Evaluation of the Use of Synthetic Zeolite as
a Backfill Material in Radioactive Waste
Disposal Facility
Presented by
Dr Ahmed Mohamed El-Kamash
Hot Lab. & Waste Management Center
AEAE, Egypt
Evaluate the feasibility of using synthetic zeolite
NaA-X prepared from fly ash (FA) as backfill
material in the proposed radioactive waste disposal
facility in Egypt.
Also, the migration behavior of cesium and strontium
ions, as two of the most important radionuclides
commonly encountered in Egyptian waste streams
through the proposed backfill material is studied
using mathematical models
Radioactive disposal system
•
The principle objectives of radioactive waste
management are to assure that workers and public
are not harmed now or in future by the effects of
radiation from the wastes and that the environment is
not adversely affected.
•
The fundamental safety concept for the disposal of
radioactive wastes is to isolate the waste from the
accessible environment for a period sufficiently long to
allow substantial decay of the radionuclides and to
limit release of residual radionuclides into the
accessible environment.
A disposal system is intended to:
•
isolate the waste from the accessible environment for
certain amount of time until waste activity reduced to
acceptable hazardous level.
•
control the radionuclides that reach the accessible
environment
•
limit the consequences of any unacceptable release to
accessible environment
Major Types of Radioactive Waste
Disposal facilities:
– Near surface disposal facility means a land
disposal facility in which radioactive waste is
disposed of in or within the upper 30 meters of the
earth’s surface.
– Deep Geological Disposal for high level waste
such as spent nuclear fuel, >400 meters
underground
Repository design components
• The engineering barrier system
– Engineered barriers can be used as physical and /chemical
obstruction to prevent or delay migration of radionuclides.
• The natural barrier system
– Consists of the geological media hosting the repository and any
other geological formations contributing to waste isolation.
Multiple barrier concept
• The long term safety of a repository relies on a series
of barriers : The Engineered Barrier and The natural Barrier
• Multiple barrier concept is employed in which the
waste form, the engineered barriers and the site itself
all contribute to the isolation of the radionuclides.
•
The failure of one or more of these barriers will be
compensated by the rest of them
Function of barriers
Barriers can either provide
• absolute containment for a period of time, such as the
metal wall of a container, or
• may retard the release of radioactive materials to the
environment, such as a backfill or host rock with high
sorption capability.
Elements of engineered barriers
Backfill materials
•
Backfills are used for a number of purposes: void filling to avoid
excessive settlement, limitation of water infiltration, sorption of
radionuclides, precipitation of radionuclides. Typical materials
used, either singly or as admixtures, include clays, cement grout,
rock, and soil.
• It is important to select the appropriate backfill. Selections of
backfill materials for radioactive waste disposal have been
derived from a much data on adsorption behaviour of
radionuclides on several natural and synthetic materials.
• For long-term performance assessment of radioactive
repositories, knowledge concerning the migration of
radionuclides in the backfill materials is required .
• Sorption reactions are expected to retard the migration of
radionuclides thereby reducing the potential radiological hazard
to humans resulting from disposal of radioactive waste.
In respect to fly ash
Fly ash is an inorganic spherical residue
obtained at coal power plants .
The spherical microscopic structure of fine fly
ash is related to the equilibrium between the
operating forces on the molten inorganic
The past applications of fly ash were restricted
to its application in industry as an additive or
as an adsorbent.
Synthesis of zeolites from fly ash
• Zeolite synthesis is one of a number of
potential applications for obtaining high
value industrial products from fly ash
for environmental technology.
• The composition similarity of fly ash to
some volcanic materials, precursor of
natural zeolites promoted the synthesis
