ion, ois he suspended ma e pa icle
densi y, Ris he mean adius o he suspended ma e and ac i e sedimen pa icles,
H"h# is he o al wa e dep h, ¸is he a e age mixing dep h ( he dis ance o
which he dissol ed phase pene a es he sedimen ), *p is he spacing in he e ical
di ec ion and /is a co ec ion ac o ha akes in o accoun he ac ha no all he
mass o he sedimen is in con ac wi h he wa e . This desc ip ion o he ans e o
adionuclides be ween he dissol ed and solid phase has been used success ully in
p e ious modelling wo ks (Pe iaHn8ez e al., 1996b; Pe iaHn8ez & Ma mHnez-Agui e,
1997a,b, Ma mHnez-Agui e & Pe iaHn8ez, 1998).
The equa ions ha gi e he h ee dimensional dispe sion o Pu, including ad ec-
ion, di!usion, se ling and deposi ion o suspended ma e , e osion o he sedimen
and ans e s be ween he liquid and solid phase, p esen ed in Pe iaHn8ez (in p ess), ha e
been modi"ed o ake in o accoun he ac ha Pu can exis in educed and oxidized
o ms. Thus, ins ead o h ee equa ions six mus be sol ed. The o m o he six
equa ions is summa ized in he Appendix.
2.5. Nume ical solu ion
The hyd odynamic equa ions a e sol ed using an explici "ni e di!e ence scheme,
al hough he e ical di!usion e m is sol ed using he Saul'e implici scheme o
e ain s abili y (Da ies, 1985b). A land bounda ies, he no mal componen o he
cu en is se o ze o. Along open bounda ies, ampli ude and phase o he su ace
ele a ion a he M2 equency a e speci"ed om obse a ions (Howa h, 1990) and
he su ace cu en componen ha is no mal o he bounda y is ob ained om
a adia ion condi ion (Kowalick & Mu y, 1993). Only he main idal componen , M2,
has been used since we a e mainly in e es ed in es ing he o mula ion o he h ee
dimensional dispe sion o Pu, including chemical eac ions. Thus, only he M2 ide
has been used since ealis ic esul s a e ob ained, as will be shown. Howe e , a esul
imp o emen should be expec ed i weake componen s (a leas S2and N2) a e
included.
The ad ec ion and ho izon al di!usion e ms a e sol ed using second o de accu-
acy schemes (Kowalick & Mu y, 1993) and e ical di!usion is again ea ed using
he Saul'e me hod. Along land bounda ies, no #uxes o suspended pa icles and Pu
a e conside ed. The open bounda y condi ion desc ibed in Pe iaHn8ez (1998a,b) has
been adop ed:
Ci" Ci~1 (9)
whe e Ci ep esen s he concen a ion o suspended ma e and Pu along he bound-
a y and Ci~1 ep esen s he concen a ion jus inside he compu a ional domain. The
non-dimensional alue "0.9 is ob ained om a calib a ion exe cise (Pe iaHn8ez,
1998a,b).
A FORTRAN code has been de eloped o sol e he equa ions in ol ed in he
model. I was implemen ed on a HP SPP-2000 X-Class compu e .
3. Model applica ion and esul s
The model domain is p esen ed in Fig. 2, whe e he loca ion o Sella"eld nuclea
uel ep ocessing plan is also shown. The model's ho izon al esolu ion is
*x"*y"5000 m. Ten laye s a e used in he e ical, hus *p"0.1, and he ime
s ep is "xed as * "60 s. Wa e dep hs a e in oduced om ba hyme ic maps and
ange om 55 m in he wes o a shallowe a ea along he B i ish coas .
The alues gi en o all he pa ame e s in ol ed in he model a e p esen ed in de ail
in Pe iaHn8ez (in p ess). The sou ce o i ually all Pu o he I ish Sea is he discha ge
om Sella"eld h ough a pipeline ha ex ends 2.5 km beyond high wa e . The
magni udes o he discha ges ha e been compiled om McKay and Pa enden (1993)
and Hun , Smi h and Camplin (1997), and ha e been used as he Pu inpu o he
model. I has also been epo ed (Pen ea h, 1985) ha abou 99% o he discha ged
Pu is associa ed wi h pa icles in a educed o m.
