CIESM Congress 2001, Monaco, article 0203

203

Rapp. Comm. int. Mer Médit., 36,2001

Introduction

The movement of radionuclides throughout water body (streams,

lake, sea, estuary, etc) is a hydrodynamic transport process depending,

additionally, on many, interaction between the radionuclides and phys-

ical, chemical and biological components of environmental system.

These interactions cause the retention of certain quantities of radionu-

clides into the system and decrease the fraction transported by ?ow.

The intensity and time duration of the radionuclides retention depend

on many features of the environment. A large fraction from the

detained radioactivity is then gradually restituted to the ?owing water

and is transported hydrodynamically downstream. It is obvious that a

mathematical model governing such processes may be developed

making use of mass-transfer Equations [1, 2] .

The governing equations

Assuming that there is only one radionuclide specie which joins the

system, but there are more types of sorbants into the natural stream.

Then, the mathematical model for general transport and retention of

radionuclides could be the following:

(1)

whereC - the radionuclide concentration in water expressed as

radioactivity (dis.s

-1

);

- the radioactivity decay constant;

- the rate exchange of the radionuclid between the sorbant n;

N - the total number of sorbant interacting with the radionu

clides

Taking into account that the bed of the Danube river after Turnu

Severin Power Dam till Cervavoda is made of silty clay, the following

interaction between the bed river and the water may be written:

(2)

where B - the water width at water free surface

t - the exchange rate upon the unit area of bottom .

But, the term

t = k

where kb is the mass-transfer coefficient

between water and bottom sediment; F

must have the dimension of

the radioactivity (disintegrations per unit time unit)

Then, S

= Bk

- K

C) (3)

- the equilibrium distribution coefficient of the radionuclide.

This, can be explained by the following equation :

(4)

The radionuclides uptaked by the animals and plants are calculated

by analogy with bed load sediments.

For the radionuclide interaction with the aquatic plants attached of

the bed river, if one accepts that these belong to only one species and

therefore react in a similar manner with the radionuclides, it seems

acceptable to assume that the intensity of such reaction is proportion-

al with the weight of plants. Denoting as Mp and Sp the weight of

plants and the corresponding bottom, relatively, then from Eq. (1),

there:

= B M

(5)

Substituting the relationships for S

and S

into Eq. (1) is obtained

the mathematical model governing the radionuclides transport and

transfer.The equations systems are composed by three simultaneous

equations with the unknown C, K

and C

.Any of these systems can

be solved using a finite scheme designed for one efficient time step

(based on the splitting technique mode) on a compound vector .

Results and discussion

The model has been tested for the simulation of the radionuclides

transfer and transport along the Danube river (Romanian sector) to the

Black Sea. [3].

It must be outlined, that a similar mathematical model has been

applied even to the entry of the Danube river in Romania, till the Turnu

Severin Iron Gates dam, in different cases of the ?ow water [1]. The

hydrodinamic parameters are taken for the cross-sections of Danube

river at Bechet, Turnu Magurele, Giurgiu, Ceatal Izmail. Into these

sections the cross-section ?ow discharge Q[mc/s] and the top width at

water-surface B[m] are 4440 mc/s

6220 mc/s and 427 m

757 m [3].

The ?ow parameters of the Danube from the entrance in Romania,

at Bazias, till the beginning of the Danube delta at Ceatal-Izmail for

years 1996-1997, are discussed .

The mass-transfer k

and distribution K

were selected by experi-

mental data for bottom sediments for natural stream (30 % clay, 40%

quartz , 22% calcite) for the specified radionuclides (

Sr,

137

Cs,

144

Ce,

Zn ).

References

[1] Oprica H.M. and Georgescu I.I., 1997. Sur un modèle mathématique

concernant le transport et transfert des radionucléides par le Danube vers

La Mer Noire. Sci. and Techn. of Environnental Protection,4: 51 - 57.

[2] Nihoul J.C.J. , Beckers J.M. and Djenidi S., 1990. Application of the

GHER 30 k - e Model, Rapp. Comm. int. Mer Médit, 32, 1: 178.

[3] Pantelica A.I., Georgescu I.I., Oprica M.H.I. and Borcia C.M., 1999.

INNA and Chemical analyzis of water and sedimentes sampled in 1996

from the Romanian Sector of the Danube River,Czehoslovak Journal of

Physics, 49 (1999), Suppl. S1 : 331-337.

ON A MATHEMATICAL MODEL TRANSPORTAND TRANSFER OF THE RADIONUCLIDES IN

DANUBE RIVER, ROMANIAN SECTOR

M.H.I. Oprica

*, I.I.Georgescu

, C.M. Borcia

University “Politehnica “, Faculty of Industrial Chemistry, Bucharest, Romania

Institute of Meteorology and Hydrology, Bucharest, Romania

Abstract

The attention has been focused on those radionuclide species which are the most frequently encountered into the radioactive polluted

waters or laboratory and many results about their behaviour are reported.

Key words : Danube river, mathematical model, radionuclides transport in river , Black Sea.

(

)

(

) + =?

n = 1

C -R

) -