COASTOX- NUMERICAL MODEL TO SIMULATE TWO DIMENSIONAL DISPERSION OF RADIONUCLIDES IN WATER BODIES

Transcription

1 COASTOX- NUMERICAL MODEL TO SIMULATE TWO DIMENSIONAL DISPERSION OF RADIONUCLIDES IN WATER BODIES DECISION SUPPORT FOR NUCLEAR EMERGENCIES

2 1.1 INTRODUCTION 1.2 COASTOX The COASTOX model wa develoed at the Cyernetic Center, Kiev (Zheleznyak, 199, Zheleznyak et al., ) to imulate the tranort and the dierion of ollutant in the Dnieer reervoir and in the Priyat River. It contain the radionuclide tranort umodel imilar to thoe ued in FETRA. The model include the ediment tranort, the tranort y the advection-diffuion, and the radionuclide - ediment interaction. It conider the dynamic of the ottom deoition and decrie the rate of the edimentation and the reuenion a a function of the difference etween the actual and equilirium concentration of the uended matter deending on the tranort caacity of the flow. The latter i calculated on the ai of the emi-emirical relationhi. The Kd aroach ha een ued for decriing the adortion/deortion and the diffuion tranfer of the radionuclide in the ytem "olution - uended ediment" and "olution - ottom deoition". The exchange rate etween the olution and the article are taken into account to otain the more realitic imulation of the kinetic of the rocee. The adortion and deortion rate are aumed to e not equal. The Finitedifferen method are ued to olve the equation. The two main difference etween FETRA and COASTOX are that the latter ha the oiility to calculate non-reverile adortion rocee and that it contain the hydrodynamic umodel. In contrat, FETRA can e ued only couled with ome other hydrodynamical comuter code. COASTOX wa alied and validated for the Kiev Reervoir, the Priyat River floodlain, the Kralova Reervoir, and the Vakh River Sumodel of tream hydraulic The two-dimenional lateral longitudinal model could e derived from the rimitive 3-D equation y their averaging over the deth. The 2-D variale f(x,y,t) are linked with the rimitive 3-D variale f'(x,y,z,t) y the formula where ( x, t) H( x ) h( x, t) 1 f ( xyt,, ) = f ( xyzt,,, ) H η η + (1) H η + = - the total water deth (ee Fig.1) z z η η H U V y Figure 1: Water ody arameter x

3 The deth-averaged current in a hallow lake or a water reervoir are determined y the alance etween the wind hear tre τ ω, the ottom hear tre τ, the vertically averaged tenor of the horizontal turulent exchange T i, and y the force driven y the urface elevation gradient η xk. The correonding ytem of the equation for the vertically averaged horizontal flow velocitie U (=1 for x direction and =2 for y direction) and the total water deth h could e written in the form of the equation of ma and momentum conervation (O.Phili,198): η ( hu k ) + = (2) t x ( hu ) k U η 1 1 w + hu k + gh = ( Tk) + ( τ τ ) (3) t x x ρ x ρ k k k where k = 1,2; = 1,2, U vertically averaged horizontal flow velocitie in the x (=1) and y (=2) direction. The hear tree at the free urface and at the ottom are determined y the quadratic friction law reectively through the wind velocity Wand tream velocity U: τ = ρ cw W (4) w w w τ = ρcu U f (5) where k = 1,2; = 1,2, The gloary of the term ued in the model i reented at the end of the uection. The utitution of the equation(2),(4), (5) into the momentum equation (3) lead to the equation in the form U U η λ λw + Uk + g = U U + WW h h t xk xk The horizontal turulent diffuion term i omitted in the equation (6) taking into account that in the numerical olution of thi equation thi term a uually ha the lower magnitude then the numerical diffuion of the finitedifference cheme. The hyerolic ytem of the equation (2), (6) i known a hallow water equation. The ottom friction arameter λ in river hydraulic i often calculated through the Chezy coefficient C cz g C cz (6) λ = (7) Thi coefficient could e calculated on the ai of the Manning formula CCz 1 n 1/6 = h (8)