The alues o he kine ic ans e coe$cien k2and he exchange eloci y X1 o he
educed and oxidized Pu mus be gi en. Ny!ele , Li and San schi (1984) measu ed
k2 o a wide se o chemical elemen s and ound a e y small a ia ion (an o de o
magni ude), e en o elemen s wi h a e y di!e en geochemical beha iou . Thus, i
has been conside ed ha k2has he same alue o educed and oxidized Pu. I has
been assumed ha k2"1.16]10~5 s~1, he alue ha has been ob ained by Ny!ele
e al. (1984) o Cs and Cd. This alue o k2has gi en good esul s in p e ious
modelling wo k when i has been used o Ra, U, Th, Cs and Pu (Pe iaHn8ez e al., 1996b;
Pe iaHn8ez & Ma mHnez-Agui e, 1997a; Pe iaHn8ez, 1998c, in p ess). The exchange eloci y
can be es ima ed om k2and he dis ibu ion coe$cien , k$, since he ollowing
Fig. 2. Model domain. Each uni in he xand yaxis is 5000 m (g id elemen numbe ). The s a is he
Sella"eld nuclea uel ep ocessing plan .
ela ion holds (Pe iaHn8ez e al., 1996b):
k$"s1
k2
3
oR. (10)
Measu ed o al Pu k$'s in he eas e n I ish Sea a e o he o de o 105lkg
~1
(McKay & Walke , 1990; Mi chell e al., 1995), in ag eemen wi h he alue ecom-
mended by IAEA (1985): 1.0]105lkg
~1. Howe e , he Pu oxida ion s a e has been
shown o ha e a majo in#uence on he k$ alue, being o he o de o 106and
104lkg
~1 o he educed and oxidized Pu espec i ely (Nelson and Lo e , 1978).
The same a ia ions ha e been obse ed in he I ish Sea (Mi chell e al., 1995). Thus, i
has been conside ed ha k$is 1.0]106and 1.0]104lkg
~1 o he educed and
oxidized Pu espec i ely. F om Eq. (10), he exchange eloci ies o educed and
oxidized Pu a e:
s3%$
1"1.51]10~4 ms
~1,
s09
1"1.51]10~6 ms
~1.
Fig. 3. Tempo al e olu ion o he pe cen ages o educed Pu in solu ion and suspended ma e , Cd and
Cs , and oxidized Pu in wa e and suspended ma e , Cdo and Cso.
To ob ain hese alues, i has been aken ha R"15 lm and o"2600 kg m~3
(Pe iaHn8ez e al., 1996b; Pe iaHn8ez, in p ess). Once he exchange eloci ies a e known,
kine ic ans e coe$cien s k11and k12 o bo h oxidized and educed Pu can be
ob ained om Eqs. (6)}(8).
A nume ical expe imen has been ca ied ou o es he alues o he ans e
coe$cien s and he eac ion eloci ies. Le us conside a olume o sea wa e ha
con ains a ce ain concen a ion o suspended ma e pa icles (1 ppm, which is
a ypical alue o he I ish Sea). A known amoun o Pu, associa ed wi h suspended
ma e , in a educed chemical o m is added. The ou di!e en ial equa ions whose
solu ions gi e he empo al e olu ion o Pu concen a ions in wa e and suspended
ma e (in bo h educed and oxidized o ms in each phase) a e in eg a ed nume ically.
These equa ions include edox eac ions in wa e and suspended ma e and ans e s
o educed and oxidized Pu be ween wa e and suspended ma e ( hey a e Eqs.
