sethi - hassanizadeh eccellenza 1 r01 - soilmech.polito.it
TRANSCRIPT
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1Sethi R., Tosco T. www.polito.it/groundwater
Part of an Excellence Ph.D. Course
Politecnico di Torino – June 27th, 2012
A talk on:
Transport of colloids and nanoparticles in saturatedporous media for environmental remediation
Rajandrea SETHI, Tiziana TOSCO, Alberto TIRAFERRI and GROUNDWATER ENGINEERING GROUP
DIATI – Politecnico di Torino
DITAG
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Program
� Transport in porous media of:
1. Ideal colloids: latex particles
2. Non-ideal colloids: iron particles for the remediation of contaminated aquifer systems
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What is a colloid?
� A colloid is a chemical mixture (not a solution) in which one
phase (dispersed phase) is evenly dispersed into another
phase (dispersion medium).
� The colloids has and homogeneous aspect.
� A colloidal system may be solid, liquid, or gaseous.
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What is a colloid?
Solid SolExample: glass
GelExamples: cheese
silicagel, opal
Solid FoamExamples: aerogel,
styrofoam, pumice
Solid
SolExamples:
pigmented ink, blood
EmulsionExamples: milk,
mayonnaise, hand cream
FoamExample: whipped
creamLiquid
Solid AerosolExamples: smoke,
cloud, air particulates
Liquid AerosolExamples: fog,
mist, hair sprays
None(All gases are
mutually miscible)Gas
Dispersion Medium
SolidLiquidGas
Dispersed PhaseMedium / Phases
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Colloids in aquifer systems(porous media)
Anthropogenic or
natural nano- and
micro-particles:
� Chemical
� Farmaceutical
� Fly ashes
� Bacteria
Natural colloids
+ sorbed contaminats
Nanoscale
zerovalent iron
Contaminants
Colloid facilitatedtransport
Remediationtechnologies
(adapted from Freyria, 2007)
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Bacteria Clay particles
Natural colloids in aquifersystems
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Nanoscale iron
15 – 100 nm
Engineered colloids
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Transport of colloids in porousmedia
� Mechanisms:
� Advection
� Hydrodynamicdispersion
� Interaction withsolid phase
� Particle-particleinteraction
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Colloids in porous media: interaction forces
Particle - particle
interactions
Sand-particle interactions
SAND
PORE
WATER
Fluid-particleinteractions
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me
ch
an
ism
s
Interaction with porous media and particle-particle:
first
then
Transport of colloids in porousmedia
Rip
en
ing
Str
ain
ing
Blo
ck
ing
CF
T
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Particle-particle interaction
� Colloidal interactions have different origins:
� Van der Vaals
� Electrostatic
� Magnetic
DLVO & extended DLVO theory
)/141(12 λss
AaVVdW
+−=
s
rESeaV
⋅−= κγζεπε 22
032
( )3
32
0
29
8
+
−=
a
s
aV s
M
ρσπµ
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Particle-particle interaction:
Particle – Particleinteractions
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Sand – particles interaction
� Favorable deposition
(different charge)
� Unfavorable deposition
(same charge)
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The presence of ions screens the surface charge of the colloids thusreducing electrostatic repulsion
Unfavorable depositionRole of ionic strength
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Role of particle size