of zeolite from this waste material.
Synthesis and characterization of
pure zeolites
Sorption studies
Long term behavior of zeolite
NaA-X blend as proposed backfill
Synthesis and characterization of
pure zeolites
Oxide
Wt %
SiO2
Al2O3 Na2O MgO P2O5 SO3
Cl
K2O
CaO
TiO2
Fe2O3
43.81
23.18
4.01 2.72
6.10
2.31
0.01
0.87
0.80
0.49 15.68
Intermediate glass content of about 66.99%
I
0.0
10
20
30
40
50
60
70
2θ angle
:mullite (3Al2O3.2SiO2) and
: α-quartz (SiO2)]
exits as crystalline substances, as identified by sharp peaks,
while the presence of amorphous phases were identified by
broad peaks (near 24 angle)
Silica-Aumina extraction by
fusion
- The available silica in fly ash was extracted by
the alkali fusion method using sodium
hydroxide.
- The amount of extracted silica was131.43g/kg fly
ash.
- The amount of extracted alumina was about
41.72 g/kg.
Synthesis of pure NaA-X zeolite
The synthesis of NaA-X zeolite blend was
carried out using the molar oxide ratios of:
SiO2/Al2O3
Na2O/SiO2
H2O/Na2O
= 2.1
= 1.4
= 39.0
Sodium aluminate solution was used externally
to adjust the SiO2/Al2O3 ratio to the desired
value
Flow sheet diagram for the synthesis of NaA-X zeolite blend from fly
ash using extraction method
Element
Wt.%
Na
Al
Si
Ca
Ti
Mg
Fe
S
K
P
other elements
27.79 33.41 38.34 0.067 0.081 0.062 <0.01 0.002 0.056 0.004
It clear that Si/Al ratio equals 1.15 which lied in
the region of zeolite-A and X as reported in Breck
ternary diagram
<0.1
I
0.0
10
20
30
2θ angle
:zeolite X and
: zeolite A
The spectrum exhibits fingerprint lines of
both zeolite X at 2θ = 6.10 and zeolite A at 2θ
= 7.20 and 9.93.
40
(a)
(b)
SEM
(c)
(d)
(a) Untreated FA Smooth and spherical particle interspersed in aggregates of crystalline
compounds which may correspond to α-quartz and mullite.
(b) After 15 min fusion with Na OH (The amorphous aluminosilicates in fly ash were
dissolved -Small surface cracks appeared - The particle surface changed, like unevenness
(c) After 30 min (The surface of FA became rough and burst - Larger cracks were appeared
librating small aggregates
(d) After 60 min ( Small cenosphere were appeared -Several crystalline materials were
precipitated onto the surface of FA particle
SEM picture of the synthesized zeolite blend providing an evidence for
cubic crystal characteristic for Na-A zeolite and
the pyramidal octahedral crystal of Na-X zeolite
Examination of Proposed backfill
material: Synthetic zeolite Na A-X as
backfill material in radioactive disposal
facility
Efficiency of the material
(Capacity)
Mechanical stability
Test
Experimental Investigations
Column Studies
Kinetics Studies
Estimation of Sorption
mechanism
Equilibrium Studies
Thermodynamic Models
(Capacity)
(Pseudo first-second order)
Dispersion coefficient,
DL
Distr. Coeff.,Kd
Chemisorption
Diffusion, Di
Effect of temperature,
Thermodynamic
Parameters, ∆H, ∆G, ∆S
Long term behavior of zeolite NaA-X as backfill
material in disposal facility
sorption studies
• Effect of pH
• The effect of pH on the sorption of Cs+ ions from aqueous
chloride solutions using prepared zeolite NaA-X material
was investigated over the pH range from 2.0 to 8.0.
• It was observed that the acidic medium has an inhibitory
effect on the sorption process. This may be due to the
competition behavior between hydrogen ions and studied
ions for sorption onto the synthesized powder.
• The uptake was continuously increased from 18.6% to
62.6% with the increase in pH value and the maximum
uptake was found to be 64.1% and it was observed at pH
range from 6.0 to 8.0.
Sorption kinetics
• Effect of time
80
qt,mg/g
60
40
20
+
A higher initial removal rate within
the first 30 minutes followed by
slower rate till reaching plateau.
Cs
2+
Sr
0
0
The amount sorbed for both ions was
increased with time and attained
equilibrium within 90-120min
The amount sorbed of : Sr2+ > Cs+
20
40
60
Time,min
80
100
120
Kinetic models
• Pseudo first order
1.6
Y1 =1.5085-0.02336 X
Y2 =1.54671-0.02787 X
1.4
k
1
log( q e  q t )  log q e 
t
2 .303
log(qe-qt)
1.2
1.0
0.8
+
Cs
2+
Sr
0.6
(Lagergren)
(a)
0.4
0
10
20
30
40
Time,min
• Straight line obtained suggest the applicability of
the pseudo first order model to fit the
experimental data over the initial stage of the
sorption process up to 40 min.
• Pseudo second order
3.5
3.0
Y1 =0.2174+0.02388 X
Y2 =0.12195+0.02078 X
t/qt,min g mg
-1
2.5
t
qt
2.0

