Nuclear test plutonium and radiocaesium dispersion in lakes ecosystems: experimental data and novel modelling approach T1.3-P11

A. Puzas*, D. Baltrūnas, E. Maceika, B. Lukšienė, V. Filistovič, N. Tarasiuk, E. Koviazina, M. Konstantinova, Š. Buivydas

Institute of Physics of Center for Physical Sciences and Technology, LITHUANIA *Andrius.Puzas@ftmc.lt

Problem

Commonly, migration of the

technogenic radionuclides from water into soil

and bottom sediments in the natural

environment is described by one-stage models.

The main drawback of such models is related

to the fact that the radionuclide diffusion

coefficient in sediments decreases with time.

However, analyses of radionuclide

vertical profiles in carbonate bottom sediments

as well as results of laboratory experiments

show that the process proceeds in two

temporal stages. The first fast migration stage

is governed by the light ion transfer. The

resulting vertical profile of the radionuclide

activity concentration in sediments is

exponentially decreasing with depth. The

second migration stage is slow. It involves the

main significant processes: bioturbation,

sedimentation as well as the first order kinetic

reactions and radioactive decay.

In the case of accidental appearance

of radionuclides in water systems the one-

phase model cannot be properly employed to

predict the long-term consequences of

radionuclide migration into zones where they

are mostly accumulated - bottom sediments

and soil solid phase. Application of the correct

model of radionuclide behavior in the

radioactive waste storage environment and in

water saturated soils is of great concern as

well.

Solution

The two-phase mathematical model of

the radionuclide vertical migration in the water

saturated solids (bottom sediments and soil).

There is considered process of slow

sorption and desorption of the radionuclide

mobile fraction by solid particles.

Transport of the radionuclide in the two-phase

environment is described by 1-D advection-

diffusion equations, separately for the liquid

volumetric activity c and flux- j(c), and solid

phase specific activity cs and flux- js(cs) :

fsecct

j

ccc vDj

sfssbsbsb ecct

j

sssss ccc vDj

ssffs cce

Where: f – rate of activity transfer

from liquid to solid phase in the

sediments [d-1],

s – rate of the transfer from

the solid to the liquid phase [g cm-3 d-1].

sb 1

Radioactive contaminant

activity vertical distribution profile

is considered as a process having

two stages (I and II):

• the first stage (I) is

related with the migration

of the contaminant from

water to the

sediments,

• whereas, the second

stage (II) – with the further

transformation of the

deposited contaminant.

ccx

cv

x

cD

xt

c f

vols

b

s

,

vols

b

ssfvols ccc

t,,

Advection-diffusion equations for

the liquid volumetric activity c and

solid phase volumetric activity cs,vol :

Boundary conditions for the stage (I) :

tgvx

txcDtxvc ee

x

exp1,

, 0

0

0

,

xx

txc

0,0

ttxc 0,

0

ts txc 0,0,

tvols txc

Advection-dispersion,

degradation and non-equilibrium

exchange between phases during

the stage (I) together with the

boundary conditions and zero

initial conditions belongs to the

boundary value problem (BVP)

solution.

0

X

TC ,

Stage (I)

Initial conditions for the stage (I) :

0 5 10 15 20 25 30 10

-4

10 -3

10 -2

10 -1

10 0

10 1

Sediment depth, cm

Activity c

on

ce

ntr

ation

,

Bq

cm

-3

Red line -

Liquid

Dark line –

Solid

Dot line T=100

days

Solid line

T=200 days

dXGwaTww

aTV

dXGwaTww

aTVTXC

T

E

RR

R

T

R

,,,;expexpexp

,,,;expexpexp,

212

0

0

212

0

0

dXGwaTww

a

w

TV

dXGwaTww

a

w

TVTXC

s

T

f

RR

RR

s

T

fs

,,,;exp1exp1

exp

,,,;exp1exp1

exp,

222

0

0

222

0

0

X

XX

X

X

P

XerfcXP

P

P

XPXG

/exp

/expexp,

424

2

1 1

1

222

1

1

n

n

k

knn

k

k

kn

T

n

a

wTwa

!!,,;

1 1

221

1

n

n

k

knn

k

k

kn

T

n

a

wTwa

!!,,;

fsa 2

sEw

sRRw

As a result of the stage (I) solution

we receive vertical distribution of the

radionuclide activity profile, depending

on depth for the liquid phase

f1(X)=С(Tmax,X) and for the solid phase

f2(X)=Сs(Tmax,X). Duration of the stage (I)

Tmax should be long enough, to reach

activity flux equilibrium between water

and sediments.

