A particle-tracking method for simulating the dispersion of non-conservative radionuclides in coastal waters

a A pa icle- ackingme hod o simula ing he dispe sion o non-conse a i e adionuclides in coas al wa e s R. Pe i!aa*nnez a, *, A.J. Ellio b Depa amen o Fı´sica Aplicada I, Uni e si y o Se illa, EU Ingenie ı´aTe ´cnica Ag ı´cola, C a. U e a km 1, 41013 Se illa, Spain b Cen e o Applied Oceanog aphy, Uni e si y o Wales, Bango , Ma ine Science Labo a o ies, Menai B idge, Anglesey LL59 5EY, UK Abs ac A pa icle- acking me hod has been used o simula e he dispe sion o non-conse a i e adionuclides in he sea. Th ee dimensional u bulen diffusion and he in e ac ions be ween wa e , suspended ma e and bo om sedimen s a e simula ed using a s ochas ic me hod. Kine ic ans e coefficien s, as in fini e diffe ence models, a e used o desc ibe he ans e s be ween he liquid and solid phases. Deposi ion o suspended ma e and e osion o sedimen a e also included in he model. The me hod has been applied o simula e he dispe sion o 137 Cs and 239,240 Pu in he English Channel and he esul s ha e been compa ed wi h hose o a fini e diffe ence model. The esul s om bo h echniques a e, in gene al, in good ag eemen . Keywo ds: Model; Dispe sion; Pa icle- acking; Fini e diffe ence; Radionuclides; English Channel 1. In oduc ion The s a e-o - he-a models used o simula e he dispe sion o adioac i i y in he sea consis o fini e elemen s o , mainly, fini e diffe ence models ha sol e he hyd odynamic equa ions oge he wi h he ad ec ion–diffusion dispe sion equa ion, in ei he a wo dimensional o a h ee dimensional o m (Ha ms, 1997; Pe i! aa* nnez & *Co esponding au ho . Tel.: +34-95-4233669; ax: +34-95-4232644. E-mail add esses: [email p o ec ed] (R. Pe i! aa* nnez), [email p o ec ed] (A.J. Ellio ) Regue a, 1999). I he model is applied o simula e he dispe sion o non- conse a i e adionuclides, hen he in e ac ions wi h he solid phases (suspended ma e and bo om sedimen s) mus also be conside ed. This implies ha he suspended ma e equa ion, including he se ling o pa icles, deposi ion and e osion o he sedimen , mus be sol ed oo (Ald idge, 1998; Ma g elash ily, Made ich, & Zheleznyak, 1997; Piasecki, 1998; Pe i! aa* nnez, 1999, 2000). Abso p ion/deso p ion eac ions a e usually desc ibed using kine ic ans e coefficien s ins ead o he less app op ia e equilib ium dis ibu ion coefficien s, kd. These models a e compu a- ionally expensi e due o he ac ha a la ge numbe o equa ions mus be sol ed. Also, since fini e diffe ence models wo k wi h adionuclide concen a ions, he whole compu a ional g id mus be swep each ime s ep. Finally, he CFL condi ion (Kowalick & Mu y, 1993) limi s he size o he ime s ep ha can be used i an explici scheme is used o sol e he hyd odynamic equa ions. In consequence, la ge CPU imes may be equi ed e en using ecen supe compu e s (Pe i! aa* nnez, 1999). An al e na i e app oach is o make use o pa icle- acking echniques. In his kind o model, he impac o he CFL c i e ion can be educed by making he hyd odynamic compu a ions off-line. Also, ad ec ion can be simula ed o a high deg ee o accu acy since nume ical dispe sion (which appea s when he ad ec ion equa ion is sol ed wi h fini e diffe ences) is no in oduced. Pa icle- acking models ha e al eady been used o simula e he dispe sion o conse a i e ace s and oils spills (Hun e , 1987; Ellio , Dale, & P oc o , 1992; P