1
h

1
qe
1.5
1.0
+
Cs
2+
Sr
(b)
0.5
(Ho and Mckay )
0.0
0
20
40
60
80
100
120
Time,min
It was shown that the sorption process of each ion
follows pseudo second order model
t
Pseudo first and second-order rate constants for the sorption of
cesium and strontium ions onto synthetic A-X zeolite blend at 298 K
and 50 mg/l concentration.
Metal
ions
First order
Rate constant,k1(min-1)
Second order
Rate constant,k2(min-1)
Cs+
0.0537
0.0031
Sr2+
0.0640
0.0039
Estimation of diffusion coefficient
 1
2
F (t )  1 
exp(  n Bt )

2
2
 n 1 n
6
1- Y =-0.13186+0.05815 X
2- Y =-0.00771+0.0587 X
2.5
2.0
1.5
Bt
B 
 2D
1.0
+
Cs
2+
Sr
0.5
i
2
r
o
(Boyed et al)
0.0
0
10
20
Time,min
•
30
40
Metal ions
Diffusion
coefficient Di
Cs+
Sr2+
6.99*10-12
6.26*10-12
effective diffusion
coefficient De
4.194*10-12
3.72 *10-12
In order to identify the step governing the removal rate of sorption process
Sorption thermodynamics
• Sorption can be described using an empirical
relationship that defines the distribution of
radionuclides between solid and liquid
• Many isotherm models can describe sorption process
such as Langmuir , Freundlch, and D-R.
• The parameters of the isotherm equations express the
surface properties and affinity of the sorbent, at fixed
temperature and pH.
Sorption of Cs+ and Sr2+ ions on zeolite NaA-X at different
temperatures (Langmuir)
1600
3500
1400
Cs
+
Sr
2+
3000
1200
qe(mmol/kg)
qe(mmol/kg)
2500
1000
800
600
298 K
313 K
333 K
400
2000
1500
298 K
313 K
333 K
1000
500
200
0
1000
2000
3000
4000
3
Ce(mmol/m )
5000
6000
7000
0
0
2000
4000
6000
3
Ce(mmol/m )
8000
Sorption of Cs+ and Sr2+ ions on zeolite NaA-X at different
temperatures (Freundlich)
4000
1600
1400
Cs
+
Sr
3500
2+
1200
1000
qe(mmol/kg)
qe(mmol/kg)
3000
800
600
298 K
313 K
333 K
400
2500
2000
298 K
313 K
333 K
1500
200
1000
0
0
1000
2000
3000
4000
3
Ce(mmol/m )
5000
6000
7000
0
2000
4000
6000
3
Ce(mmol/m )
The metal concentration retained in the solid phase (mg/g) was calculated
using the following equation :
( c 0  c e )V
qe 
M
8000
Sorption of Cs+ and Sr2+ ions on zeolite NaA-X at different
temperatures (D-R)
4000
1600
Cs
1400
+
Sr
3500
2+
1200
qe(mmol/kg)
qe(mmol/kg)
3000
1000
800
600
298 K
313 K
333 K
400
200
2500
2000
298 K
313 K
333 K
1500
1000
0
0
1000
2000
3000
4000
3
Ce (mmol/m )
5000
6000
7000
0
2000
4000
6000
3
Ce(mmol/m )
8000
Isotherm models
• Langmuir Isotherm model
3.0
5
1- Y =0.68176+6.46796E-4 X
2- Y =0.52506+6.42354E-4 X
3- Y =0.41304+6.26764E-4 X
4
2.5
Y1 =0.13334+2.889E-4 X
Y2 =0.10257+2.86104E-4 X
