Numerical modeling of two-phase fluid flow and oil slick transport in estuarine water

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1 In. J. Envron. Sc. Tch., 7 (4), , Auumn 2 ISSN: M. Naghby; M. Kolahdoozan IRSEN, CEERS, IAU Numrcal modlng of o-pha flud flo and ol lck ranpor n uarn ar M. Naghby; *M. Kolahdoozan Dparmn of Cvl and Envronmnal Engnrng, Amrkabr Unvry, Thran, Iran Rcvd 8 Jannuary 2; rvd 6 May 2; accpd 26 Jun 2 ABSTRACT: Ol pll on of h mo mporan hazard n h uarn and coaal ar. In rcn dcad, ngnr ry o prdc h au of ol lck o manag h polluon pradng. Th prdcon of ol lck ranpor carrd ou manly by man of numrcal modl. In h currn udy, h dvlopmn and applcaon of a o-pha flud flo modl o mula ol ranpor n h marn nvronmn ar prnd. Dffrn ranpor and fa proc ar ncludd n h dvlopd modl. Th modl con of h Lagrangan mhod for h advcon proc, h Random Walk chnqu for horzonal dffuon proc and h mprcal quaon for h fa proc. Th major forc for drvng ol parcl ar flud currn, nd pd and urbuln flo. Thrfor, h mul-componn hydrocarbon mhod ha bn ncludd o h dvlopd modl n ordr o prdc fa proc. A prdcon of parcl vlocy componn of major mporanc for ol lck advcon, hrfor h bnomal nrpolaon procdur ha bn chon for h parcl vlocy componn compuaon. In addon, horln boundary condon ncludd n h dvlopd modl o mula hor rpon o ol lck ranpor nar h bach. Th rul of h modl applcaon ar compard h h analycal oluon, xprmnal maurmn and ohr numrcal modl cd n lraur. Comparon of dffrn of rul rprn h capably of dvlopd modl o prdc h ol lck ranpor. In addon, h dvlopd modl d for o ol pll ca n h Pran Gulf. Kyord: Advcon; Dffuon; Lagrangan modl; Mahmacal modlng; Ol pll; Parcl rackng; Polluon INTRODUCTION Ol pll ar h rou nvronmnal hazard hch ofn xhb long-rm mpac. In ordr o conrol h damag caud by ol polluon, opraonal modllng ndd o provd ral-m prdcon of h ranpor and fa of h pll. Th modl can b ud n dcon makng proc o lc h mo ffcn and appropra oluon (Chng al., 2; L, 2; Vnko al., 24; Lu and Wrz, 26; Bandyopadhyay and Chaopadhyay, 27; Tuzkaya and Gulun, 28). Th ol pll n aar ha h complx phycal, chmcal and bologcal proc hch hould b condrd n numrcal modlng (Gallardo and Maru, 27). Th proc ar dvdd no hr pha: ol on h urfac layr, ol n h ar column and ol n h bd layr. In ach pha, om proc ar of major mporanc. Furhrmor, h ma xchang x n h nrfac (Paankar and Joph, 2; Moalanjad, 29). Ol pll modl can b *Corrpondng Auhor Emal: mklhdzan@au.ac.r Tl.: ; Fax: dvlopd by hr Eulran or Lagrangan approach. Ung Lagrangan modl, h phnomna moly rprnd by a larg numbr of mall parcl hch ar advcd by flud vlocy a h ar urfac. Inroducng h phycal propr of h phnomna bad on h parcl rackng approach vry complx and nd pcal anon rgardng dffrn apc of modlng (Naghby, 26). In h Eulran approach, h ma and momnum quaon ar appld o h ol lck layr. By comparng h o approach, can b concludd ha alhough h Lagrangan approach mor complx, can ll rprn h locaon of ol lck and alo prdc h ol lck brakag du o h flo parn (ASCE Tak Comm, 996; Rohan al., 27). Gnrally, n mulpha problm n hch h floang pha do no affc h oud doman, uch a h ranpor of ol n h ar, mulaon r mad bad on h Lagrangan approach (Yapa al., 999; Yapa and Chn, 24). Thrfor, a Lagrangan dcr parcl algorhm ud o mula h ol lck ranpor.