(A1)}(A4) in he Appendix i e ms in ol ing ad ec ion, di!usion, se ling, e osion,
deposi ion and ans e s wi h sedimen s a e emo ed). The esul is p esen ed in Fig. 3,
whe e he ime e olu ion o he % o Pu in educed and oxidized o ms (in bo h wa e
and suspended ma e ) is gi en. I can be seen ha equilib ium is eached a e some
20 d, as has been epo ed by o he au ho s (Bous e al., 1996). A e 35 d, he amoun
o Pu associa ed wi h solid pa icles ( educed plus oxidized) is 11.4%. Mole o,
Sanchez-Cabeza, Me ino, Vi es i Ba lle, Mi chell and Vidal-Cuad as (1995) ound
ha 11% o he o al Pu concen a ion is abso bed on o suspended ma e in
he Medi e anean Sea. Li ings on and Bowen (1977) showed ha 30% o Pu was
"xed o suspended pa icles in A lan ic wa e s. Mi chell, Vi es i Ba lle, Ryan, Schell,
Fig. 8. Measu ed and compu ed 239,240Pu speci"c ac i i ies in wa e (a) suspended ma e (b) and bo om
sedimen s (c) no hwes (posi i e dis ances) and sou hwes (nega i e dis ances) om Sella"eld.
I should also be commen ed ha , since he model o mula ion is h ee dimensional,
i can be applied o s udy e ical a ia ions o pa ame e s like adionuclide concen-
a ions in wa e and suspended ma e and dis ibu ion coe$cien s. Discussion o
his poin can be ound in Pe iaHn8ez (in p ess) and will no be epea ed he e.
4. Model sensi i i y o b1and b2
The model sensi i i y o he choice o bounda y condi ions o he dispe sion
equa ions, di!usion coe$cien s, pa ame e s in ol ed in he suspended ma e sub-
model, kine ic ans e coe$cien k2and exchange eloci y s1has al eady been
s udied (Pe iaHn8ez, in p ess). Resul s will no be epea ed he e.
The model sensi i i y o changes in eac ion eloci ies has been in es iga ed due o
he unce ain ies associa ed wi h hese pa ame e s. The nume ical expe imen de-
sc ibed in Sec ion 3 has been epea ed o di!e en alues o b1and b2. The esul s a e
summa ized in Table 1, whe e he pe cen age o Pu "xed o he solid ma e , he

Fig. 9. Compu ed dis ibu ion coe$cien s (L kg~1): (a) o al Pu (]105), (b) educed Pu (]106),
(c) oxidized Pu(]104).
pe cen age o oxidized Pu in he wa e and he pe cen age o educed Pu in he
suspended ma e a e gi en oge he wi h he alues o b1and b2in each expe imen .
Expe imen 1 is ca ied ou wi h he pa ame e s used in he model (expe imen
p esen ed in Sec ion 3). I can be seen ha %ox is in ag eemen wi h measu emen s
Table 1
Model sensi i i y o he eac ion eloci ies.
Expe imen b1(s~1)b2(s~1) % solid % ox % ed
1 1.85]10~6 4.48]10~7 11.4 88.0 81.0
2 3.70]10~6 4.48]10~7 7.0 93.4 67.2
3 3.70]10~6 2.24]10~7 4.17 96.6 59.5
4 1.85]10~6 8.96]10~7 18.1 78.7 84.2
5 1.85]10~6 1.34]10~6 23.0 70.9 85.6
6 9.25]10~7 8.96]10~7 26.1 65.4 91.5
7 9.25]10~7 1.34]10~6 31.1 55.6 92.2
8 6.17]10~7 1.34]10~6 35.5 45.4 94.8
% solid is he pe cen age o Pu associa ed wi h suspended ma e a e 35 d, %ox is he pe cen age o
oxidized Pu in solu ion and % ed is he pe cen age o educed Pu in suspended ma e .
(Mi chell e al., 1995), bu % ed is sligh ly low when compa ed wi h obse a ions
(Mi chell e al., 1995). In expe imen s 2 and 3 oxida ion is enhanced by inc easing b1
(expe imen 2) o inc easing b1and simul aneously dec easing b2(expe imen 3). In
hese cases, %ox is s ill in ag eemen wi h obse a ions bu oo low alues o % ed
occu . In expe imen s 4}8 educ ion is enhanced by inc easing b2o by simul a-
neously inc easing b2and dec easing b1. As educ ion inc eases % ed shi s o alues
close o obse a ions, bu oo low alues o %ox a e ob ained (see expe imen 8).
