Basics of Contaminant Transport in Aquifers (Lecture)

Chapter 5
Basics of Transport of
Pollutant in Aquifers
Amro Elfeki, PhD

Contaminant anything in water that renders
it unsuitable for a particular use
Contaminant (Pollution)

Many Sources and Types of
Contaminants

Various Forms of Pollution in
Groundwater

Classification of Pollutant
• Dissolution in Water: Solutes – Heavy metals
• Density: LNAPLS, DNAPLS
• LNAPLs: light, nonaqueous phase liquid
– lighter than water
– floats on surface of a water table
• DNAPLs: dense, nonaqueous phase liquid
– heavier than water
– sinks to the bottom of a water table

Classification of Pollutant (cont.)
• Reactions with soil: Conservative and non-
conservative
• Organic: Organic (Carbon and Nitrogen) and
Inorganic
• Microbial: Microorganisms, Bacteria and
Viruses

Organics
(gasoline, DDT, detergents)
Volatile organics
(TCE, DCE, Benzene)
Contaminant by Organic
Materials

Inorganics
(chloride, cyanide, nitrate)
Contaminant by Inorganic
Materials

Nitrate concentrations > 10 mg/kg in drinking water pose a health
threat to infants,
Nitrate Pollution

Heavy Metals
(arsenic, cadmium, chromium)
Contaminant by Heavy Metals

Organisms
(Giardia, E. Coli)
Contaminant by Micro-Organisms

LNAPLS(Lighter):“BTEX” Compounds

DNAPL (Denser):Chlorohydrocarbons

Transport Processes
1) Physical :
Advection-Diffusion-Dispersion
2) Chemical:
Adsorption- Ion Exchange- etc.
3) Biological:
Micro-organisms Activity
(Bacteria&Microbes)
4) Decay:
Radioactive Decay-Natural Attenuation.

Physical Processes
1. Advection
2. Molecular Diffusion
3. Mechanical Dispersion
4. Hydrodynamic Dispersion

Advection
• Movement of contaminants with a moving
fluid (e.g., groundwater)
• Controlled by difference in hydraulic head
vs = interstitial velocity or seepage velocity
(L/T)
= Ki/n (Darcy’s law);
K = hydraulic conductivity, L/T;
i = hydraulic gradient, h/L; and
n = porosity.
x
C
v
t
C
s





18
x = vt

Advection (Convection)
adv
J Cq
Advective Solute Mass Flux:
.q = K 
is the advective solute mass flux,
is the solute concentration, and
is the water flux (specific discharge)
given by Darcy's law:
C
q
adv
J
Advection
solute moves
with groundwater

Dispersion/Diffusion
• Molecular Diffusion
– Molecules move from regions of high concentration
to regions of lower concentration
– Length of scale of motion = molecular → slow
• Turbulent Diffusion
– Bulk motion in random directions
• Mechanical Dispersion
– Microscopic velocity variation within the pore space
– Differences in pore sizes along the flow paths
– Mechanical dispersion leads to longitudinal as well
as transverse dispersion, with the former one more
significant than the latter one 20

Diffusion
Diffusive Flux in Bulk: (Fick’s Law of Diffusion)
is the diffusive solute mass flux in bulk,
dif
o oJ =- D C
dif
oJ
is the solute concentration gradient,
C
is the molecular diffusive coefficient in bulk.
oD
Random Particle motion
Time
t1
t2
t3
t4
Diffusion
moving from higher
to lower concentrations

Diffusion
22
A net transport of molecules from a region of higher concentration to one of
lower concentration by random molecular motion

Molecular Diffusion (Dd)
23
L
Lp

Tortuosity factor, ω: the distance a molecule travels to get through porous
media divided by the straight line of the two points
Diffusion in porous media, Dd
*
Dd
* = ωDd
Lp = distance a molecule travels from points A to B
L = straight distance between points A and B
ω=f(1/τ)
=0.01~0.5

Molecular Diffusion
dif
effJ =- D C 

O
eff
D
D 
Diffusive Flux in Porous Medium
is the effective molecular diffusion
coefficient in porous medium,
effD
 is a tortuosity factor ( = 1.4)
0.7eff oD D

Mechanical Dispersion
dis
J =- C .D
Depressive Flux in Porous Media (Fick’s Law):
is the depressive solute mass flux,
is the solute concentration gradient,
is the dispersion tensor,
is the effective porosity
dis
J

C
D
xx xy xz
yx yy yz
zx zy zz
D D D
D D D
D D D
 
 
  
 
 
D
[after Kinzelbach, 1986]
Causes of Mechanical Dispersion

Mechanical Dispersion (Dm)
26
 Function of the shape of the soil particles and the distance between them

Hydrodynamic Dispersion (Dh)
• Hydrodynamic dispersion coe. (Dh) = Mechanical dispersion
coe. (Dm) + Diffusion coe. (Dd)
Dh = Dm + Dd
*
Dh = αv + ωDd
where α = dynamic dispersivity (m) = 0.0175 Lp
1.46 and
Lp = length of the flow path or plum length (m)
α = 0.83 [log Lp]2.414 (Xu and Eckstein, 1995)
• At column scale, dispersivity = 0.01~1.0 cm
• In field experiments, dispersivity = 0.1~2.0 m
27