2 M. Naghby; M. Kolahdoozan In h rcn dcad, many rarchr hav udd h ranpor and fa proc of ol pll bad on h rajcory mhod and ma balanc approach,.. (Yapa al., 994; 22; ASCE Tak Comm, 996; Rd al., 999) a rpord by Chao al. 23. Som ll-ablhd modl uch a OILMAP dvlopd by h Appld Scnc Aocaon n 997, SINTEF dvlopd by Rd n 2 and GNOME dvlopd by h Naonal Ocanc and Amophrc Admnraon (NOAA) n 2, ar bng ud currnly o prdc ol ranpor and drbuon n a ar body (Chao al., 23, Nour al., 28; 29; Adam al., 29). Among h ol pll modl, many focu on h urfac ranpor. In h udy, a o-dmnonal o-pha numrcal modl dvlopd o prdc h ranpor and fa of ol lck, hch ruld n h concnraon drbuon of ol o b on h ar urfac. To dmnonal govrnng quaon of flud flo hch con of ma and momnum r olvd ung h fn dffrnc mhod on h rucurd aggrd grd ym (Falconr, 976). Th ruld algbrc quaon r olvd by h alrnang drcon mplc (ADI) chnqu. In addon h nd pd and h corol ffc r ncludd n h currn hydrodynamc modl. Th ranpor of h ol lck a prdcd by h o dmnonal parcl rackng approach conng of h Lagrangan mhod for h advcon proc, h Random Walk chnqu for h horzonal dffuon proc and h mprcal quaon for h fa proc. Fa proc r mulad ung mul-componn mhod n ordr o condr h ol compoon (Tabl ). In addon h horln rpon o ol lck ranpor a alo ncludd n h dvlopd modl. Th udy a carrd ou n Thran, Polychnc durng and uppord fnancally by Th Tabl : Clafcaon of ol propr (Koronko and Mamdov, 24) No. Typ Bolng pon Vol. (%) C 6-C Cº 2 C 3-C Cº 25 3 C 6-C Cº 5 4 C 3-C Cº 5 5 C 6-C 8-24 Cº 5 6 C 2-C Cº 5 7 C 9-C Cº 5 8 rmandr >4 Cº Naonal Iranan Rfnng and Drbuon Company. MATERIALS AND METHODS Mchanm of phycal-chmcal nracon of ol pll To dffrn proc r rcognzd hn ol plld no h ar. Th fr proc domnad h ranpor of h ol lck du o h coaal currn, hch nclud advcon, pradng and urbuln dffuon. Th cond proc a rlad o h nrfac nracon of h ol lck h ar and ar. A ol-ar nrfac, vaporaon could b obrvd, hl a h ol-ar nrfac doluon, mulfcaon and dmnaon r domnad (Han al., 2). Ol pll proc ar rlad o ol propr, hydrodynamc and nvronmnal condon. Whn ol plld no h aar, prad o form a hn flm. Th ol lck ranpor by h advcon and urbuln dffuon du o h urfac currn, av and nd. Furhrmor, h lck prad du o a balanc of forc. From h phycal pon of v, h ranpor of ol lck nclud h fa proc rulng n a hnnr layr of ol on ar urfac. Fnally, hn lck com o a crcal hckn, ll b dvdd no mall poron (Kozy and Madrch, 23). Advcon and urbuln dffuon Th man proc nvolvd n h ranpor of ol on h ar urfac ar advcon and urbuln dffuon. Advcon manly du o h nd, urfac currn and av (Hun al., 22). Th comparon of rul oband from Lagrangan and Eulran modl hod ha rul oband from h arlr on ar mor accura, pcally n h advcon proc compuaon (ASCE Tak Comm, 996). In addon, h lck brakag can b prdcd by h Lagrangan approach (Shn and Yapa, 988). Th ol lck nroducd by a larg numbr of parcl hch mov h h urroundng ar body. Toal vlocy ( U r ) for movng parcl a compud by (Al-Rabh al., 989, 992; Chao al., 2, 23): r r r U = U a + U Whr, U r () advcon vlocy du o h urfac a currn (oband from h flo modl) and nd r drf and U dffuv vlocy du o h horzonal 772

3 In. J. Envron. M. Naghby; Sc. Tch., M. 7 (4), Kolahdoozan , Auumn 2 urbuln dffuon. Advcv vlocy dcrbd a (Al-Rabh al., 989, 992; Chao al., 2, 23): r r r U a = K U + K Whr, U r U (2) urfac currn vlocy for ach parcl, oband from flo modl. Th magnud of vlocy componn a h parcl locaon a oband by blnar nrpolaon ruld n mor accura prdcon of parcl vlocy (Naghby and Kolahdoozan, 28): r U = ( j).( k). u + u Whr, u, u 2, u 3 and u 4 ar h flo vlocy componn, U r nd vlocy a a hgh of m abov h ar urfac, K currn facor and K nd drf facor. In h ohr hand, h dffuv vlocy (U r ) can b drvd by random alk modl. In ohr ord, bad on Al-Rabh udy, h danc ( S ) hrough hch a parcl ranpor by h horzonal dffuon can b xprd by (Al-Rabh al., 989, 992; Chao al., 2, 23): S = [ R] 2Dh Whr, and + j.