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Colloids in porous media: different approaches
� Microscale
Laboratory tests
Mathematical models
Bradford et al., 2005
Messina, Boccardo, 2012 Icardi, 2012
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Forces acting on a particle
Drag force
Gravity force
Brownian force
Electric doublelayer
Van der Waalsforce
( )vuFaF ppD
rrr−= ρπ 3
3
4
( )gaF fppG
rrρρπ −= 3
3
4
( )( ) ( )
−
+−
+= −
−
−
h
cp
cp
h
h
cp
prEDL ee
eaF
κ
κ
κ
ξξ
ξξκξξεε
222
22
0 212
r
( )2214
)28(
6 h
h
h
HaF
p
VdW+
+−=
λ
λλr
t
kTRFB
∆=
ξ2
Messina, 2012
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Macroscale
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Macroscopic approach
Mobile particles
Immobile particles
Momentum balance
Flow equation( ) ( ),i
EB
i
qhS s Q Q c s
t xρ
∂∂+ = +
∂ ∂
( ) ( )0 0
0 0
ij om m m
i i j
j
gK s chv q e
x
ρ ρ ρµε
µ µ ρ
−∂= = − + ∂
( )( ) ( ) ( ) ( )f
m m m mol disp
b i ij ij
i i j
cs c s v c D D
t t x x xε ρ ε ε
∂ ∂ ∂ ∂ ∂+ = − + +
∂ ∂ ∂ ∂ ∂
( ) ( ),bs f c s
tρ
∂=
∂
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Colloidal transport
� 2 coupled equations:
� Mobile phase
(water)
� Immobile phase
(sand)
( ) ( ) ( )
( )
=∂
∂
∂
∂−
∂
∂
∂
∂=
∂
∂+
∂
∂
scft
s
x
cq
x
cD
xt
s
t
c
b
mm
bm
,ρ
ερε
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me
ch
an
ism
s
Exchange term
� Different formulations/mechanisms:
Str
ain
ing
Rip
en
ing
Blo
ckin
gL
inear
C
FT
skckd
xd
t
sdbamb
str
ρερ
β
−
+=
∂
∂−
50
50
( ) skcksAt
sdbaripmb
rip ρερβ
−+=∂
∂1
skcks
s
t
sdbamb ρερ −
−=
∂
∂
max
1
skckt
sdbamb ρερ −=
∂
∂
Langmuirian
Tosco, Sethi
Bradford
ckt
samb ερ =
∂
∂
Linear
CFT (irreversible)
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General use of ripening equation
( ) skcksAt
sdbaripmb
rip ρερβ
−+=∂
∂1
=
=
0
0
d
rip
k
A
>
>
0
0
rip
ripA
β0=ripA
� TSE can be used to simulate different mechanisms:
clean bed blocking
lineare rev. ripening
**c
k
ks
db
am
ρ
ε=
*
*
*
cAkk
cks
ripamdb
am
ερ
ε
−=
=
−=
1
1
max
rip
rips
A
β
( ) aripm
db
ksA
skc
ripβε
ρ*
*
*
1+=
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Experimental setupLaboratory scale
Sonicating bath
Peristaltic pump
� 1D system, saturated porous medium
� Colloidal particles: latex, d=2 µm
� Porous medium: sand, d50=250 µm
� Column: � dint = 1.6 10-2 m� L = 0.1 m� n = 0.42� aL = 5.8 10-4 m
� Water:� q = 7.9 10-5 m/s� pH = 7.0� Ionic strength = 0 - 300 mM
Spectrophotometer
column
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� Silica Sand
� SEM image Particle Size distribution
Column tests:Materials
0
10
20
30
40
50
60
70
80
90
100
0 100 200 300 400 500
size (um)
po
pu
lati
on
(%
)
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� Particles: latex microspheres
Column tests:Materials
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0 2000 4000 6000 8000 10000 120000
10
20
30
t (s)
Ct (m
M)
0 2000 4000 6000 8000 10000 120000
0.5
1
t (s)
C/C
0 (-)
0 2000 4000 6000 8000 10000 12000-0.5
0
0.5
1
C/C
0 (-)
Constant I. S. Transient I. S.
Column
Input
Column
Output
Available models ?? … New model
Column tests:Design
Sa
lt (
mM
)C
ollo
idC
ollo
id
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Column tests:Results
Constant IS Variable IS
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One site model
� One-site models are usually presented in these forms:
Linear attachment function Langmuirian attachment function
These models can be useful in many cases, but did not proved to be
satisfactory when modeling our column experiments.