oc o , Ellio , & Fla he , 1994a, b). In such applica ions, a elease o adioac i i y o he sea is modelled as a numbe o disc e e pa icles, each pa icle being equi alen o a numbe o uni s (Bq, moles, a oms, e c.). Then he pa h ollowed by each indi idual pa icle is compu ed, u bulen diffusion being modelled as a h ee dimensional andom walk (Mon e Ca lo) p ocess. The densi y o pa icles is calcula ed o ob ain he adioac i i y concen a ions a he end o he simula ion. The main difficul y ha appea s in he simula ion o he dispe sion o non-conse a i e adionuclides is he ea men o abso p ion and deso p ion: how o decide i each pa icle is fixed o suspended ma e o bo om sedimen s (i ini ially dissol ed) o i i is edissol ed (i ini ially p esen in he suspended ma e o he bo om sedimen ). The main con ibu ion o his pape consis s o a new me hod de eloped o sol e his p oblem: a o mula ion (sui able o a pa icle- acking model) o desc ibe he ans e s o adionuclides be ween wa e , suspended ma e and bo om sedimen s, based upon kine ic ans e coefficien s and a s ochas ic me hod, is p esen ed. I is impo an o poin ou ha exac ly he same physical pa ame e s as in he equi alen fini e diffe ence models a e used. The pa icle- acking modelling echnique is well sui ed o p oblems in which high con aminan g adien s a e in ol ed, since nume ical diffusion is no in oduced. This, oge he wi h he ac ha i can gi e e y as answe s, e en in a PC, allows he echnique o be conside ed as a e y use ul p edic i e ool in he assessmen o con amina ion ollowing acciden al o delibe a e eleases o adionuclides. The pa icle- acking model is p esen ed in he nex sec ion, hen an applica ion o he English Channel is shown. The model has been used o simula e he dispe sion o an ins an aneous hypo he ical elease o adionuclides om La Hague nuclea uel ep ocessing plan , loca ed on he F ench sho e o he English Channel. Simula ions ha e been ca ied ou o wo adionuclides wi h e y diffe en geochemical beha iou s: he ela i ely conse a i e 137 Cs and he high eac i e 239,240 Pu. A fini e diffe ence model o he Channel has been p e iously de eloped and alida ed h ough he s udy o he dispe sion o hese adionuclides, compa ing obse ed and compu ed concen a ions in wa e , suspended ma e and bo om sedimen s (Pe i! aa* nnez and Regue a 1999; Pe i! aa* nnez, 2000). Thus esul s o he pa icle- acking model will be compa ed wi h he ou pu o he fini e diffe ence model in equi alen simula ions and he ela i e ad an ages o each echnique will be assessed. 2. The pa icle- acking model 2.1. Ad ec i e anspo The posi ion ec o o a gi en pa icle, þD ðÞ, a ime þD is compu ed om þD ðÞ ðÞ D ¼q ðÞ;ð1Þ whe e D is he ime s ep used in he model and q he cu en ec o o componen s u and along he xand yaxes, espec i ely. Cu en s a e ob ained by unning a hyd odynamic model in ad ance. S anda d idal analysis is used o de e mine he idal cons an s ( ide ampli ude and phase) o each g id cell o he hyd odynamic model. These cons an s a e e alua ed o bo h componen s o he flow and can be de i ed o as many idal cons i uen s as desi ed. In his wo k, only he wo main semidiu nal ides, M2and S2, will be conside ed. Once he idal cons an s a e known, compu a ion o he flow ec o , q, jus in ol es he calcula ion and addi ion o a ew cosine e ms. As a consequence, he e alua ion o he idal ad ec i e anspo o pa icles is e y as and is no limi ed by he CFL c i e