( k). u2 + ( j). k. u3 j. k. [R] a random numbr bn o, D h h horzonal dffuon coffcn. Th dplacmn of h ol lck du o h advcon and horzonal dffuon can b calculad by (Al-Rabh al., 989, 992): Lx( ) = U ax + S coθ L = U + S nθ y( ) ay Whr Lx( ) and Ly( ) ar dplacmn n h x and y drcon, rpcvly, U ax and U ay ar advcv vlocy componn n h x and y drcon, rpcvly and θ = π[ R hr 2 θ ] [ R θ ] a random numbr bn o. Fnally, h parcl a m n ranpord o h n locaon a m n+ a: X = X + L n+ n x ( ) n+ n = + y( ) (6) Y Y L 4 (3) (4) (5) Whr, X and Y ar parcl coordna, h numbr of parcl, and n and n+ ar h m lvl. Spradng Accordng o Fay hypoh, h pradng proc h horzonal xpanon of h ol lck du o h counrbalanc of mchancal forc ncludng gravy, urfac non, nra and vcoy (ASCE Tak Comm, 996; Shn and Yapa, 988). Th proc domna h ranpor a h bgnnng of ol pllng. Lhr dvlopd a rlaonhp bad on Fay udy (Chao al., 2, 23). Accordng o Fay, an llpcal ara covrd by h ol lck n hch h larg damr n h drcon of nd. Lhr rlaonhp ar a follo (Chao al., 2, 23): L L A mn max = = = 53 L. 76 mn ρ ρ + ρ 227 ρ ρ + 4 ρ / 3 / 3 V V ol ol / 3 4 / 3 / 3 3 / 4 / 4 Whr, L max, L mn ar h lngh of h major and mnor ax of llp, rpcvly (m), A h ara of ol lck (m 2 ), ρ = ρ ρ, ρ, ρ ar h dn of ar and ol, rpcvly, V ol h oal volum of an ol pll n barrl ( barrl =.589 m 3 ), U h nd pd n kno and m (mn). Th Lhr formulaon dployd n h dvlopd modl. Evaporaon Evaporaon play a crcal rol durng h arly ag of an ol pll and rduc h ol ma. Ol propr (vcoy and dny) ar bng changd durng h vaporaon (ASCE Tak Comm, 996). Mackay propod a mahmacal modl bad on h mul-componn hory o ma h ra of ol vaporaon (Chao al., 2, 23) hch can b xprd a follo: E K AZ P M U / 2 / 3 3 U V ol / 2 4 / 3 = (9) RT ρ (7) (8) 773

4 Numrcal M. Naghby; modlng M. of ol Kolahdoozan lck ranpor Whr, E h magnud of componn lo by h vaporaon (m 3 ), K h ma ranfr coffcn of vaporaon (m/), A h ol lck ara (m 2 ), Z h amoun of ol fracon dfnd a Z = E / ΣE (%), P h vapor prur of componn (am), M h molcular gh (g/mol), ρ h dny of ol componn (gr/m 3 ), h m p (), R h ga conan ( am.m 3 / mol.ºk) and T h ar mpraur abov h lck (ºK). Th maon of K d bad on Mackay hypoh and dfnd a (Chao al., 2; 23): K =.292U h S c Whr, U h nd vlocy (m/), h h ol lck hckn (m) and Sc h Schmd numbr hch rprn h urfac roughn and aumd o b qual o 2.7 n h udy (Khorav, 99). Doluon Som of h ol componn, hch ar ubjcd o vaporaon, can alo b dolvd no h ar column. Th proc for mulang doluon mlar o h vaporaon. In h ca, a mulcomponn modl bad on Mackay hypoh a dployd a follo (Chao al., 2, 23): D = K d M AZ S ρ Whr, D h magnud of componn lo by doluon (m 3 ), K d h ma ranfr coffcn of doluon (m/), A h ol lck ara (m 2 ), Z h amoun of ol fracon (%), S h olubly of fracon, M h molcular gh (g/mol), ρ h dny of ol componn (g/m 3 ) and h m p (). Th maon of bad on Mackay ud and dfnd a (Chao al., 2, 23): 6 K d = 2.36 Whr.4 = for alkan for aromac for olfn () () (2) Vrcal dpron and mxng Dpron h brak-up of h cohrn ol lck no mall dropl of varyng z, and h prad and dffuon of h dropl n h ar column. Smallr dropl ll rman upndd n h ar hra h largr on ll r back o h urfac o hr rform h ol lck or prad ou o form a vry hn flm of ol. Dlvgn and Sny propod a rlaonhp for compung h ol nranmn ra bad on ol yp, brakng av nrgy and parcl z a (Chao al., 2; 23): Q ( d ) = K n D.57 ba S cov F c d.7 p d (3) Whr, d p h ol parcl z (m), d h parcl z nrval (m), Q (d) h ra of ol parcl nranmn h z n an nrval d around d (Kg/ m 2 ), K n a proporonaly conan, dnfd a h nranmn coffcn, D ba h dpad brakng av nrgy pr un urfac ara (J/m 2 ), S cov h fracon of urfac ara covrd by ol ( S cov ), and F c h fracon of a urfac h by brakng av pr un m. D ba and F c ar gvn a (Chao al., 2; 23): D F 2 ba =.34ρ gh rm (4) c =.32( U U or 3.85 ) / T n aar (5) Whr, p ar dny (Kg/m 3 ), g h acclraon du o gravy (m/ 2 ), H rm h roo man quar (rm) av hgh (m), U nd pd (m/), U h hrhold nd pd for a av brakng (5 m/) and T h brakng av prod (). Adorpon of ol by dmn Ol can b rappd n h pac bn dmn parcl. Th proc dvdd no o cagor: -urfac aborpon du o onc acvy n h urfac of bd dmn. -capllary aborpon du o h dmn por. Condrng h abov o cagor, h oal aborpon can b xprd a (Chao al., 2; 23): bkc Q = Q + Q = + K d m 2 p + KC (6) Whr, Q h oal aborpon capacy, C o ol concnraon afr aborpon balanc, d h dmn parcl damr and m, K p, K and b ar aborpon paramr bad on mprcal rlaonhp of Chao al., (23), hch can b hon a: 774