4 For the emirical friction factor n there are a lot of recommendation on the definition of it value for different water odie. For teady flow condition the efficient numerical method to calculate flow velocity ditriution could e otained in diffuive aroximation of the U hallow water equation. The advective acceleration term Uk,could e omitted in the equation (6) for the water odie without har velocity gradient. Then the ytem (2), (6) taking into account formula (7), (8),.could e written 2 η gn g = U U + λww W (9) 4 / 3 x h (hu k) = (1) xk In correondence with the continuity equation (1) the tream function i defined a follow Φ x Φ Uh y ; Uh x. y = = (11) The equation (9) without wind tre could e rewritten 2 2 n ( x, y) A( Φ) Φ n ( x, y) A( Φ) Φ = x h ( x, y) x y h ( x, y) y where 2 2 xk (12) Φ Φ A( Φ ) = +, x y The omitted in (12) wind tre term could not change a lot the rocedure of the numerical olution of thi equation. For the channel flow contrained y the oundarie B1 and B2 the oundary condition for the tream function are B1: Φ= : B2: Φ= cont = Q, (13) where Q - total water dicharge in the flow. The condition of normal flux though the oen oundarie are alied at the utream and down-tream end of the conidered area: Φ =., (14) m where m - the normal to the oen oundary. In the ecific cae of the traight channel of the ermanent hae (the deth ditriution i the ame in any croection) the equation (12) ha the analytical olution. We would conider x-oriented channel in the area x Lx, y. The deth of the flow i aumed to e contant in direction x, therefore hxy (, ) = H( y) (15)

5 For uch a tream, taking into account the oundary condition (13) at B1= and B2= the equation (12) ha the olution y Q 53 y h ( y L ) dy y 53 ( ) Φ = h y dy ( ) (16) The analytical formulae could e received from (16) for the ecific hae of the channel cro-ection. If the water deth i decried y the function ( ) h y From (16) we otain 2H y, y 2 = y 2H 1, y 2 (17) ( y) y 2 Q, y, 2 Q 1 2 1, y. y 2 Φ = Thi analytical olution wa ued to verify the numerical method develoed to olve the equation(13). The gloary of term ued in the model i reented at the end of the uection Sediment tranort umodel The uended ediment tranort in the river channel i decried y the 2- D advection -diffuion equation that include a ink-ource term decriing the edimentation of the uended ediment and their reuenion from the erodile ed. The deth averaged advection-diffuion equation of the uended ediment tranort i written (18) hs S + (hsu k)= heik + qre q t x k x k xi ed (19) where S and S * are the vertically averaged uended ediment concentration and the equilirium uended ediment concentration reectively. The vertical fluxe of the ediment the edimentation rate q ed and the reuenion rate q re are calculated through the difference of the actual and equilirium concentration of the uended ediment q = ββ w F S S re ed ER q = β w F S S ( ), (2) ( ) where F(x) i the function defined a x+ x x, x > F( x) = (21) 2, x <

6 The coefficient of the erodiility β ER characterize the ottom rotection from eroion due to coheion and natural armoring of the uer layer of the river ed, vegetation. Thi emirical coefficient a uually ha value of the magnitude β - i the ratio of the near-ottom uended ediment concentration to the deth averaged concentration; The E ik - coefficient of the horizontal dierion for ediment i aumed the ame a for the dierion of the olule ollutant. There are calculated on the ai of the formula (Holly,1985) E11 = D co θ + D in θ, e ( e ) 2 2 E12 = D D inθ coθ E22 D in θ D co θ = +, (22) e 2 2 where θ - angle etween the local flow direction and the x-axi;. D e and are the dierion coefficient in the direction arallel and erendicular, reectively, to the local velocity vector. Thee coefficient are determined y the Elder formula De = α EUh *, (23) D = α Uh, * D where U * -the ottom hear tre, αe and α - the emirical arameter of the longitudinal and tranvere diffuion. The deth averaged equilirium concentration of the uended ediment S * i calculated y the Biker method (Biker, 1968), and include the effect of the ottom hear tre, generated y wave, on the magnitude of S *. The thickne of the uer contaminated layer of ediment can e decried y the equation of the ottom deformation: ρ ε Z t * (1- ) q q = (24) where the edimentation and the reuenion rate are calculated through the difference of the actual and equilirium concentration of the uended ediment (Zheleznyak et al., 1992). After the imulation of a tream hydrodynamic the numerical olution of the equation(19), (24)i ued for the modelling of 2-D uended ediment tranort in tream Sumodel of radinuclide tranort Thi umodel of COASTOX decrie the advection diffuion tranort of the cro-ectionally averaged concentration of radionuclide in the olution C, the concentration of radionuclide on the uended ediment C and the concentration C in the to layer of the ottom deoition. The adortion/deortion and the diffuive contamination tranort in the ytem "olution - uended ediment" and "olution - ottom deoition" are treated via the Kd aroach for the equilirium tate, additionally taking into account the exchange rate a i, etween the olution and the article for the more realitic imulation of the kinetic of the rocee