−=∂
∂
∂
∂−
∂
∂=
∂
∂+
∂
∂
skcnkt
s
x
cv
c
cnD
t
s
t
cn
dbab
b
ρρ
ρ2
2
−
−=
∂
∂
∂
∂−
∂
∂=
∂
∂+
∂
∂
skcks
sn
t
s
x
cv
c
cnD
t
s
t
cn
dbab
b
ρρ
ρ
max
2
2
1
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0 1 2 3 4 5 6 7 8 9 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Lab data
Stanmod
Matlab
0 1 2 3 4 5 6 7 8 9 100
0.2
0.4
0.6
0.8
1
1.2
1.4
lab data
Stanmod
Matlab
One-site model…
� Can’t fit experimental curves at high IS
F.I. = 1mM F.I. = 100 mM
C/C
0(-
)
C/C
0(-
)
PV (-) PV (-)
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� Heteroneous silica sand + feldspar
SEM image Size distribution
Column tests:Materials
0
10
20
30
40
50
60
70
80
90
100
0 100 200 300 400 500
size (um)
po
pu
lati
on
(%
)
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Two sites model
� Differential equations for the two-interaction-site model:
blocking attachment
function
linear attachment
function
� Model implementation (MNM1D www.polito.it/groundwater):
� Matlab code, finite-differences approach
� Non linear-problem, solved with an iterative scheme
� Code validated with well-established analitycal (Stanmod) and numerical (Hydrus1D) solutions
−=∂
∂
−
−=
∂
∂
∂
∂−
∂
∂=
∂
∂+
∂
∂+
∂
∂
22,2,2
11,1,
1max,
11
2
2
21
1
skcnkt
s
skcks
sn
t
s
x
cv
c
cnD
t
s
t
s
t
cn
dbab
dbab
bb
ρρ
ρρ
ρρ
32Sethi R., Tosco T. www.polito.it/groundwater
Colloids in porous media: modeling the influence of I.S.
� MNM1D (Micro-and Nanoparticle transport Modelin porous media in 1D geometry):� Development of the model at CONSTANT ionic strength
� Fitting of the first part of experimental curve (I.S. 1 – 300 mM);
� Definition of semi-empirical relationships for
attachment/detachment coefficients VS ionic strength
� Development of the model in TRANSIENT ionic strength
� Application of MNM1D for the fitting of the whole experimental
curves
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Colloids in porous media: modeling the influence of I.S
� Fitting of the first part of the breakthrough curves, at constant ionic strength (1 – 300 mM)
C/C
0(-
)C
/C0
(-)
34Sethi R., Tosco T. www.polito.it/groundwater
Colloids in porous media: modeling the influence of I.S.
� MNM1D (Micro-and Nanoparticle transport Modelin porous media in 1D geometry):� Development of the model at CONSTANT ionic strength
� Fitting of the first part of experimental curve (I.S. 1 – 300 mM);
� Definition of semi-empirical relationships for
attachment/detachment coefficients vs ionic strength
� Development of the model in TRANSIENT ionic strength
conditions
� Application of MNM1D to the whole test
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Two sites model:influence of the IS
� Dependence of coefficients on IS:
1,
1
,1
1,
1
a
t
a
a
c
CDC
kk
β
+
= ∞
1,
1
0,1
1,
1
d
CRC
c
kk
t
d
d β
+
=1,
1,1max,
s
ts csβ
α=
36Sethi R., Tosco T. www.polito.it/groundwater
Colloids in porous media: modeling the influence of I.S.
� MNM1D (Micro-and Nanoparticle transport Modelin porous media in 1D geometry):� Development of the model at CONSTANT ionic strength
� Application for the fitting of the first part of experimental (I.S.
1 – 300 mM);
� Definition of semi-empirical relatioships for
attachment/detachment coefficients VS ionic strength
� Development of the model in TRANSIENT ionic strength
conditions
� Application of MNM1D to the whole test
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� A further PDE is added to account for the evolution of IS:
Colloids in porous media: modeling the influence of I.S.