5 In. J. Envron. M. Naghby; Sc. Tch., 7 M. (4), Kolahdoozan , Auumn b=.96 d K = 68.3d K p = 8.4 m =.78 (7) Emulfcaon Emulon h chang of mxur of ol and ar du o h brakng av and ar urbulnc. Th formaon of mulon can rongly chang h ol propr. Th dny of h mulon could b.3 m dnr han h nal ol dny. Th fr lv hour of pllng h mo mporan m h rgard o chang n dny (ASCE ak comm, 996). Vcoy h mo gnfcan paramr a ncra from a f hundrd cs o approxmaly 5 cs. For h mulon maon, Mackay rlaonhp a ud n h currn udy (Shn and Yapa, 988): V = C 3 xp ( + U ) C 3 (8) Whr V h ar conn of h mulon, U h nd pd (m/), C 3 h conan vcoy qual o.7 for havy ol and.25 for lgh ol, and m (). Chang of ol propr Emulon and vaporaon of ol ncra h ol vcoy and dny. Thrfor, h ol propr hould b corrcd durng h ol lck ranpor. Accordng o Mackay rlaonhp h vcoy of rmanng ol and h dny of mulon ar a follo: (Wang al., 25): 2.5V µ = µ xp ( C 3V ) ρ = V ρ + ( V )( ρ + C F c Whr, µ h vcoy of h rmanng ol, h nal valu of h ol vcoy (cp), ρ h dny of ar (Kg/m 3 ), ρ h dny of mulon (Kg/m 3 ), ρ c h nal ol dny (Kg/m 3 ), F h vaporaon fracon and V h ar conn of h mulon. Shorln boundary condon Th nracon of ol and h horln a vry complx proc boh n rm of h nvronmnal and numrcal modlng. Th damag caud by h Exxon Valdz accdn (989) rprn h mporanc of h 3 ) (9) µ phnomnon. Many ffcv phnomna uch a av, currn and nd nd o cra coaal rpon and cau complx problm. Thrfor, horln hould b condrd a a boundary condon for ol lck ranpor (ASCE ak comm, 996). Torgrmon ud h half-lf mhod bad on xponnal dcay funcon (Shn and Yapa, 988). In h mhod, a holdng capacy a agnd for ach yp of bach. Half-lf paramr xpr coaal ably for ol holdng. Tabl 2 ho h half-lf and vulnrably ndx for om bach (Shn and Yapa, 988). In h udy, bad on h half-lf mhod, h volum of ol rmanng on h bach rlad o orgnal volum a follo (Shn and Yapa, 988): 2 = k ( 2 ) (2) Whr, and ar volum of ol on h bach 2 a m and 2 rpcvly, λ h half-lf and k can b oband by (Shn and Yapa, 988): Ln(/ 2) k = λ (2) Accordng o Al-Rabh ud, h rurn probably funcon of h ol parcl from hor o h a can b xprd a (Al-Rabh al., 989, 992): Pr =.5 / λ Thrfor, ho parcl hch afy quaon 22, can b rurnd o h a. rand (,) < P r (22) (23) Whr, Rand (,) a random numbr n a pcfd rang and P r h rurn probably of h ol o h a. Concnraon convron Accordng o quaon (24), h numbr of parcl ranformd no a concnraon a ach grd cll (Kang, 998): M NP o x,y,z, S ( x,y,z, ) = NP Vol (24) x,y,z, Whr, S (x,y,z,) h ol parcl concnraon of a grd cll, M h oal ma of ol plld no h o compuaonal doman, NP h oal numbr of parcl n h compuaonal doman, NP x, y, z, h oal numbr of parcl n a grd cll, and Vol x, y, z, h volum of a grd cll. 775

6 M. Naghby; M. Kolahdoozan Ol pll mulaon In ordr o mula ol ranpor n uarn ar, a o-dmnonal mul-pha ol lck ranpor modl a dvlopd n h currn udy. Th modl con of o ub-modl namly hydrodynamc and ol lck ranpor. In ach m nrval, flo parn a oband from h hydrodynamc ub-modl (DIVAST). To dmnonal govrnng quaon of flud flo hch con of ma and momnum conrvaon r olvd ung an mplc fn dffrnc mhod on h rucurd aggrd grd ym. Th ruld algbrc ym of quaon r olvd by h ADI chnqu. Afr drmnng h horzonal vlocy componn a ach Eulran mh pon, h ol ranpor ub-modl a calld n ordr o mula ol lck ranpor. In h ub-modl, aumd ha ol lck producd by ndvdual parcl. I obvou ha h numbr of parcl ha drc ffc on h accuracy of numrcal modlng rul. Th nal condon a nroducd n a ay ha an nal poron of h ara undr h udy covrd by an ol lck. Th n locaon of ol parcl a calculad by condrng ranpor and fa proc bad on h prnd rlaonhp. I nal o pon ou ha a h ol parcl hav no major ffc on h flo paramr (Chao al., 2, 23), hrfor vlocy of ol