Thus, changes in b1and b2due o changes in en i onmen al condi ions may a!ec he
dis ibu ion o Pu be ween oxidized and educed o ms. I hese a ia ions in eac ion
eloci ies and also di!e en alues o hem in wa e , suspended ma e and bo om
sedimen s a e included in he model, esul s would p obably be imp o ed (in pa icu-
la he Pu dis ibu ion be ween educed and oxidized o ms in suspended ma e and
bo om sedimen s).
5. Conclusions
A nume ical model ha simula es he physico-chemical specia ion o Pu in he
eas e n I ish Sea has been de eloped. The model simul aneously sol es he hy-
d odynamic equa ions, he suspended ma e equa ion and six equa ions whose
solu ion gi es he empo al e olu ion o educed and oxidized Pu concen a ions in
wa e , suspended ma e and bo om sedimen s. Reduc ion and oxida ion eac ions
a e desc ibed in e ms o he eac ion eloci ies, which ha e been deduced om
labo a o y expe imen s. The ans e o adionuclides be ween wa e and he solid
phase is desc ibed in e ms o kine ic ans e coe$cien s, which ha e di!e en alues
o educed and oxidized Pu.
In gene al, he obse ed and compu ed Pu dis ibu ions in wa e and bo om
sedimen s a e in ag eemen . I has been ob ained ha mos Pu in solu ion is in
oxidized o m. Also, he Pu dis ibu ion be ween educed and oxidized o ms, in
solu ion, emains a he uni o m o e he sea, which is in ag eemen wi h p e ious
measu emen s. On he o he hand, Pu in suspended ma e is mainly in a educed
o m, al hough in a pe cen age ha is lowe han obse a ions. Also, i has been ound
ha mos Pu in he sedimen is in an oxidized o m. These wo esul s may be
a consequence o he simple model ha has been used o desc ibe edox eac ions,
since p obably eac ion eloci ies in he sedimen should be di!e en o hese in he
wa e column.
Compu ed dis ibu ion coe$cien s o educed, oxidized and o al Pu a e, in
gene al, in ag eemen wi h obse a ions. A dec ease in he o al k$wi h inc easing
dis ance om he Sella"eld discha ge poin has been ob ained, which is in ag eemen
wi h p e ious obse a ions.
Acknowledgemen s
Wo k pa ially suppo ed by EU con ac FI4PCT960046, Spanish CICYT con-
ac AMB97-1720-CE and ENRESA.
Appendix A
A.1. Dissol ed phase
The equa ion ha gi es he empo al e olu ion o oxidized Pu in solu ion,
C09
d(Bq m~3), is
LC09
d
L "(ad #di )3D!(k09
11#nk09
12)C09
d#k2AmC09
s#nA09
s¸om /
*pH]103B
!jC09
d#b1C3%$
d!b2C09
d(A.1)
whe e (ad #di )3D ep esen s h ee dimensional ad ec ion plus di!usion o
adionuclides. n"0 unless we a e sol ing he equa ion o he wa e laye ha is in
con ac wi h he sedimen ; in his case n"1 o allow he ans e o adionuclides
be ween wa e and he bo om sedimen . C09
sand A09
sa e oxidized Pu concen a ions
in suspended ma e and sedimen s, bo h in Bq g~1. The sedimen bulk densi y, om,is
exp essed in kg m~3 and jis he adioac i e decay cons an . gi es he ac ion o
ac i e sedimen s. The ex e nal sou ce should be added o his equa ion i i exis s.
A simila equa ion is deduced o educed Pu in solu ion, C3%$
d(Bq m~3):
LC3%$
d
L "(ad #di )3D!(k3%$
11 #nk3%$
12 )C3%$
d#k2AmC3%$
s#nA3%$
s¸om /
*pH]103B
!jC3%$
d#b2C09
d!b1C3%$
d(A.2)
wi h ob ious meanings o he no a ion.