ion. Fo eal applica ions, fi s o de accu acy in he pa icle- acking scheme is adequa e. In simula ions o he mo emen o d ogues in an es ua ine en i onmen , Ellio and Cla ke (1998) ound no imp o emen in he esul s when a second o de accu acy scheme was used o simula e he mo emen o su ace d i e s by he pa icle- acking echnique. Mo eo e , in ocean dispe sion p oblems, he effec s o u bulence will mask any small e o s in he ad ec ion scheme. The ne esidual cu en in he modelled a ea mus be added o qsince a esidual anspo canno be gene a ed wi h he pu e ha monic idal cu en s ha a e used in pa icle- acking calcula ions. The esidual flow ec o s can also be ob ained om he (p e iously un) hyd odynamic model. Wind-induced anspo can be included in he model by assuming ha he su ace wind-induced cu en is a pe cen age o he wind speed, gene ally 2–3% (P oc o e al., 1994b). This cu en dec eases loga i hmically below a dep h z1( he hickness o he wind-d i en su ace laye ) o ze o a a dep h z2. Eckman heo y (Pugh, 1987) p edic s ha he su ace wind- induced cu en due o a s eady wind blowing o e deep wa e should be deflec ed o he igh o he wind di ec ion (in he no he n hemisphe e). Howe e , obse a ional e idence sugges s ha his deflec ion angle can be neglec ed (P oc o e al., 1994b) in shallow coas al wa e s. 2.2. Tu bulen diffusion Th ee dimensional diffusion is simula ed using a andom walk me hod. I has been shown (P oc o e al., 1994b; Hun e , 1987) ha i is a simula o o Fickian diffusion p o ided ha he maximum size o he ho izon al s ep gi en by he pa icle, Dh,is Dh¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 12KhD pð2Þ in he di ec ion 2pRAN, whe e RAN is a andom numbe be ween 0 and 1. This equa ion gi es he maximum size o he s ep. In p ac ice, i is mul iplied by RAN o ob ain he eal size a a gi en ime and o a gi en pa icle. Simila ly, he size o he e ical s ep is D ¼ffiffiffiffiffiffiffiffiffiffiffiffiffi 2K D pð3Þ gi en ei he owa ds he sea su ace o he sea bo om. Khand K a e he ho izon al and e ical diffusion coefficien s, espec i ely. 2.3. Radioac i e decay Conside he adioac i e decay equa ion: qC q ¼lC;ð4Þ whe e lis he adioac i e decay cons an . This equa ion can be ea ed using a s ochas ic me hod i i is assumed ha he p obabili y po emo al o a pa icle a each ime s ep is (Hun e , 1987; P oc o e al., 1994b) p¼1elD :ð5Þ In p ac ice, a andom numbe is gene a ed o each pa icle on each ime s ep. I RAN4p hen he pa icle is emo ed om he compu a ion. 2.4. T ans e s be ween wa e , suspended ma e and bo om sedimen s Conside a wo phase sys em. I he ans e s o adionuclides be ween he wo phases a e desc ibed h ough he kine ic ans e coefficien s k1and k2, he equa ions ha gi e he ime e olu ion o ac i i y in he wo phases a e qA1 q ¼k1A1þk2A2;ð6Þ qA2 q ¼k1A1k2A2: These equa ions a e easily sol ed using fini e diffe ences. In pa icle acking, a label is gi en o each pa icle o diffe en ia e i i is in phase l o 2. I he pa icle is in phase 1, he p obabili y p1 ha he pa icle goes o phase 2 in each ime s ep is p1¼1ek1D :ð7Þ Simila ly, i he pa icle is in phase 2, he p obabili y p2 ha i goes o phase 1 each ime s ep is p2¼1ek2D :ð8Þ Thus, in pa icle acking, he exchanges be ween wo phases can be modelled as wo decay p ocesses wi h p obabili ies p1and p2. These p ocesses a e ea ed as he adioac i e decay p ocess desc ibed abo e. I a gi en pa icle goes om one phase o he