Y3 =0.07485+2.83973E-4 X
2.0
3
Ce/qe, kg/m
3
Ce/qe(m /kg)
3
2
298 K
313 K
333 K
1
1.5
1.0
0.5
298 K
313 K
333 K
0.0
0
Langmuir Sr-zeolite
0
1000
2000
3000
4000
3
5000
6000
-0.5
-2000
7000
Ce(mmol/m )
0
2000
Langmuir cs-zeolite
4000
Ce, mmol/m
o
o
( C / q )  (1 / Q b )  (1 / Q ) C e
e e
6000
3
8000
10000
Langmuir model parameters
Table: Langmuir isotherm parameters for Cs+ and Sr2+ sorbed
onto Zeolite NaA-X
Metal ion
Temperature
(K)
Q0(mmol/kg) b(L/mmol)
R2
RL
Cs+
298
313
333
1546.0
1556.7
1595.6
0.948
1.223
1.517
0.995
0.995
0.996
0.123
0.098
0.087
Sr2+
298
313
333
3461.4
3495.2
3521.5
2.166
2.789
3.793
0.997
0.998
0.997
0.042
0.031
0.024
The value of saturation capacity Q0 corresponds to the monolayer
capacity
Q0 and b increased with temperature showing that the sorption
capacity and intensity of sorption are enhanced at higher
temperatures.
Isotherm models
• Freundlich isotherm model
3.6
1- Y =1.91241+0.32219 X
2- Y =2.0962+0.27791 X
3.2
Y2 =2.54197+0.27235 X
Y3 =2.7094+0.22861 X
log qe(qe,mmol/kg)
3- Y =2.26438+0.23861 X
3.1
log qe(qe,mmol/kg)
Y1 =2.41705+0.30261 X
3.5
3.0
2.9
298 K
313 K
333 K
2.8
2.7
3.4
3.3
3.2
298 K
313 K
333 K
3.1
3.0
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3
log Ce(Ce,mmol/m )
Freundlich Cs-zeolite
3.4
3.6
3.8
4.0
Sr-zeolite
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3
log Ce(Ce,mmol/m )
log q e  log K f  (1 / n ) log C e
3.0
3.2
3.4
3.6
3.8
Freundlich model parameters
Table: Freundlich isotherm parameters for Cs+ and Sr2+ sorbed
onto Zeolite NaA-X
Kf (mmol/kg)
R2
Metal ion
Temperature (K)
1/n
Cs+
298
313
333
0.3222
0.2779
0.2386
81.730
124.79
183.81
0.985
0.985
0.982
Sr2+
298
313
333
0.2681
0.2428
0.2082
342.45
416.19
573.90
0.964
0.965
0.974
1/n :value is dependent on the nature and strength of sorption process.
Kf represent sorption capacity of both ions on zeolite NaA-X.
Isotherm models
• D-R isotherm model
-6.4
1- Y =-6.01334-0.00389 X
-6.6
-5.6
Y1 =-5.14828-0.00334 X
Y2 =-5.19247-0.00265 X
2- Y =-6.08442-0.00293 X
-5.8
3- Y =-5.97132-0.00275 X
Y3 =-5.27976-0.00187 X
-6.0
-7.0
ln qe(qe,mol/g)
ln qe(qe,(mol/g))
-6.8
-7.2
-7.4
-7.6
298 K
313 K
333 K
-7.8
200
400
2
600
 (,kJ/mol)
800
Sr
1000
2+
-6.4
298 K
313 K
333 K
-6.6
-6.8
-8.0
0
-6.2
-7.0
200
300
+
D-R isotherm plots for sorption of Cs ions
onto Zeolite NaA-X at different temperatures
ln q e  ln q  
m
400
500
2
2
600
2
 (kJ /mol )
2
700
800
900
D-R model parameters
Table (6) D-R isotherm parameters for Cs+ and Sr2+ sorbed onto Zeolite NaA-X
Metal ion
Temperature (K)