parcl aumd o b h am a vlocy of ar. In ach m p, f h ol parcl rach h horln, a rlad calculaon a commncd. RESULTS AND DISCUSSION Modl valdaon and vrfcaon Valdaon and vrfcaon of h numrcal modl r carrd ou h hr ca ud cd n h lraur. Rul r compard h analycal Tabl 2: Shorln dcrpor and dfaul paramr (Shn and Yapa, 988) Shorln dcrpor Half lf Vulnrably ndx Expod hadland h Wav-cu plaform h 2 Pock bach day 3 Sand bach day 4 Sand and gravl bach day 5 Sand and cobbl bach y 6 Expod d fla h 7 Shlrd rock hor y 8 Shlrd d fla y 9 Shlrd marh y Land y oluon, laboraory maurmn and ohr numrcal modl cd n h lraur. Opn channl flo In h ca, a rcangular channl 2 m lngh and m dh condrd. Unform grd z of. m ud boh n h x and y drcon. Undrconal flo h. m/ vlocy aumd along h longudnal ax of h channl. Dpron coffcn o. m 2 / n boh x and y drcon. Th nal poon of h parcl y = 5 m. Smulaon m a o cond (Kang, 998). Tabl 3 prn h nal condon for h ca udy. Dffrn ca r lcd for h nvy analy purpo and r ummarzd n Tabl 4. Dph, vlocy and dpron coffcn ar aumd conan. Th urfac concnraon of ol can b valuad analycally ung advcondffuon quaon (Kang, 998): 2 M ( y y ) S ( x,y,z, ) = H 4π D xp ( x x D u ) 4D x y 2.xp 4D (25) Whr M h oal ma of racr njcd a y = 5 m and =, u h man vlocy, D x and D y ar h dpron coffcn n h x and y drcon, rpcvly, H h dph and = m (). Fg. rprn h ffc of h numbr of parcl and h m p on h accuracy of h rul. From Fg., can b obrvd ha by ncrang h numbr of parcl and/or dcrang h m p, mor rul ha ar accura can b achvd. Fg. ho ha h combnaon of, parcl and m p lad o a mor accura rul n h ca udy. Fg. 2 rprn h quanav mulaon rul oband from h numrcal and analycal approach n h cnrln of h channl. Th accuracy and conncy of numrcal prdcon n comparon h h analycal compuaon rprn h applcably of h ncorporad approach o h dvlopd numrcal modl. Ol lck ranpor du o urfac currn, nd and urbuln dffuon In h ca udy, h combnaon of nd nducd and ar urfac varaon currn hav bn condrd o oban h ol lck rajcory. Th oal y. 776

7 In. J. Envron. M. Naghby; Sc. Tch., M. 7 (4), Kolahdoozan , Auumn 2 numbr of parcl o 5, hch r rlad a pon (4, 8). Toal mulaon m a o 24 h h 36-cond m p. Currn vlocy componn ar aumd o b.3 and. m/ for h x and y drcon rpcvly. Wnd vlocy m/ conan n h y drcon. In addon, dpron coffcn ar o a conan valu of and 2 m 2 / for h x and y drcon rpcvly (Tkalch al., 23). Numrcal modl rul r compard h an Eulran modl orgnally dvlopd by Tkalch and Chao n 2 (Fg. 3) (Chao al., 2; Tkalch al., 23). Th comparon of h o of rul ho ha n arly ag of h udy boh modl hav narly h am prdcon, bu afr om-m h dcrpancy of rul bn o modl can b obrvd. To fnd ou hch on of h abovmnond approach mor accura, a laboraory xprmnal maurmn a chon hch ll b prnd n h nx con. Ol pll n laboraory To valda h dvlopd numrcal modl, h laboraory xprmnal maurmn of Borhck and Joyn (992) chon. Th of xprmn r carrd ou n h Hydraulc laboraory of h Dparmn of Cvl Engnrng a h Unvry of Salford, UK. Alo, h rul of Eulran numrcal modl dvlopd by Borhck compard h h dvlopd modl and h accuracy of Eulran and Lagrangan approach ar compard. Th xprmnal ank ha an ovrall plan ara of 3.5 m 7.24 m and lvad.7 m abov h laboraory floor (Borhck and Joyn, 992). Rgular Inal Poon Rla NP parcl a x = and y = 5 m Vlocy u =. & v =. m/ dprvy D x = D y =. m 2 / Dph. m Compung m T com = No. of parcl Tabl 3: Inal condon Tabl 4: Ca numbr for nvy analy = =, Ca Ca 2, Ca 3 Ca 4 av r producd a on nd of h ban by a pon-yp paddl drvn a 4 hp, 5 rpm varablpd ngn. Th maxmum plan ara of h ar urfac a rrcd o 3.5 m 5. m bn h plan-pndng bach and paddl gnraor (Borhck and Joyn, 992). A half-prodc nuodal lor bach a fabrcad, nurng ha h crculaon parn a dvlopd n accordanc h h fndng of Noda (974) and da lva Lma (98) a rpord by Borhck and Joyn (992). For h xprmnal udy dcrbd n h con, h dp ar a.255 m a h paddl locaon (Borhck and Joyn, 992). Numrcal modlng bad on h Eulran approach a carrd ou by h man of a r grd h.2 m and.35 m pacng n h offhor x-drcon and long hor y-drcon, rpcvly (Borhck and Joyn, 992). Durng h man, onc ady-a currn condon rachd, h ol a plld from a bakr no h ban a (3.7,.4) m and an lvaon of no mor han 4 cm abov h ar urfac n l han on cond. Th xprmnal pcfcaon r lcd by ral and rror o avod h pradng of h ol o h d all durng h arly ag of h (Borhck and Joyn, 992). Rgular av r gnrad h h prod of.29 and offhor dp-ar hgh of.98 m (a h paddl) n boh numrcal modl and xprmnal apparau. Borhck ha lcd a.255 m p for h Eulran numrcal modl hl n h currn udy a.2 a chon, hch corrpond o h couran numbr l han on. parcl ar chon for numrcal modllng purpo hl for h flo modl a unform grd pacng of.25 m ar ncorporad. I nal o pon ou ha h numbr of parcl canv, hrfor n ach ca udy an appropra numbr of parcl hch a funcon of many paramr. phycal phnomna, gomry of udy ara, c. nd o b found. In rm of Borhck Eulran modl, a rcangular grd cll h.2 m and.35 m pacng n h x and y drcon rpcvly hav bn ud, hl for h ol lck modl, a grd z of.5 m ha bn chon o achv a mor accura rul (Borhck and Joyn, 992). Th dffuon coffcn ar o.4 m 2 / n boh h x and y drcon for boh Lagrangan and Eulran modl. Th ol lck ranpor condrd 777

8 Numrcal M. Naghby; modlng M. of Kolahdoozan ol lck ranpor Ca Ca 2 S/Smax.5 S/Smax X (m) X (m) Analycal Numrcal Analycal Numrcal Ca 3 Ca 4 S/Smax.5 S/Smax Analycal X (m) Numrcall Analycal l X (m) Numrcal l Fg. : Comparon of normalzd concnraon along x drcon for varou ca = 2 S/Smax.5 = 6 = X (m) Analycal l Numrcal Fg. 2: Normalzd concnraon a h cnrln of h channl n dffrn m (ca 4, Tabl 4) 778

9 In. J. Envron. M. Sc. Naghby; Tch., 7 M. (4), Kolahdoozan , Auumn 2 hrough h oal compuaonal m of 38.7 (3 av prod). Th comparon of xprmnal maurmn, Eulran and Lagrangan modl rul ar hon n Fg. 4. From Fg. 4, can b concludd ha rul oband from dvlopd Lagrangan modl ar much clor o h maurmn n comparon h Borhck Eulran modl. Accordng o Borhck, h dffrnc bn xprmnal maurmn and numrcal modl rul ar du o cal rror and alo h dvry of phnomnon paramr,.g., ol dny, urfac non, urbulnc ddy z, c. (Borhck and Joyn, 992). Th comparon of h xprmnal maurmn and modlng rul ho ha from h bgnnng of h pll up o.6 (9 av prod), rul ar n good dgr of mlary (Fg. 4). Th major rol of ol pradng clo o h brakr ln h longhor currn, hch manly occurrd durng 5.48 o (2 and 8 av prod). A 2 av prod, h phycal lck bcom mor or l crcular. Thn, a h lck a advcd furhr alonghor, h rp currn bgan o rch h lck n h y-drcon, rulng n an llpcal hap h h major ax n a doubl h lngh of h mnor ax (bn 8 and 27 av prod). In conra, h mulad lck a rchd n h y-drcon by h longhor currn unl rachd h nranc of h rp currn (Borhck and Joyn, 992). A quanav comparon of hr of rul llurad n Fg. 5. Fg. 5 ho ha rul oband from h dvlopd modl ar much clor o h xprmnal maurmn rahr han Bohck Eulran modl rul, provng ha h Lagrangan approach mor accura n comparon h Eulran approach n rm of ol lck ranpor prdcon. Modl applcaon Applcaon o Pran Gulf To dmonra h capably of modl n ral ca, o vrual ol pll vn n Pran Gulf hav bn chon. Pran Gulf on of h major orld aray n rm of commrcal and conomc acv, pcally xporng ol from h rgon. Approxmaly 4 % of oal ol ranpor n h orld ar carrd ou hrough h rgon. Th 6 % of oal ar polluon n h Pran Gulf du o ol pll. Pran Gulf approxmaly covr 25 km ara. Th man ar dph around 35 m and ncra nar h Hormouz Sra o m. Pran Gulf conncd o Oman Sa and Indan Ocan hrough h Hormouz Sra (Naghby and Kolahdoozan, 28). Accordng o prvou rarch n h rgon, boh nd and dal currn ar h mo mporan hydrodynamc phnomna n h rgon and dny and hrmal currn ar l mporan (Naghby and Kolahdoozan, 28). To prdc h flo parn n h udy ara, a odmnonal horzonal modl hch dvlopd orgnally by Falconr (976) and hn rfnd by Kolahdoozan (999) and Kolahdoozan and Falconr (23) a ud. In ach m p, flo paramr r calculad by h hydrodynamc modul of h modl and hn h paramr ar ung n h ol pll ubmodl o prdc h ol lck rajcory n h udy ara. Flo parn n Pran Gulf To prcrb h flo parn, a rcangular mh of 2 m n boh x and y drcon hav bn chon. Opn