o he , i s label is changed and he new co esponding decay p ocess is conside ed a he nex ime s ep. This me hod has been compa ed wi h he fini e diffe ence solu ion o he sys em o Eq. (6). I has been conside ed ha all adionuclides a e, a ¼0, in phase 1. Thus, he solu ion gi en by each me hod e e s o he pe cen ages o adionuclides ha a e in phase 1 a each ollowing ime s ep. Resul s ob ained by bo h me hods a e p esen ed in Fig. 1, using 200 and 10,000 pa icles in he s ochas ic simula ion. High fluc ua ions occu wi h 200 pa icles, bu he fini e diffe ence solu ion is well modelled i 10,000 pa icles a e used in he pa icle- acking calcula ion. The mean alue and s anda d de ia ion o he diffe ence be ween fini e diffe ence and s ochas ic solu ions a e p esen ed in Table 1 o diffe en numbe s o pa icles in Fig. 1. Time e olu ion o he pe cen age o adionuclides in phase 1 gi en by he solu ion o he diffe en ial equa ions using fini e diffe ences and he pa icle- acking me hod, wi h 200 and 10,000 pa icles. he s ochas ic me hod. I can be seen ha bo h he mean alue and s anda d de ia ion o he diffe ence dec ease as he numbe o pa icles conside ed in he s ochas ic simula ion inc eases. Accep able esul s a e ob ained o numbe s o pa icles o he o de o 10,000. The s ochas ic me hod can be ex ended o he case in which he e a e h ee diffe en phases: wa e , suspended ma e and ac i e bo om sedimen s (pa icles wi h a diame e 562.4 mm). I is conside ed ha he ans e o adionuclides om he solid phases o wa e is go e ned by a kine ic ans e coefficien k2, he ans e om wa e o suspended ma e by k1m and he ans e om wa e o he sedimen by k1s. The abso p ion o adionuclides depends on he su ace o pa icles pe wa e olume uni . Thus he exchange su ace and exchange eloci y concep s ha e been used (Pe i! aa* nnez, Ab il, & Ga c! ııa-Le! oon, 1996; Pe i! aa* nnez & Ma ! ıınez-Agui e, 1997; Pe i! aa* nnez, 1999, 2000). Following hese pape s: k1m ¼w1 3m R;ð9Þ k1s ¼w1 3L RH ;ð10Þ whe e w1is he exchange eloci y, mis he suspended ma e concen a ion, and R a e he densi y and mean adius o suspended ma e pa icles, Lis he a e age mixing dep h ( he dis ance o which he dissol ed phase pene a es he sedimen ), is a co ec ion ac o ha akes in o accoun ha no all he mass o he sedimen is in con ac wi h wa e and Hgi es he hickness o he wa e laye abo e he sea bo om ha in e ac s wi h he sedimen . In a wo dimensional dep h-a e aged model, His equal o he wa e dep h. Since pa icle acking is h ee dimensional, H is le as a ee pa ame e o be calib a ed. The decay equa ions ha a e equi alen o he diffe en ial equa ions ha desc ibe ans e s be ween he h ee phases, p esen ed o ins ance in Pe i! aa* nnez (2000), a e qCd q ¼k1mCdk1sCd;ð11Þ Table 1 Mean alue and s anda d de ia ion o he diffe ence be ween he pe cen age o adionuclides in phase 1 gi en by fini e diffe ences and he s ochas ic me hod a NP hDis 100 0.654 2.861 200 0.637 2.220 500 0.296 1.557 1000 0.335 1.021 10,000 1.56 10 2 0.309 100,000 6.17 10 2 0.114 a NP is he numbe o pa icles used in he simula ion. qCs q ¼k2Cs;ð12Þ qAs q ¼k2 As:ð13Þ whe e Cd,Csand Asa e adionuclide concen a ions in wa e , suspended ma e and ac i e bo om sedimen s, espec i ely. A label is gi en o each pa icle o classi y in which phase i is p esen . Depending on he label o he pa icle, he co esponding decay equa ion is ea ed. I he pa icle is in suspended ma e , he p obabili y