Cs+
298
313
333
-0.00389
-0.00293
-0.00275
2445.9
2278.0
2550.9
0.966
0.963
0.958
11.337
13.063
13.480
Sr2+
298
313
333
-0.0032
-0.0025
-0.0018
5508
5318
4934
0.986
0.988
0.988
12.50
14.00
16.62
qm(mmol/kg)
R2
E(kJ/mol)
qm The maximum sorption capacity , the values of the mean free energy ,E,
of sorption in all cases is in the range of 8-16 k J/mol, which are within the
energy ranges of ion exchange reaction
Effect of Temperature
In order to gain insight into
the thermodynamic nature of
the sorption process, several
thermodynamic parameters
for the present systems were
calculated .
 G   RT ln K c
o
ln K c 
2.5
Y =7.51968-1640.95029 X
ln Kc
2.0
1.5
1.0
+
Cs
2+
Sr
0.5
Y =5.17944-1426.91259 X
0.0030
0.0031
0.0032
1/T K
-1
0.0033
0.0034
S
R


H
RT

Thermodynamic Parameters
Table (7): Values of thermodynamic parameters for sorption of Cs+ and Sr2+ions
onto Zeolite NaA-X
Metal
Temperature
Kc
ΔGo
ΔHo
ΔSo
(kJ/mol)
(kJ/mol)
(J/mol).K
ion
K
Cs+
298
1.466
-0.947
313
1.904
-1.670
333
2.420
-2.446
298
7.49
-4.988
313
9.74
-5.921
333
13.36
-7.176
Sr2+
11.86
43.058
13.64
62.35
-The -ve values of ΔGo confirm the spontaneous nature of the
sorption processes with preference towards Sr2+ than Cs + ions.
- The +ve values of ΔHo for both studied ions confirms the
endothermic nature of the sorption processes.
- The entropy change was +ve and was greater in Sr2+>Cs+
Column investigations
• Fixed bed column sorption experiments were carried out
to study the sorption dynamics. The fixed bed column
operation allows more efficient utilization of the sorptive
capacity than batch process.
• The breakthrough curves measured are useful to
determine the main transport parameters under dynamic
conditions.
Breakthrough curves for Cs+ and Sr2+ ions
sorbed onto zeolite NaA-X
1.2
1.2
2+
Flow rate=3 mL/min
Bed depth=3 cm
Sr
0.8
0.6
0.4
150 mg/L
100 mg/L
50 mg/L
0.2
+
Flow rate=3 mL/min
Bed depth=3 cm
1.0
Breakthrough, Ct/Co
Breakthrough, Ct/Co
1.0
Cs
0.8
0.6
0.4
150 mg/L
100 mg/L
50 mg/L
0.2
0.0
0.0
0
200
400
600
800
Effluent Volume, mL
1000
1200
0
200
400
600
800
Effluent Volume, mL
1000
1200
Fixed Bed Data
Table( 8): fixed bed data of Cs+ and Sr2+ions onto Zeolite NaA-X at
different metal ions feed concentrations
metal
ions C0(mg/L)
Cs+
Sr2+
qtot(mg)
Column
Bed
performance% capacity(mg/g)
X(mg)
50
39.0
23.35
59
23.35
100
47
28.5
55
28.5
150
58.5
30.5
52
30.5
50
57.5
37.5
65
37.5
100
75
48.75
60
48.75
150
78.75
45
57
53.5
Estimation of dispersion coefficient
The dispersion coefficient may then be calculated from
the breakthrough curve using the following equation
dC
dt
C

C0
c
c0
1
 erf
2

2
 DL
d C
dx
2
vf
dC
dx
 L vft
v L

  exp  f  erf
 D 
2 D t 
 L 
L 


1 

erfc
2 

 L  v f t 


 2 D t 
L 


1U

1

2
 2 (UD L / v f L )


 

Long term behavior of the proposed backfill
material (Zeolite NaA-X) in disposal facility.
Transport mechanisms and governing equations
•
Diffusion
F  D
dC
(Fick`s law)
dx
• Advection-Dispersion
• Radioactive decay
f  nvC  nD
C
t
• Sorption
  C
qe = Kd Ce
C
z
Modeling migration of radionuclides in the
waste disposal facility
System description
Development of conceptual
model
Selection of mathematical
models
Selection of numerical
technique
Carry out
simulation
Performance assessment steps
Conceptual model
Cover
Waste packages
Backfill
Host rock
Concrete vault
Simplified diagram
Groundwater table
Modeling migration through waste
form
2
2
D  C  C 