boundary condon a o ar lvaon a Hormouz Sra. Th no-lp boundary condon a lcd for boom boundar. Accordng o prvou ud n h rgon, h bd roughn of 4 mm uabl and producd calbrad rul for flo parn and ar lvaon nar h Buhhr Bay (War Rarch Cnr, 2). Ol pll prdcon n Pran Gulf Toal mulaon m o 5 day. A a rul of cold ar for h flo modl, h ol pll modl ar o prdc h ol lck ranpor a h bgnnng of h cond day. Tm p of 72 ar for boh flo and ol pll ub-modl. A hr no daa avalabl n rm of ol ranpor n h rgon for calbraon purpo, hrfor only h applcably of modl udd. To ol pll vn hav bn aumd h h 285 m 3 (7926 barrl) volum of ol. Tdal characrc of 2 nd. Ocobr 23 hav bn condrd for modlng purpo. Th locaon of ol pll r aumd o b approxmaly n 5 km danc from Buhhr Bay (5º 8" laud and 29 º 5" longud for fr vn and 5º 8" laud and 29º 35" longud for h cond vn). A 4 m/ nd pd h h 45-dgr blong a h ouharn drcon for fr vn and norharn for cond on hav bn aumd. Th and and gravl bach h a half-lf of 24 h ha bn condrd. Ol characrc and nal condon ar ummarzd n Tabl 5. Fg. 6 ho h nal locaon of ol pll and ol lck ranpor afr 3 day for h fr vn. From Fg. 6, obrvd ha h pah of ol lck a dvrd 779

10 M. Naghby; M. Kolahdoozan 24 = 7.7 h 3.5 (a) nd = m/ = 2.48 h 27.9 y (m) 6 2 = 7.8 h y (m) = 3.2 h u =.3 m/ Inal poon x (m) Modl rul Tkalch modl Fg. 3: Advcon and Dpron of ol parcl du o currn and nd o h Buhhr Coa. Th ol lck ara nd o an llp h h major damr n h nd drcon n h arly ag of modlng. A h flo currn n h rgon manly con of dal currn and ndnducd currn, hrfor h drcon of llp major ax no xacly n h nd drcon. In Fg. 7, h fa of ol lck du o h vaporaon and doluon prnd. Fg. 7 ho ha 35 % of ol vaporad n h fr 26 h and only 5 % of ol nrd no h ar column. Ol lck on h ar urfac con of 6 % of h volum, hch orgnally plld no h ar. Th ol lck ara ncrad accordng o Fay hypoh and rachd h fnal valu. In h cond vn, h mpac of ol lck o h horln ha bn udd. Ol lck paramr ar h am a h fr vn. Th ol rajcory and ol concnraon ar prnd n Fg. 8. Fg. 9 dmonra h ol pll balanc n h rgon a dffrn m. From Fg. 9, can b concludd ha 4 % of ol a vaporad n l han h. Th 4 % of ol a aborbd by bach n 2 h and l han 2 % of o l a rmand n h ar urfac. From Fg. 9 alo can b obrvd ha bach aborpon on of h mo mporan phnomna nar h coaln. Ol lck hckn dcrad n only 8 h and rach fnal valu afr 4 h (Fg. ). y (m) y (m) x (m) (b) x (m) (c) x (m) Fg. 4: Ol Slck ranpor [(a): dvlopd lagrangan modl, (b): borhck ulran modl, (c): xprmnal maurmn] 78

11 In. J. Envron. M. Sc. Naghby; Tch., 7 (4), M , Kolahdoozan Auumn Inal ol pll Wnd Day y (m).75 2 Day Iran 29 N 3 Day x (m) Bouhhr Numrca l Mo dl Broh ck Mo dl E xprmn al Mo d l 5 E 25km Fg. 5: Comparon of h ol lck locaon durng h m bn numrcal modl and xprmnal daa Fg. 6: Inal locaon of ol pll and ol lck ranpor oard Buhhr Bay Fa Volum (%) Tm (h) Evaporaon Doluon Fg. 7: Fa of ol lck du o vaporaon and doluon Tabl 5: Ol characrc and nal condon Ol-modl paramr Amoun Ol yp Havy Toal volum 285 m 3 Ol dny 965 Kg/m 3 Ol vcoy 38 cp Ar mpraur 28 ºC Mnmum hckn. mm Currn facor (K ). Wnd drf facor (K ).3 Horzonal dffuon coffcn (D h) Numbr of ol parcl 25 Bd dmn concnraon.2 Kg/m 3 Sdmn parcl damr.43 mm CONCLUSION Th Eulran - Lagrangan modl a dvlopd o mula o-pha flud flo. Th modl prdc h ol lck ranpor, h fa proc and h concnraon drbuon of ol on h ar urfac. By couplng a o-dmnonal dph avragd hydrodynamc modl h h dvlopd ol lck modl, ol lck ranpor can b mulad. Wnd ffc, a ll a ar currn du o d ncludd n h hydrodynamc modul. To oban mor accura mulaon rul, h bnomal nrpolaon chnqu a dployd for h prdcon of parcl vlocy componn. In addon, h mul-componn hydrocarbon mhod a ncorporad o ma h amoun of ol, hch d don hrough h fa proc. Aborpon of ol rach o h horln boundary alo ncludd n h dvlopd numrcal modl. Th valdaon and vrfcaon of h modl r carrd ou by comparng numrcal rul h analycal oluon, laboraory maurmn and/or rul oband by numrcal modl cd n h lraur. Th comparon of modl rul (Borhck Eulran and dvlopd Lagrangan modl) ho ha Lagrangan approach mor accura han h Eulran on n rm of ol lck ranpor prdcon. Alo, h comparon of modl rul h analycal oluon rprn h capably of h modl n an dalzd ca udy. Rul oband from abov ca, ho ha h ncorporad approach n hch ncludd n h dvlopd modl hrough h udy can lad o h 78