MNM1D
( )( ) ( )
( ) ( )
−=∂
∂
−
−=
∂
∂
∂
∂−
∂
∂=
∂
∂+
∂
∂+
∂
∂
∂
∂−
∂
∂=
∂
∂
22,2,
2
11,1,
1max,
11
2
2
21
2
2
1
sckccnkt
s
sckcckcs
sn
t
s
x
cv
x
cnD
t
s
t
s
t
cn
x
cv
x
cnD
t
cn
tdbtab
tdbta
t
b
bb
ttt
ρρ
ρρ
ρρ
1
1
,1
1
1
a
t
a
a
c
CDC
kk
β
+
= ∞
1
1
0,1
1
1
d
CRC
c
kk
t
d
d β
+
=
1
11maxS
tS csβα=
Conservative tracer
38Sethi R., Tosco T. www.polito.it/groundwater
Two sites model + IS dependence
( )( ) ( )
( ) ( )
−=∂
∂
−
−=
∂
∂
∂
∂−
∂
∂=
∂
∂+
∂
∂+
∂
∂
∂
∂−
∂
∂=
∂
∂
22,2,
2
11,1,
1max,
11
2
2
21
2
2
1
sckcckt
s
sckcckcs
s
t
s
x
cq
x
cD
t
s
t
s
t
c
x
cq
x
cD
t
c
tdbtamb
tdbta
t
mb
mbbm
ttm
tm
ρερ
ρερ
ερρε
εε
di
i
t
di
id
CRC
c
kk
β
+
=
1
0,
,
ai
t
i
ai
ia
c
CDC
kk
β
+
= ∞
1
,
,
1
11max,
S
tS csβ
α=
20
39Sethi R., Tosco T. www.polito.it/groundwater
Colloids in porous media: modeling the influence of I.S.
� MNM1D (Micro-and Nanoparticle
transport Model in porous media in
1D geometry):
� Development of the model at CONSTANT ionic strength
� Application for the fitting of the first part of experimental (I.S. 1 – 300
mM);
� Definition of semi-empiricalrelatioships forattachment/detachment coefficientsvs ionic strength
� Development of the model in TRANSIENT ionic strength
� MNM1D can be downloaded from: http://areeweb.polito.it/ricerca/groundwater/software/MNM1D.html
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Colloids in porous media: modeling the influence of I.S.
� Fitting of the complete column testI.S. = 1mM
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Colloids in porous media: modeling the influence of I.S.
� Fitting of the complete column testI.S. = 10mM
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Colloids in porous media: modeling the influence of I.S.
� Fitting of the complete column testI.S. = 100mM
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Colloids in porous media: modeling the influence of I.S.
� Fitting of the complete column testI.S. = 300mM
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Solid phase concentration
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Colloids in porous media: modeling the influence of I.S.
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References
� Tosco, T.; Tiraferri, A.; Sethi, R. Ionic Strength Dependent Transport of Microparticles in Saturated Porous Media: Modeling Mobilization and Immobilization Phenomena under Transient Chemical Conditions.Environmental Science & Technology 2009, 43(12), 4425-4431.
� Tosco, T.; Sethi, R. MNM1D: a numerical code for colloid transport in porous media: implementation and validation. American Journal of Environmental Sciences 2009, 5(4), 517-525.
� Tiraferri, A., T. Tosco, e R. Sethi (2010), Transport and Retention of Microparticles in Packed Sand Columns at Low and Intermediate Salinities: Experiments and Mathematical Modeling. Environmental Earth Sciences(submitted) 2010.
� Tiraferri, A.; Chen, K.L.; Sethi, R.; Elimelech, M. Reduced aggregation and sedimentation of zero-valent iron nanoparticles in the presence of guar gum.Journal of Colloid and Interface Science 2008, 324(1-2), 71-79.
� Tiraferri, A.; Sethi, R. Enhanced transport of zerovalent iron nanoparticles in saturated porous media by guar gum. J Nanopart Res 2009, 11(3), 635-645.