 C
 2 
2 
t
Rd   x
y 
C
Where
: decay constant, s-1
x : spatial coordinate in x direction
x: spatial coordinate in y direction
t: time, s
C: contaminant concentration in the waste, Bq/ml
D: diffusivity of contaminant in the waste.
Rd: retardation coefficient in the waste
Rate  A  D
where A: area of the interface
C w
x
dA
Numerical solution and computer
simulation
2
2
D  C  C 

 C
 2 
2 
t
Rd   x
y 
C
C
n 1
n
C
i, j
i, j
2 n 1
2 n 
  2 C n  1  2 C n
 C
 C
D  x i, j
x i, j
y i, j
y i, j 
n



   C i, j
2
2
Rd
2(x)
2(y )




t
  x  y
n 1
ui, j
n
 ui, j 


2
x
2
y
1
2

R 
2
n 1
R  x ui, j
n
n
n
n
D t
Rd 
2
C=u
2
n
2
n 1
 x u i , j  y u i , j
n
n
u i , j  u i1, j  2 u i , j  u i 1, j
n
n
u i , j  u i , j 1  2 u i , j  u i , j 1
2
n
 y u i , j

Alternating Direction Implicit method
(ADI)
First step



1 n

 n 1 / 2
n 1 / 2
n 1 / 2
n
n
n
 u i 1, j  u i 1, j  v i , j  v i , j 1  2 v i , j  v i , j 1
  2 u i , j
R
R


Second step


1 n1 / 2

 n1
n1
n 1
n 1 / 2
n1 / 2
 2vi, j
 v i , j 1
  2 u i , j  u i  1, j  u i 1, j  v i , j
R
R

Equations in Matrix form

R  2

 1

 
 

 



 0


R  2

 1

 
 

 



 0

1



0
0



0
0






















0



1

2
R



R
1




0
0



0
0






















0



1
2
R

R













2

 u1 
 
u
 2
u 3 
 
u 4 

 

u 
 n











2

 v1 
 
v
 2
v3 
 
v 4 

 

v 
 n
=
=



 BCND (1)  ( R  2 ) v 1  v 2 





















 BCND ( n )  (   2 ) v  v 
n
n 1


R



 BCND (1)  ( R  2 ) u 1  u 2 





















 BCND ( n )  (   2 ) u  u 
n
n 1


R
Computer program flow chart for waste
model
Start
A
Input
Time = 0.0
B
C
Time=time *t
Get values for
the second row
Data
Yes
Time
>Tma
x
Calculate R
Back
substitution for
the u vector
No
Get values in v
vector top
&bottom
Stop
Setup the coeffs.
Matrices
Get values in the
u vector top &
bottom
Yes
Calculate the
rate
M>3
No
No
Get values in the
u vector other
rows
Output
the rate
Get values in the
second row
M>3
Yes
Perform L.U.
decomposition
on v and u
Coeffs.
No
M<3
No
Get values in the
B.C.
Vector for u
Yes
Output the
concentratio
n profile
M<3
Yes
Get values in the
B. C.
Vector for v
Calculate the
concentration
profile
Get values in the
v vector for
other rows
Back
substitution for
the v vector
End
Modeling migration through
backfill
C
t

n 1 / 2
2 C i, j
C
n
i, j

t

n1 / 2
 v x C i1, j
A
D 
2
t
2
t

2
 D xx

D xx

2
x
C

2D


yy
2
 D yy
2
n 1 / 2
i 1, j
n1 / 2
 C i 1, j
2D
xx

2
2
 C
B 
y
 2C
v
xx
x

2


2
n 1 / 2
i, j
  v C
y
 vx
C
n
i , j1
C
x
yy

2
v

y

C
 vy
n 1 / 2
i 1, j

 C
y
D yy

2
C

n
n
i , j 1
D
C 
yy

2
D
F 
 2 C i , j  C i , j 1
n1 / 2
 C i , j 1   C i , j
D
D
E 
 C
yy

2
v

y

v

y

n
n

Equations in Matrix form
 A

C

 0

 
 

 
 0

 A

C

 0

 
 

 
 0

B
0
0


A
B
0


C
A
B
0
















0
0
0
0
C
B
0
0


A
B
0


C
A
B
0
















0
0
0
0
C
0 

0

0 

 
 

 B
A 
0 

0

0 

 
 