7 The deth averaged equation of the tranort of the diluted contamination i written a: where: hc + ( hcu k) = t xk C λ xk x ρ ε ( ) ( ) A ( ) heik - hc-ha1-2s Kd C-C - 1- Z* 1-3 KdC-C i (25) The tranort equation for C i defined a follow: hsc SC + (hsc U k)= heik - t x k x k xi - λ hsc +ha S(K C-C )+C q -C q (26) 1-2 d re The contamination of the uer layer of ottom deoit can e decried y the equation Z* C 1 =Z * A1-3(KdC-C ) - (C qre -C qed ) t ρ(1- ε ) ed (27) The coefficient of the exchange rate etween the comartment olute (ucrit {} 1 ), uended ediment {} 2 and ottom deoition {} 3 decrie non-reverile kinetic, i.e. A 1 2 A 1 3 a1,2, KdC > C = a2,1, KdC < C a1,3, KdC > C = a3,1, KdC < C (28) (29) where a1,2 and a 1,3 are adortion rate coefficient, reectively, for the ytem uended ediment - water and ottom ediment - water ; a2,1 and a 3,1 - deortion rate coefficient for the ame ytem. Gloary of term ued for COASTOX decrition U m/ec vertically averaged horizontal flow velocitie in the x (=1) and y (=2) direction W m/ec Horizontal wind velocitie ρ w Kg/ m 3 c w c f air denity air friction coefficient ottom friction coefficient h M total water deth η M water urface elevation ( deviation from the equilirium water level) H M water deth meaured from the equilirium water level r M width of a tream

8 Q m 3 /ec water dicharge through croection Φ m 3 /ec tream function CCz m/ec 2 Chezy coefficient n m 5/6 ec 2 w τ kg/(m ec 2 ) τ Manning friction factor hear tre driven y wind at water urface kg/(m ottom hear tre driven y current ec 2 ) S Kg/m 3 concentration of uended ediment averaged over a deth S Kg/m 3 equilirium concentration of uended ediment averaged over a deth q re Kg/m 2 ec reuenion (eroion) rate er unit area of the ottom (uward directed flux) q ed Kg/m 2 edimentation rate er unit area of the ottom β ec (dawnward directed flux) ratio of the near-ottom uended ediment concentration to1e deth averaged concentration;; β ER coefficient of erodiility of ottom. w M 2 /ec Sediment fall velocity E ik M 2 /ec Comonent of dierion coefficient (i=1,2;k=1,2) in 2-D flow D e M 2 /ec Dierion coefficient in the direction arallel to the local velocity vector D M 2 /ec Dierion coefficient in the direction erendicular to the local velocity vector α E emirical arameter of longitudinal diffuion α Emirical arameter of tranvere diffuion. U * M/ec ottom hear tre velocity * Z M thickne of the ottom ediment uer layer ρ S Kg/m 3 denity of the uended ediment ( default value 26 ) ρ w Kg/m 3 water denity ( default value 1 ) ε oroity of the ottom ediment C Bq/m 3 Radionuclide concentration in the olution S C Bq/kg Radionuclide concentration on the uended ediment C Bq/kg Radionuclide concentration in the ottom deoition C l Bq/m 3 radionuclide concentration in the olution of the lateral inflow S C l Bq/kg radionuclide concentration on the uended ediment in the lateral inflow m 2 /ec Radionuclide longitudinal dierion coefficient E C λ ec -1 Decay coefficient 1,2 a ec -1 Coefficient of the adortion rate for waterd d di t t