ha i goes o he dissol ed phase, in each ime s ep, is p¼1ek2D :ð14Þ Simila ly, i he pa icle is in he bo om sedimen , he p obabili y ha i is edissol ed is p¼1ek2 D :ð15Þ I he pa icle is ini ially dissol ed and i s dis ance o he sea bo om is smalle han H, i can go o any o he wo solid phases wi h a p obabili y p¼1ek1mþk1s ðÞD :ð16Þ A andom numbe is gene a ed o decide i he pa icle is effec i ely emo ed om solu ion. I i is, he no malized p obabili y ha he pa icle goes o he sedimen is calcula ed as p¼ps pmþps ;ð17Þ whe e pm¼1ek1mD ;ð18Þ ps¼1ek1sD :ð19Þ A second andom numbe is hen gene a ed. I RAN5p, hen he pa icle goes o he sedimen . I RAN >p, hen i goes o he suspended ma e . O cou se, i he dis ance o he pa icle o he sea bo om is la ge han H, only he decay o suspended ma e is conside ed since such pa icles canno in e ac wi h he sedimen . A nume ical expe imen has been ca ied ou o es he me hod in which a olume o wa e wi h a gi en suspended ma e concen a ion and ac i e sedimen on he bo om is conside ed. A dissol ed adioac i e ace is added and he equa ions ha gi e he ime e olu ion o ac i i ies in he h ee phases a e sol ed using fini e diffe ences and he s ochas ic me hod. The ollowing ealis ic pa ame e s ha e been used: w1¼2:1108m/s, k2¼1:2105s 1 ,m¼10 ppm, R¼15 mm, ¼2600 kg/m 3 ,L¼0:01 m, ¼1, ¼0:1, H¼0:2 m wi h 10,000 pa icles being used in he pa icle- acking simula ion. The compa ison be ween bo h me hods is p esen ed in Fig. 2, whe e he ime e olu ion o he ac ion o ace ha is dissol ed, in suspended ma e and in he sedimen is p esen ed. The simula ion shows ha he s ochas ic me hod solu ion is in e y good ag eemen wi h he fini e diffe ence solu ion o he h ee phases. Indeed, solu ions co esponding o bo h me hods canno be dis inguished in he case o wa e and sedimen . 2.5. Suspended ma e deposi ion and sedimen e osion The suspended ma e concen a ions o e he model domain can be ob ained by unning in ad ance a fini e diffe ence suspended ma e model. Resul s a e hen analyzed in a simila way o cu en s, so ha he suspended ma e concen a ion a each poin and o any ime can be ob ained as he simple calcula ion o cosine unc ions. Suspended ma e alls o he sea bo om wi h a se ling eloci y ws. I a pa icle (in he pa icle- acking sense, no a suspended ma e pa icle) is fixed o suspended ma e , i s posi ion abo e he bo om, z, a ime þD is ob ained om z þD ðÞz ðÞ D ¼ws:ð20Þ I z þD ðÞ40, hen he pa icle is conside ed o fix o he sedimen and i s label is app op ia ely changed. A s anda d o mula o floccula ion has been used o ep esen he inc ease in he se ling eloci y as he suspended ma e concen a ion inc eases (Cla ke & Ellio , 1998; Eisma, 1993; Pe i! aa* nnez, 2000) ws¼a1ma2;ð21Þ whe e a1and a2a e ob ained om measu emen s o om model calib a ion. The pa icle- acking model is h ee dimensional. I he fini e diffe ence suspended ma e model is dep h-a e aged, i s ou pu is he dep h-a e aged suspended ma e concen a ion. A Rouse p ofile is hen used o esol e he e ical s uc u e o suspended ma e . This allows he calcula ion o he suspended ma e concen a ion a heigh zabo e he bo om, mz, om he dep h-a e aged suspended ma e concen a ion m(Cla ke & Ellio , 1998): mz¼m1ws=bku*  h z  ws=bku *;ð22Þ whe e his wa e dep h, kis he on Ka man cons an (0.4), bis an a bi a y cons an usually aken as 1 (Eisma, 1993; Cla ke & Ellio , 1998) and u*is he scala ic ion eloci y u*¼kq jj ln