A.2. Suspended ma e
In he case o oxidized Pu, C09
s(Bq g~1):
L(mC09
s)
L "(ad #di )3D!se 09#n( es09!dep09)#k09
11C09
d!k2mC09
s
!jmC09
s#m(b1C3%$
s!b2C09
s) (A.3)
whe e mis he suspended ma e concen a ion in g m~3 and se , es and dep means
se ling, esuspension and e osion (see Pe iaHn8ez (in p ess) o de ails). The equa ion o
educed Pu is
L(mC3%$
s)
L "(ad #di )3D!se 3%$#n( es3%$!dep3%$)#k3%$
11 C3%$
d!k2mC3%$
s
!jmC3%$
s#m(b2C09
s!b1C3%$
s) (A.4)
A.3. Ac i e bo om sedimen s
Oxidized Pu:
LA09
s
L "k09
12
C09
d(b)H*p
¸om ]10~3!k2A09
s/
#(dep09! es09)!jA09
s#b1A3%$
s!b2A09
s(A.5)
whe e (d) means ha his pa ame e mus be e alua ed a he deepes wa e laye (in
con ac wi h he sedimen ). dep and es means deposi ion and esuspension (see
Pe iaHn8ez (in p ess) o de ails).
Reduced Pu:
LA3%$
s
L "k3%$
12
C3%$
d(b)H*p
¸om ]10~3!k2A3%$
s/
#(dep3%$! es3%$)!jA3%$
s#b2A09
s!b1A3%$
s. (A.6)
The o al ac i i y ( educed plus oxidized) in he sedimen (ac i e plus non ac i e)
can be ob ained as
A" (A09
s#A3%$
s). (A.7)
A.4. Dis ibu ion coezcien s
Oxidized Pu:
k09
d"C09
s
C09
d
(A.8)
Reduced Pu:
k3%$
d"C3%$
s
C3%$
d
(A.9)
To al k$:
k$"(C09
s#C3%$
s)
(C09
d#C3%$
d). (A.10)
Re e ences
Ab il, J. M., & Ga cmHa-LeoHn, M. (1993a). A 2D 4 phase ma ine dispe sion model o adionuclides. Pa 1:
concep ual and compu a ional model. Jou nal o En i onmen al Radioac i i y,20,71}88.
Ab il, J. M., & Ga cmHa-LeoHn, M. (1993b). A 2D 4 phase ma ine dispe sion model o adionuclides. Pa 2:
wo applica ion cases, 137Cs and 239,240Pu dispe sion in he I ish Sea. Jou nal o En i onmen al
Radioac i i y,20,89}115.
Belde son, R. H. (1964). Holocene sedimen a ion in he wes e n hal o he I ish Sea. Ma ine Geology,2,
147}163.
Benes, P., Ce nik, M., & Sla ik, O. (1994). Modelling o mig a ion o 137Cs acciden ally eleased in o a small
i e . Jou nal o En i onmen al Radioac i i y,22, 279}293.
Bous , D., Mi chell, P. I., Ga cia, K., Cond en, O. M., LeoHn-Vin oH, L., & Lecle c, G. (1996). A compa a i e
s udy o he specia ion and beha iou o plu onium in he ma ine en i onmen o wo ep ocessing
plan s. Radiochimica Ac a,74, 203}210.
Cla ke, S. (1995). Ad ec i e/diwusi e p ocesses in he Fi h o Fo h. Bango , UK: Ph. D. hesis. Uni e si y o
Wales.
Da ies, A. M. (1985a). A h ee dimensional modal model o wind induced #ow in a sea egion. P og ess in
Oceanog aphy,15,71}128.
Da ies, A. M. (1985b). Applica ion o he Du o -F ankel and he Saul'e me hods wi h ime spli ing o he
o mula ion o a h ee dimensional hyd odynamic sea model. In e na ional Jou nal on Nume ical
Me hods in Fluids,3,33}60.
Da ies, A. M., & Law ence, J. (1994). A h ee dimensional model o he M4 ide in he I ish Sea: The
impo ance o open bounda y condi ions and he in#uence o wind. Jou nal o Geophysical Resea ch,
99(C8), 16917}17227.
Da ies, A. M., Kwong, S. C. M., & Fla he , R. A. (1997). Fo mula ion o a a iable unc ion h ee
dimensional model wi h applica ions o he M2and M4 ide on he no hwes Eu opean Con inen al
Shel . Con inen al Shel Resea h,17, 165}204.
Eisma, D. (1981). Supply and deposi ion o suspended ma e in he No h Sea. Spec. Publs. In . Ass.
Sedimen ,5, 415}428.