9 uended ediment ytem a 2,1 ec -1 coefficient of the deortion rate for water-uended ediment ytem a 1,3 ec -1 coefficient of the adortion rate for water-ottom ediment ytem a 3,1 ec -1 coefficient of the deortion rate of water-ottom ediment ytem K ds m 3 /kg ditriution coefficient in water-uended ediment ytem K d m 3 /kg ditriution coefficient in water-ottom deoition ytem COASTOX inut data COASTOX conit eentially of two main comuting module. The calculation of velocity field are erformed in the module HYD_2D. The calculation contamination field are erformed in the module TOX_2D. HYD_2D inut data file: file of athymetry; file of geometry; file of arameter; file of hydrological cenario. TOX_2D inut data file: file of name of file of initial, oundary and other condition; file of inflow and outflow geometry ; file of model arameter and arameter of imulated radionuclide; file of initial condition for ediment concentration, concentration for each of radionuclide imulated in olute, on uended ediment, in the ottom deoition and on a urface of water; file of oundary condition for ediment concentration, concentration for each of radionuclide imulated in olute and on uended ediment COASTOX imlementation and teting The Kralova Reervoir, Vakh River i the firt reervoir downtream Bohunice NPP that could e contaminated after accidental releae from the lant. The accidental releae of 1989 (Slavik et.al 1997) wa ued to validate the COASTOX model in cloe cooeration with the Reearch Intitute of Nuclear Power Plant (VUJE), Trnava, Slovakia. The detailed decrition of the cae tudy i reented in the relevant RODOS WG4 reort. Here i reented only the rief overview of the main reult of thi validation tudy. The COASTOX wa adoted for the Kralova Reervoir with the following et of arameter value: Kd = 14 m3 /kg, a1,2 =3 day -1, Kd = 2 m3 /kg, a1,3 =.25 day -1, a3,1 =.15, Z* =5 cm

10 The model wa couled with the HDM-RODOS model RIVTOX that rovide the imulation of the radionuclide tranort from the Bohunice NPP to inflow croection to the Kralova Reervoir (Slavek et al., 1999). The imulation of 137C dierion in the Kralova Reervoir demontrate that the dominant roce in contamination of the reervoir ottom iaettling of the contaminated ediment. The imulation of dierion of June 1989 releae reveal that the highet concentration of 137C hould e in the central art of the reervoir, in the lace where the intenive edimentation downtream the tee ottom loe take lace (Fig.3). Such reliminary rediction that ha een done in 1994 wa confirmed later y the field monitoring exercie that wa carried out y common effort of the VUJE and Ukrainian Hydrometeorological Intitute, Kiev, in During the monitoring exercie the maximum 137 C concentration in the reervoir - aout Bq/kg in the to ediment layer and aout 6-8 Bq/kg in the deeer ediment layer were found in the ame location of the contaminated ot that ha een redicted during the imulation.(fig.2), at the ioline 76 Bq/kg). The HDM-COASTOX i imlemented for the Kralova Reervoir and relevant data et of inut information i reented with thi oftware (Fig.3) Figure 2: Simulated 137 C concentration (Bq/kg) in uer ottom layer of Kralova Reervoir - 4 day after the accidental releae

11 Figure3: Imlementation of HDM COASTOX interface for Kralova Reervoir COASTOX wa alied to decrie the lake IJelmeer which i a art of the Rhine River Bain. A releae of radionuclide from a Nuclear Power Plant located at the River Iel, the triutary of the River Rhine (q=1 m 3 /, c=2 Bq/ m 3 =cont.) wa aumed. The COASTOX wa widely ued to imulate radionuclide wahing out from the Priyat River floodlain at Chernoyl NPP and in everal other cae tudie (Zheleznyak et al )