 B
A 
 u1 
 
u
 2
u 3 
 
u 4 

 

u 
 n
 v1 
 
v
 2
v3 
 
v 4 

 

v 
 n
=
=
 D v 1  Ev 2

D v 2  Ev 3

 D v 3  Ev 4








 D v  Ev
n
n 1

 Fv 0


 Fv 1

 Fv 2 





 Fv n 1 
 D u 1  Eu 2  Fu 0 


D u 2  Eu 3  Fu 1


 D u 3  Eu 4  Fu 2 













 D u  Eu
 Fu n 1 
n
n 1

Computer program flow chart for backfill
model
A
B
Initialization
For the B.C.
and initial
condition
Set up the coefficient
matrices for both waste
and backfill by
overwriting on the
diagonal and certain off
diagnonal elements
Get values into B.C.
vector for u matrix in
the waste and
backfill
Get values into B.C.
vector for v matrix in
the waste and
backfill
Perform L.U.
decomposition on
the diagonal terms
for the waste and
backfill
If Time>
Tmax
A
Forward substitution
for the waste
equations
Perform
convolution
integral
Backward
substitution for the
waste equations
Differentiate to
find
concentration
gradient
Differentiate to find
gradient
Integrate and
multiply by Db*Zb to
find the release rate
from the backfill
Integrate and
multiply by Dw*Z w to
find the release rate
from the waste
Forward substitution
for the backfill
equations
Backward substitution for
the backfill to find the
concentration profile due
to instantaneous unit
release
B
Output
END
Model validation
1
Numeriacl
0.9
Analytical
0.8
0.7
C/Co
,
0.6
0.5
0.4
0.3
0.2
0.1
0
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Distance, m
 R . x  Vt
C0 
C ( x, t ) 
 erfc 
2 DR t
2 
L



  exp


(Ogata, 1970)
 Vx

D
 L
 R . x  Vt

 erfc 

 2 D Rt

L




 
Results of the long term studies
Concentration profile of Cs in zeolite backfill after 300 y
600
500
400
C 300
200
C,Bq/m3
100
0.4
0.2
0.35
0.3
0.25
X ,m
(Cs)
0.2
0.15
0.1
0.05
0
0.05
Y ,m
Concentration profile of Sr in zeolite backfill after 300 y
80
70
60
50
C 40
C,Bq/m3
30
20
0.4
0.3
10
0
0.15
0.05 0.1
0.15 0.2
0.25 0.3
X ,m
(Sr)
0.05
Y ,m
Release rate of Cs and Sr radionuclide from
the proposed zeolite backfill
1.E+01
Release Rate (GBq/Y)
1.E+00
1.E-01
1.E-02
1.E-03
1.E-04
Sr
1.E-05
Cs
1.E-06
0
50
100
150
Time (y)
200
250
300
Release rate for the Cs radionuclides from the waste form
,the proposed and commonly applied backfill
1 .E + 02
1 .E + 01
1 .E + 00
1 .E -02
1 .E -03
1 .E -04
/Y
)
Waste Form
(G B q
Release Rate
1 .E -01
1 .E -05
Zeolite
Bentonite
&crushed rock
1 .E -06
0
50
100
150
Time
200
(y )
250
300
Conclusions
The results obtained in this work show the
following:
• The synthetic zeolite NaA-X proposed as backfill
material was successfully prepared and completely
characterized using XRD, XRF, and SEM techniques.
• The sorption studies indicated the feasibility of using
the prepared zeolite NaA-X as backfill material
compared to bentonite because of its high capacity
and selectivity for the concerned radionuclides (Cs
and Sr) these characteristics are fundamental to the
performance of such zeolite in radioactive waste
interactions.
conclusions
•
Column investigation yield a realistic picture of the sorptrion of
Cs and Sr on zeolite NaA-X and lead to determination of
dispersion coefficient which in turn used in migration modeling.
•
Transport properties of zeolite NaA-X packed column have been
determined. The classical advection-dispersion model described
successfully Cs and Sr breakthrough curves under saturated flow
conditions. Based on this experimental data the dispersion
coefficient needed for long-term migration study was determined.
• The mathematical simulation performed in the long-term studies
show the capability of the prepared zeolite NaA-X to prevent the
migration of Cs and Sr from the repository to the environment.