Gu bu , P. A., Ke shaw, P. J., & Du ance, J. A. (1987). Modelling he dis ibu ion o soluble and pa icle
abso bed adionuclides in he I ish Sea. In J. C. Gua y, P. Gueguenia , & R. J. Pen ea h, Radionuclides.
A ool o oceanog aphy (pp. 395}407). Ams e dam: Else ie .
He he ing on, J. A. (1976). The beha iou o plu onium in he I ish Sea. In M. N. Mille , & J. N. S anna ,
En i onmen al oxici y o aqua ic adionuclides. Models and mechanisms (pp. 81}106). Ann A bo : Ann
A bo Science Publishe s.
Howa h M. J. (1990). A las on idal ele a ions and cu en s a ound he B i ish Isles. Depa men o Ene gy
London. OTR 89 293.
Hun , G. J., Smi h, B. D., & Camplin, W. C. (1997). Recen changes in he liquid adioac i e was e
discha ges om Sella"eld. Pa 1: inpu s and up ake by coas al bio a. Radiop o ec ion Colloques,32(C2),
17}22.

IAEA (1985). Sedimen kdand concen a ion ac o s o adionuclides in he ma ine en i onmen . Technical
Repo Se ies 247, Vienna.
Jones, J. E., & Da ies, A. M. (1996). A high esolu ion h ee dimensional model o he M2,M4,M6,S2,N2,K1
and O1 idesin heeas e nI ishSea.Es ua ine Coas al and Shel Science,42,311}346.
Kowalick, Z., & Mu y, T. S. (1993). Nume ical modelling o ocean dynamics. Singapo e: Wo ld Scien i"c.
Li ings on, H. D., & Bowen, V. T. (1977). Windscale e%uen in he wa e s and sedimen s o he Minch.
Na u e,269, 586}588.
Ma g elash ily, N., Made ich, V., & Zheleznyak, M. (1997). Th ee ox*A compu e code o simula e h ee
dimensional dispe sion o adionuclides in s a i"ed wa e bodies. Radia ion P o ec ion Dosime y,73,
177}180.
Ma mHnez-Agui e, A., & Pe iaHn8ez, R. (1998). Soil o plan ans e o 226Ra in a ma sh a ea: Modelling
applica ion. Jou nal o En i onmen al Radioac i i y,39, 199}213.
McKay, W. A., & Walke , M. I. (1990). Plu onium and ame icium beha iou in Cumb ian nea sho e
wa e s. Jou nal o En i onmen al Radioac i i y,39, 199}213.
McKay, W. A., & Pa enden, N. J. (1993). The beha iou o plu onium and ame icium in he sho eline
wa e s o he I ish Sea: a e iew o Ha well s udies in he 1980s. Jou nal o En i onmen al Radioac i i y,
18,99}132.
Meh a, A. J. (1989). On es ua ine cohesi e sedimen suspension beha iou . Jou nal o Geophysical Resea ch,
94(C10), 14303}14314.
Mi chell, P. I., Vi es i Ba lle, J., Ryan, T. P., Schell, W. R., Sanchez-Cabeza, J. A., & Vidal-Cuad as, A.
(1991). S udies on he specia ion o plu onium and ame icium in he wes e n I ish Sea. In P. J. Ke shaw,
& D. S. Woodhead, Radionuclides in he s udy o ma ine p ocesses (pp. 37}51). London: Else ie Applied
Science.
Mi chell, P. I., Vi es i Ba lle, J., Downes, A. B., Cond en, O. M., LeoHn-Vin oH, L., & SaHnchez-Cabeza, J. A.
(1995). Recen obse a ions on he physico chemical specia ion o plu onium in he I ish Sea and he
wes e n Medi e anean. Applied Radia ion and Iso opes,46, 1175}1190.
Mole o, J., Sanchez-Cabeza, J. A., Me ino, J., Vi es i Ba lle, J., Mi chell, P. I., & Vidal-Cuad as, A. (1995).
Pa icula e dis ibu ion o plu onium and ame icium in su ace wa e s om he Spanish Medi e anean
Coas . Jou nal o En i onmen al Radioac i i y,28, 271}283.