Hydrodynamic Dispersion
    i j
ij efft ij l t
v v
= |v|+ + -D D
|v|
   
_hydo dis
J =- C .D
Hydrodynamic Depressive Flux in Porous Media (Fick’s Law):
The components of the dispersion tensor in isotropic soil
is given by [Bear, 1972],
is Kronecker delta, =1 for i=j and =0 for i j,ij
are velocity components in two perpendicular directions,
i jv v
is the magnitude of the resultant velocity,v 2 2 2
i j kv v v v  
is the longitudinal pore-(micro-) scale dispersivity, andl
t is the transverse pore-(micro-) scale dispersivity
ij ij

Hydrodynamic Dispersion (Cont.)
In case of flow coincides with the horizontal x-direction
all off-diagonal terms are zeros and one gets,
0 0
0 0
0 0
xx
yy
zz
D
D
D
 
   
  
D
xx effl
yy efft
zz efft
= |v|+D D
= |v|+D D
= |v|+D D



, 0.5
, 0.0157
3.5 Random packing
is the grain diameter
l l p l
t t p t
p
c d c
c d c
d
 
 

 
 


Microscopic Dispersion Simulation
30

Peclet number, Pe
• Ratio of advective flux to diffusive flux
31
d
e
D
vL
P 
v = average linear velocity (L/T);
L = characteristic length (average diameter of grains, d50, in porous
media); and
Dd = molecular diffusion coefficient, L2/T.
 Pe > 1 means diffusive flux is more important than advective flux
 Pe < 1 means diffusive flux is negligible compared to advective flux

Dispersion Regimes at Micro-Scale
D
VL
Pe
eff
cc

Peclet Number:
Advection/Dispersion
Perkins and Johnston, 1963

Chemical Processes
• Sorption & De-sorption.
• Ion Exchange.
• Retardation.

Conservative
do not react with soil / groundwater
Sorbed onto mineral grains
as well as organic matter
Reactive
Conservative and Reactive
Solutes

Adsorption Isotherms
)(CfS 
m
bCS 
CKS d
21 kCkS 
4
3
1 k
Ck
S


Freundlich (1926)
Langmuir (1915, 1918)

Biological Processes
•Biological Degradation
and Natural Attenuation.
•Micro-organisms
Activity.
•Decay.
C
dt
Cd

 )(
 is the decay coefficient

Transport Through Porous Media

Derivation of Transport Equation in
Rectangular Coordinates
Flow In – Flow Out = rate of change within the control volume

Solute Flux in the x-direction
( )
( )
( )
in adv dis
x x x
adv dis
out adv dis x x
x x x
J J J y z
J J
J J J x y z
x


   
 
      
 

Solute Flux in the y-direction
( )
( )
( )
in adv dis
y y y
adv dis
y yout adv dis
y y y
J J J x z
J J
J J J y x z
y


   
 
      
  

Solute Flux in the z-direction
( )
( )
( )
in adv dis
z z z
adv dis
out adv dis z z
z z z
J J J y x
J J
J J J z y x
z


   
 
      
 

From Continuity of Solute Mass
( )solute
in out
M
J J C x y z
t t
 

 
      
Where  is the porosity, and
C is Concentration of the solute.

From Continuity of Solute Mass
( ) ( ) ( )
( )
( )
( )
( )
( )
( )
( )
adv dis adv dis adv dis
x x y y z z
adv dis
adv dis x x
x x
adv dis
y yadv dis
y y
adv dis
adv dis z z
z z
J J y z J J x z J J y x
J J
J J x y z
x
J J
J J y x z
y
J J
J J z y x
z
C x y z
t









          
 
      
 
 
      
  
 
      
 
   

By canceling out terms
( )( ) ( )
adv disadv dis adv dis
y yx x z z
J JJ J J J
z y x
x y z
 
  
  
      
  
(C x y z
t



    )
( )( ) ( )
( )
adv disadv dis adv dis
y yx x z z
J JJ J J J
x y z
C
t
 
  



  
   
  


Assuming Advection and Hydrodynamic
Dispersion
,
,
,
adv dis
x x x xx xx
adv dis
y y y yy yy
adv dis
z z z zz zz
C
J = Cq J = - D C - D
x
C
J = Cq J = - D C - D
y
C
J = Cq J = - D C - D
z
 
 
 

 


 


 

. .
. .
. .