12 Numrcal M. Naghby; modlng M. of Kolahdoozan ol lck ranpor E-6 8E-6 6E E-6 8E-6 6E C (m 3 / m 2 ) C (m 3 / m 2 ) Iran Iran k m 4 m k m h Day 4 m E-6 8E-6 6E E-6 8E-6 6E C (m 3 / m 2 ) C (m 3 / m 2 ) Iran Iran k m 4 m 4 m 2 Day k m 3 Day Fg. 8: Smulaon of ol lck pah oard h horln Ol amoun (%) Ol lck hgh (m) Tm (h) Ol on ar urafc Evaporaon Ol on bach Ol n ar column Fg. 9: Ma balanc of ol hrough varou phnomna Tm (h) Fg. : Avrag ol lck hckn 782

13 In. J. Envron. M. Naghby; Sc. Tch., 7 M. (4), Kolahdoozan , Auumn 2 mor accura numrcal modlng maon. In addon, o vrual ca r chon for h Pran Gulf, dmonrang h ponal of h ol pll modl prdcon n ral ca ud. ACKNOWLEDGEMENTS Th auhor h o acknoldg h Naonal Iranan Rfnng and Drbuon Company for h fnancal uppor mad for h rarch udy for hr uppor. In addon, h auhor hank Dr. Chao (Rarchr n h Naonal Cnr for Compuaonal Hydro Scnc and Engnrng) for h advc. NOMENCLATURE A ol lck ara b, K, K p, m adorpon paramr C 3 conan vcoy C o ol concnraon afr adorpon balanc Dba dpad brakng av nrgy pr un urfac ara Dh horzonal dffuon coffcn D magnud of componn lo by doluon d p ol parcl z d dmn parcl damr E magnud of componn lo by vaporaon F vaporaon fracon Fc fracon of a urfac h by brakng av pr un m g acclraon du o gravy h ol lck hckn H rm roo man quar (rm) av hgh I numbr of parcl Kd ma ranfr coffcn of doluon K ma ranfr coffcn of vaporaon Kn proporonaly conan dnfd a h nranmn coffcn K currn facor K nd drf facor L,L max mn lngh of h major and mnor ax Lx( ), Ly( ) dplacmn n x and y drcon M molcular gh Mo oal ma of ol plld no h compuaonal doman n, n+ m lvl. NP oal numbr of parcl n h compuaonal doman NP x, y, z, oal numbr of parcl n a grd P vapor prur P r rurn probably of ol o h a Q(d ) ra of ol parcl nranmn Q oal adorpon capacy R ga conan Rand(,)a random numbr n a pcfd rang [R a random numbr bn o ] S olubly of fracon Sc Schmd numbr S cov fracon of urfac ara covrd by ol S x, y, z, ol parcl concnraon of a grd cll T ar mpraur abov h lck T brakng av prod U r advcon vlocy a U ax, Uay advcv vlocy componn n x and y drcon u flo vlocy componn U r urfac currn vlocy U r oal parcl vlocy U hrhold nd pd for a av brakng U r nd vlocy a a hgh of m abov h ar urfac r U dffuv vlocy V ar conn of h mulon V ol oal volum of an ol pll Vol x, y, z, volum of a grd cll X, Y parcl coordna Z amoun of ol fracon λ half-lf µ vcoy of h rmanng ol µ nal valu of h ol vcoy ρc nal ol dny ρ dny of mulon ρ dny of ol componn ρ, ρ dn of ar and ol S danc ha a parcl ravl m p d parcl z nrval, volum of ol on h bach a m 2 and 2 REFERENCES Adam, R. H.; Olán-Caro, D.; Guzmán-Ooro, F. J.; Díaz- Ramrz, I. J., (29). Rlaonhp bn gomorphology and conamnaon h ahrd hydrocarbon n an old rvr lv/marh aocaon. In. J. Envron. Sc. Tch., 6 (4), (2 pag). Al-Rabh, A. H.; Ckrg, H. M.; Gunay, N., (989). A ochac mulaon modl of ol pll fa and ranpor., Appl. Mah. Modl., 3 (6), (8 pag). Al-Rabh, A. H.; Ckrg, H. M.; Gunay, N., (992). Modlng h Fa and Tranpor of Al-Ahmad Ol Spll. War Ar Sol Pollu., 65, (3 pag). ASCE ak comm on modlng of ol pll of h ar rourc ngnrng dvon, (996). Sa-of-h-ar rv of modlng ranpor and fa of ol pll., ASCE, J. Hydraul. Eng., 22 (), (6 pag). Bandyopadhyay, G.; Chaopadhyay, S., (27). Sngl hddn layr arfcal nural nork modl vru mulpl lnar rgron modl n forcang h m r of oal ozon. In. J. Envron. Sc. Tch., 4 (), 4-5 ( pag) Borhck, A. G. L.; Joyn, S.A., (992). Laboraory udy of ol lck ubjcd o narhor crculaon., J. Envron. Eng., 8 (6), (8 pag). Chao, X.; Shankar, J.; Chong, H. F., (2). To-and hrdmnonal ol pll modl for coaal ar. Ocan Eng., 28, (2), (7 pag). Chao, X.; Shankar, J.; Wang, S. S. Y., (23). Dvlopmn and 783

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