0

0

gvx

cDcv r

x

xfxfxc EE 1110 ,, exp,

xfxfxc EEs 2220 ,, exp,

Stage (II)

Profile of the contamination distribution,

obtained from the stage (I), is used as an

initial conditions for calculating the solution of

the two phases concentration distributions in

the stage (II).

Boundary conditions for the stage (II) :

Initial conditions for the stage (II) :

0

,

xx

txc

0 20 40 60 80 100 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Sediment depth, cm

Activity c

on

ce

ntr

ation

,

Bq c

m-3

Red line -

Liquid

Dark line –

Solid

Dot line

T=5000 days

Solid line

T=10000 days

dXGTHT

afXGTHf

TXGfTXC

T

EEEsE

EE

0

1212

12202

121

,,,,

,,

;,,;,,

;,,

dXGTHTa

fdXGTHf

TXfTXC

T

E

T

EEE

sEEs

0

221

0

221201

22

,,,,

,,

;,,;,,

exp,

TaITTH nsn 22exp, (n = 0, 1)

X

XX

X

XX

X

X

X

X

P

XerfcXP

P

P

PXerfcXP

P

P

PXerfcX

PXG

22

2

211

2

1

2

21

2

11

2

2

exp

exp

exp

exp;,

In(x) – is modified the nth order Bessel function of

the first kind, erfc(x) – error function complement.

Integrals are solved numerically by using

Chebyshev–Gauss quadrature method.

Where:

Where:

Measurements

Lake Juodis, located near Vilnius city, Lithuania

Parameter Value

Parameters for stage I

L – Length of the sediment layer 100 cm

v – Darcy velocity 0.008 cm day-1

D – dispersion (diffusion) coefficient 0.2 cm2 day

-1

s –sediment dry matter density 1.0 g cm-3

b –sediment balk density 0.043 g cm-3

= 1 - b / s – porosity 0.96

kD – exchangeable part KD 500 cm3 g

-1 or L kg

-1

12 f – exchang. part velocity f = ln(2)/20 = 0.0347 day-1

21 s – exchang. part velocity s =f / (kD*b) = 0.0016 day-1

f – degradation (decay) constant ln(2) / (30*365.25) = 0.000063 day-1

s – degradation (decay) constant 0.000063 day-1

ge – initial water activity in Lake 1.0 Bq cm-3

e – activity decrease in Lake const. ln(2) / 30 = 0.023 day-1

v0 – activity deposition rate in Lake water 0.1 cm day-1

Additional parameters for stage II

fe1 – initial activity at x=0 (water ph.) 0.697 Bq cm-3

e1 – expon. decrease rate by depth 0.0807 cm-1

fe2 – initial activity at x=0 (solid ph.) 0.591 Bq cm-3

e2 – expon. decrease rate by depth 0.0875 cm-1

21 – from solid phase to water phase 0.0385 day-1

μ1 – degradation+decay+exch. const. 0.0362 day-1

12 – from water phase to solid phase 0.0346 day-1

μ 2 – degradation+decay+exch. const. 0.0369 day-1

Measured 137Cs activity in flooded soil core of the lake Juodis

Conclusion

The two stage and two phase (liquid and solid) radionuclide migration in the

water-sediments ecosystem model is suitable to be used for better prediction of the

long-term consequences of radionuclide accumulation and transport after the

accidental contamination of lake water.

Nuclear tests

Chernobyl

Fukushima

Vertical profiles of plutonium isotope activity concentrations

and activity concentration 238Pu/239,240Pu ratios in the flooded

soil core of the lake Juodis

Plutonium isotope activity concentrations and activity

concentration 238Pu/239,240Pu ratios in the sediment vertical profile

from the lake Juodis

Volumetric activities [Bq m−3] depending on the depth of

sediments x [cm] for the liquid phase of the sediments cL

(red), for the solid-phase kinetic parts cSK (blue) of the total

aggregated volumetric activities in solid phase (kinetic and

fast) cS (green) and measured volumetric activities (total

aggregated) cS,exp (points)

Simulation of 137Cs volume activities cSK and cL [Bq m−3] in

sediment solid and liquid phases, respectively, depending on

the sediment depth x [cm] and on time after the acute release

of 137Cs activity into the lake, obtained using the mathematical

model

Vertical profiles of 239,240Pu and 137Cs activity

concentrations in the sediment core taken in the lake

Juodis in July, 2012. Vertical lines indicate 137Cs/239,240Pu

ratio for the global fallout (29 ± 3 value, reference year

2012)

Volumetric activity of the kinetic part of a solid phase

and b liquid phase of sediments depending on the depth

of sediments at different equilibrium values of partition

coefficients KDS [m3 kg]

References:

1. B. Lukšienė et al. J Radioanal Nucl Chem (2014) 300:277–286

2. V. Filistovič et al. Water Air Soil Pollut (2015) 226:202