h=z0  1;ð23Þ whe e z0is he bo om oughness. The co esponding alue o mzis used o calcula e k1m a he posi ion o each pa icle om Eq. (9). E osion o he sedimen has been desc ibed in e ms o he e osion cons an concep (Nicholson & O’Conno , 1986). Thus, he p obabili y ha a pa icle is emo ed om he sedimen and inco po a ed o he wa e column as suspended ma e is p¼1eE jqjMD ;ð24Þ whe e Eis he e osion cons an and Mis some powe o he wa e eloci y ypically in he ange 2–5 (P andle, 1997). Thus, he e osion desc ip ion used in p e ious fini e diffe ence models (Pe i! aa* nnez, 1999, 2000) has been con e ed in o a s ochas ic o m. I is conside ed ha e osion can only ake place i he wa e eloci y is la ge han a Fig. 2. Time e olu ion o he ac ion o adionuclides in wa e , suspended ma e and bo om sedimen s gi en by fini e diffe ences and by he pa icle- acking me hod wi h 10,000 pa icles. Solid lines co espond o he s ochas ic solu ion and dashed lines o he fini e diffe ence solu ion. 3.2. Discussion Pa icle acking is a powe ul ool ha can be applied in he assessmen o adioac i e con amina ion ollowing an acciden al elease in aqua ic en i onmen s in gene al. Also, he me hod can be applied o bo h conse a i e and non-conse a i e adionuclides, using he same concep ual app oach o he in e ac ions be ween Fig. 6 (con inued). Fig. 7. 239,240 Pu ac i i y concen a ions in wa e (mBq/l), suspended ma e (Bq/g) and ac i e sedimen (Bq/g) gi en by he fini e diffe ence (a) and he pa icle- acking (b) models. liquid and solid phases as used in fini e diffe ence models. The pa icle- acking echnique, combined wi h idal analysis and mean flow da abases o he hyd odynamics, p esen s wo clea ad an ages o e fini e diffe ences: speed o Fig. 7 (con inued). compu a ion and he ac ha i does no in oduce nume ical diffusion. The numbe o pa icles used in simula ions depends on he speed o compu a ion and/o he accu acy equi ed. Fo example, P oc o e al. (1994b) used 4000 pa icles o simula e an oil spill du ing eal- ime o ecas ing o an inciden in he A abian Gul . Howe e , i is possible ha , due o he geochemical beha iou o ce ain adionuclides, he ac i i y concen a ions in some o he phases may no be esol ed. This is he case o 137 Cs in suspended ma e . The numbe o pa icles used in he simula ion should be o he o de o 10 6 o be able o calcula e, wi h easonable accu acy, ac i i y concen a ions in suspended ma e bu hen he compu ing ime would be simila o ha o he fini e diffe ence model. Howe e , i we a e in e es ed in he assessmen o con amina ion ollowing an acciden , i is p obably enough o calcula e ac i i ies in wa e and bo om sedimen s, which a e he phases whe e almos all he adioac i i y is p esen . I he mos impo an aspec is he speed o compu a ion, he numbe o pa icles can be educed. Fo ins ance, i 137 Cs dispe sion is simula ed using 20,000 pa icles, good esul s a e s ill ob ained in wa e and bo om sedimen s and he compu a ion ime is educed o 2.6% o ha equi ed by he fini e diffe ence model. In he case o 239,240 Pu, he numbe o pa icles could be educed mo e and ac i i ies in he h ee phases may s ill be calcula ed since Pu is mo e widely dis ibu ed be ween he h ee phases han Cs. The pa icle- acking me hod is ully 3-D and akes accoun o ho izon al ad ec ion plus u bulen diffusion in he x–y–zdi ec ions. In he p esen applica ion, he idal and esidual flows ha e been compu ed by a dep h-a e aged 2-D hyd odynamic model. A 2-D hyd odynamical model is adequa e due o he e y s ong idal cu en s and he e ically well-mixed cha ac e o he coas al wa e s. Howe e , he pa icle- acking me hod is sui able o use wi h a 3-D hyd odynamic model (e.g. Ha ms, Ka che , & De hleff, 2000) and he manne in which e ical s abili y can inhibi e ical mixing can be pa ame e ised in such applica ions by making he e ical s ep-size a unc ion o he s abili y o he wa e column. 