Nelson, D. M., & Lo e , M. B. (1978). Oxida ion s a es o plu onium in he I ish Sea. Na u e,276, 599}601.
Ny!ele , U. P., Li, Y. H., & San schi, P. H. (1984). A kine ic app oach o desc ibe ace elemen dis ibu ion
be ween pa icles and solu ion in na u al aqua ic sys ems. Geochimica and Cosmoschimica Ac a,48,
1513}1522.
Pej up, M. (1988). Suspended sedimen anspo ac oss a idal #a . Ma ine Geology,82, 187}198.
Pen ea h, R. J. (1985). Beha iou o adionuclides eleased in o coas al wa e s. Vienna: IAEA TECDOC 329.
Pen ea h, R. J., Ha ey, B. R., & Lo e , M. B. (1986). Chemical specia ion o ansu anium adionuclides
discha ged in o he ma ine en i onmen . In R. A. Bulman, & J. R. Coope , Specia ion o xssion and
ac i a ion p oduc s in he en i onmen (p. 312). London: Else ie Applied Science.
Pe iaHn8ez, R. (in p ess). Th ee dimensional modelling o he idal dispe sion o non-conse a i e adionucl-
ides in he ma ine en i onmen . Applica ion o 239,240Pu dispe sion in he eas e n I ish Sea. Jou nal o
Ma ine Sys ems, in p ess.
Pe iaHn8ez, R. (1998a). A h ee dimensional pcoo dina e model o simula e he dispe sion o adionuclides in
he ma ine en i onmen . Ecological Modelling,114,59}70.
Pe iaHn8ez, R. (1998b). Th ee dimensional modelling o he ide induced dispe sion o adionuclides in he sea.
Jou nal o En i onmen al Radioac i i y,40, 215}237.
Pe iaHn8ez, R. (1998c). Modelling he dis ibu ion o adionuclides in deep ocean wa e columns. Applica ion
o 3H, 137Cs and 239,240Pu. Jou nal o En i onmen al Radioac i i y,38, 173}194.
Pe iaHn8ez, R., & Ma mHnez-Agui e, A. (1997a). U anium and ho ium concen a ions in an es ua y a!ec ed
by phospha e e ilize p ocessing: Expe imen al esul s and a modelling s udy. Jou nal o En i onmen al
Radioac i i y,35, 281}304.
Pe iaHn8ez, R., & Ma mHnez-Agui e, A. (1997b). A six phase model o simula e he con amina ion by
non-conse a i e adionuclides o sedimen s, soils and plan s in a ma sh a ea. Applica ion o he Odiel
ma sh in sou hwes Spain. Jou nal o En i onmen al Radioac i i y,37,29}54.
Pe iaHn8ez, R., Ab il, J. M., & Ga cmHa-LeoHn, M. (1994). A modelling s udy o 226Ra dispe sion in an es ua ine
sys em in sou hwes Spain. Jou nal o En i onmen al Radioac i i y,24, 159}179.
Pe iaHn8ez, R., Ab il, J. M., & Ga cmHa-LeoHn, M. (1996a). Modelling he dispe sion o non-conse a i e
adionuclides in idal wa e s. Pa 1: concep ual and ma hema ical model. Jou nal o En i onmen al
Radioac i i y,31, 127}141.
Pe iaHn8ez, R., Ab il, J. M., & Ga cmHa-LeoHn, M. (1996b). Modelling he dispe sion o non-conse a i e
adionuclides in idal wa e s. Pa 2: applica ion o 226Ra dispe sion in an es ua ine sys em. Jou nal o
En i onmen al Radioac i i y,31, 253}272.
Pe iaHn8ez, R., Ab il, J. M., & Ga cmHa-LeoHn, M. (1996c). Modelling he suspended ma e dis ibu ion in an
es ua ine sys em. Applica ion o he Odiel i e in sou hwes Spain. Ecological Modelling,87, 169}179.
Ramsay, J. D. F., & Raw, G. (1987). S udies on en i onmen al adioac i i y in Cumb ia. Pa 9: physical
cha ac e is ics o colloids and pa icula es in coas al sedimen s and sea wa e . London: AERE R12086,
HMSO.