Solute Transport Through Porous Media by
advection and dispersion processes
( )
y yyx xx z zz
CC C
Cq - DCq - D Cq - D
yx z
x y z
C
t
    
  



      
              
 
 
 

.. .
( ) ( ) ( )
Hyperbolic Part
x y z
Parabolic Part
xx yy zz
C
v C v C v C
t x y z
C C C
D D D
x x y y z z
   
   
     
     
   
    
      
    
6 4 4 4 4 44 7 4 4 4 4 4 48
6 4 4 4 4 4 4 4 44 7 4 4 4 4 4 4 4 448

General Form of The Transport Equation
 
}
}
/
( ')
Dispersion Diffusion
Advection Source SinkChemical reaction
Decay
ij i
i j i
C C S C C W
v C + Q CD
t x x x

 


     
    
     
6 44 7 4 48 64 7 48 6 4 7 48
where
C is the concentration field at time t,
Dij is the hydrodynamic dispersion tensor,
Q is the volumetric flow rate per unit volume of the source or sink,
S is solute concentration of species in the source or sink fluid,
i, j are counters,
C’ is the concentration of the dissolved solutes in a source or sink,
W is a general term for source or sink and
vi is the component of the Eulerian interstitial velocity in xi direction
defined as follows,
ij
i
j
K
=-v
x

where
Kij is the hydraulic conductivity tensor, and  is the porosity of the medium.

Schematic Description of Processes
Figure 7. Schematic Description of the Effects of Advection, Dispersion, Adsorption, and Degradation on Pollution
Transport [after Kinzelbach, 1986].
Advection+Dispersion
Advection
Advection+Dispersion+Adsorption
Advection+Dispersion+Adsorption+Degradation

Methods of Solution
1) Analytical Approaches:
2) Numerical Approaches:
i) Eulerian Methods:(FDM,FEM).
ii) Lagrangian Methods:(RWM).
iii) Eulerian-Lagrangian Methods:
(MOC).

Pulse versus Continuous Injection
Concentration Distribution in case of Pulse and Continuous Injections in a 2D Field
[after Kinzelbach, 1986].






tV4
)Y-(y
+
tV4
)tV-X-(x
-
tV4tV4
H)/(M=t)y,C(x,
xt
2
o
xl
2
xo
xtxl
o


exp  
d
tV4
Y-y
+
tV4
tV-X-x
-
tV4
HM=ty,x,C
t
xt
2
o
xl
2
xo
tlx
o
 









0
)(
)(
)(
)((
exp
1)(/
)( 





Flow
t = 0
f
t = Flowing Time
Var(X)
The spread of the front is a measure of the heterogeneity
Random Walk

Transport of a Solute
52
1
0.5
0
Relative
Concentration,C/C0
Distance, x
Concentration Profile at Time t
in One-Dimensional Flow
Advection only
x = vt
Diffusion onlyDispersion only

Mechanical dispersion - caused by motion of the fluid
Longitudinal dispersion – along the streamline
Transverse dispersion – perpendicular to flow path
Flow
Direction

Dispersion

DL
2C
x2
- vx
C
 x
=
C
 t
DL = coefficient of longitudinal hydrodynamic dispersion
C = solute concentration in liquid phase
vx = average linear groundwater velocity
t = time
b = bulk density of aquifer
= porosity (saturated aquifer)
C* = amount of solute sorbed per unit weight of solid
-
b

dispersion advection sorption
C*
 t
One Dimension Advection Dispersion
& Sorption

Slows the rate of transport
Retardation and Sorption

Types of Contamination Sources
Continuous Source t1
t4t2 t3
One time release
t2t1
t3
Contaminant Transport

Comparison between Analytical
Solution and RW-method






tV4
)Y-(y
+
tV4
)tV-X-(x
-
tV4tV4
H)/(M=t)y,C(x,
xt
2
o
xl
2
xo
xtxl
o


exp
 
d
tV4
Y-y
+
tV4
tV-X-x
-
tV4
HM=ty,x,C
t
xt
2
o
xl
2
xo
tlx
o
 









0
)(
)(
)(
)((
exp
1)(/
)( 





3D graphical representation of
pollution injection

Concentration Profiles in case of
Continuous Injection

Groundwater Restoration
– Dig and remove contamination - Arsenic
– Pump and treat - Nitrate
– Mitigate in ground (in situ)
– Hydrogen Peroxide
- Lower water table
- Seal contamination (Contamination Containment)
- Bioremediation
- Install permeable treatment bed (Permeable
reactive barrier)

National Water Quality Assessment Program
http://water.usgs.gov/nawqa/
Some useful web links for gw contamination:
Superfund Sites in Massachusetts
http://www.epa.gov/superfund/sites/npl/ma.htm
EPA Superfund Homepage
http://www.epa.gov/superfund/index.htm
EPA Major Environmental Laws
http://www.epa.gov/region5/defs/index.html
USGS Toxic Hydrology Program
http://toxics.usgs.gov/
Massachusetts Contingency Plan
http://www.state.ma.us/dep/bwsc/files/mcp/mcptoc.htm

Contaminant Hydrogeology Journals
Water Resources Research
Ground Water
Ground Water Monitoring and Remediation
Environmental Science and Technology
Journal of Contaminant Hydrology

Basics of Contaminant Transport in Aquifers (Lecture)

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