4. Conclusions The pu pose o his pape is o demons a e he iabili y o new pa icle- acking algo i hms o he simula ion o p ocesses ha in ol e chemical specia ion. The pa icle- acking me hod is commonly used o oil and chemical spill applica ions whe e he e is a need o apid esponse simula ions. In such applica ions, a significan inc ease in compu a ional speed is achie ed by compu ing he hyd odynamics ‘off-line’ and hen using idal p edic ion and mean flow da abases o econs uc he wa e mo emen . This a oids he CFL c i e ion du ing he apid esponse applica ion, al hough he pa icle- acking ime-s ep mus be kep easonably sho in o de o main ain he accu acy o he fi s o de ad ec ion scheme ha is used o compu e he pa icle mo emen . While i would also be easible o sol e fini e diffe ence specia ion equa ions using a p e-compu ed flow field, he p oposed echnique has he ad an age ha he compu a ional ime will be e y sho i a ela i ely small numbe o pa icles is used in he simula ion. Mo eo e , he me hod will be mo e efficien i he con aminan pa ch co e s only a small ac ion o he g id domain (Hun e , 1987) and he accu acy o he esul s can be imp o ed by eleasing la ge numbe s o pa icles}al hough a he expense o an inc eased simula ion ime. One o he main ad an ages o he pa icle- acking me hod is he ad-hoc manne in which pa icle cha ac e is ics can be defined. Fo example, non-Fickian dispe sion can be eadily simula ed by a aching an age o each pa icle (equal o he ime since he elease o he pa icle in o he compu a ion) and hen making he diffusi e s ep o he pa icle a unc ion o i s diffusion ime. In he new model, he in e ac ions be ween he liquid and solid (suspended ma e and bo om sedimen ) phases ha e been desc ibed in e ms o kine ic ans e coefficien s, as in ac ual fini e diffe ence models. A s ochas ic me hod has been de eloped o simula e such in e ac ions. Deposi ion o pa icles and e osion o he sedimen a e also included in he model. A Rouse p ofile is also used o es ima e he e ical s uc u e o suspended ma e concen a ions. As a demons a ion o he me hod, he pa icle- acking model has been used o simula e he dispe sion o adionuclides in he English Channel. A fini e diffe ence model was p e iously de eloped and alida ed o he Channel. Thus he ou pu om bo h models has been compa ed. Two adionuclides wi h diffe en geochemical beha iou s, 137 Cs and 239,240 Pu, ha e been used o he compa isons. The ag eemen be ween bo h models is, in gene al, a he good. Howe e , i is possible ha , due o he pa icula beha iou s o ce ain adionuclides, ac i i y concen a ions in one o he phases canno be calcula ed. Acknowledgemen s R Pe i! aa* nnez was suppo ed by ENRESA and he EU unde con ac FIGE- CT2000-00085. A J Ellio was unded by he Chie Scien is ’s G oup o MAFF unde con ac AE1021 and by he P ocu emen Execu i e o he MoD unde con ac NPC1B/2012. Re e ences Ald idge, J. N. (1998). 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