16 - 20 Sept 2007Wetland Pollutant Dynamics and Control 1 ARTIFICIAL WETLAND MODELLING FOR...
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Transcript of 16 - 20 Sept 2007Wetland Pollutant Dynamics and Control 1 ARTIFICIAL WETLAND MODELLING FOR...
16 - 20 Sept 2007 Wetland Pollutant Dynamics and Control
1
ARTIFICIAL WETLAND MODELLING FOR PESTICIDES FATE AND TRANSPORT
USING A 2D MIXED HYBRID FINITE ELEMENT APPROXIMATION
Part 2/2
Wanko, A., Tapia, G., Mosé, R., Gregoire, C
16 - 20 Sept 2007 Wetland Pollutant Dynamics and Control
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PESTICIDES DYNAMICS MODELING
Processes Model
t,z,xWzhKt
hhC
Flow : Mass Balance Concept / Richards Equation
Transport : Tanks (series or parallel) / Convection-dispersion
t,z,xf)Cq(CDtS
tC
Adsorption : Freundlich isotherm / linear distribution
Kinetics : Zero order, first order, Michaelis – Menten.
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PESTICIDES DYNAMICS MODELING2D Discretization : Triangular meshs
Unknown parameters :o Pressure head and solute concentrations (edges, mesh center)
o Water and transport fluxes through the edges
CqCDdispadvq
RT0
Numerical method : Mixte Hybrid Finite Element (MHFE)
-Particularly well adapted to the simulation of heterogeneous flow field
- The unknown parameters have the same order approximation
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OSCILLATION CONTROL FOR ADVECTION DOMINANT PROBLEM - FLUX LIMITER
- Vx ,Vz the pore water velocity in x and z directions, respectively (LT-1 ),
- x, z the grid spacing in the x and z direction, respectively (L),
- Dxx, Dzz, Dxz the dispersion coefficients (L2 T-1).
In the literature this problem is solve by using : Operator Spliting Technique (OST) + a slope limiting tool
(Ackerer et al.,1999 ; Siegel et al., 1997 ; Oltean., 2001; Hoteit et al., 2002 ; Hoteit et al., 2004 )
Advection dominant problem :
Pe (Peclet number) =
2 2
2 2
Vx Vzx z
2Dxx Dzz Dxz
x zx z
Numerical oscillations
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OSCILLATION CONTROL FOR ADVECTION DOMINANT PROBLEM - FLUX LIMITER
Advection dominant problem : eP 2
A new approche including a flux limiter
3
1j
3
1jiE,K
1j,i,KKiE,K
1j,i,KiE,Kdispadv QBCTCBQ
oTransport fluxes (the previous formulation)
oTransport fluxes (the new formulation)
3
1jiE,KiE,KKiE,K
3
1j
1j,i,KKjE,K
1j,i,KiE,Kdispadv TCQ1CQ1
2
1BCTCBQ
3
1jiE,KiE,KKiE,K
3
1j
1j,i,KKjE,K
1j,i,KiE,Kdispadv TCQ1CQ1
2
1BCTCBQ
The weight of advection is decreased
The weight of advection is increased
Water fluxes
K,EiIf Q 0
K,EiIf Q 0 [0 ; 1]
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One-dimensional Transport verification – The flux limiter
r sKs
(cm/d)
cm-1)n he
(cm)
0.1060
0.4686
13.1 0.0104
1.3954
0
Glendale clay loam soil parameter (Kirkland et al., 1992)
d/cm64.80t,0zq
cm2000t,cm100z0h l/g1.00t,0zC
l/g0.10t,0zC
Condition Hydrodynamics Transport
Initial
Boundary
Initial and Boundary Conditions
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One-dimensional Transport - Flux limiter effect for different Peclet number
a) max Pe=1.02
b) max Pe=1.02x103
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b) max Pe=1.02x107
One-dimensional Transport - Flux limiter effect for different Peclet number
Sensitivity analysis of the parameter
a) max Pe = 10.2 b) max Pe=1.02x103 c) max Pe=1.02x106
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Two-dimensional Transport - Flux limiter effect for different Peclet number
Two dimensional convection-dispersion problem (left) and regular mesh (right)
Case Vx(m d-
1)
Vy(m d-
1)
L
(m2 d-
1)
T
(m2 d-
1)
Pe
1 1.0 0.0 1.0 0.1 0.91
2 1.0 0.0 0.1 0.01 7.14
3 1.0 0.0 1x10-
5
1x10-
67.14x104
Parameters used in various cases
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Two-dimensional Transport - Flux limiter effect for different Peclet number
a) MHFE numerical solution b) analytical solution
Vx(m d-1)
Vy(m d-1)
L
(m2 d-1)
T
(m2 d-1)
Δx(m)
Δy(m)
Pe
1.0 0.0 1.0 0.1 1.0 1.0 0.91
Case 1 : parameters used
X
Y
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Two-dimensional Transport - Flux limiter effect for different Peclet number
Case 2 : parameters used
Vx(m d-1)
Vy(m d-1)
L
(m2 d-1)
T
(m2 d-1)
Δx(m)
Δy(m)
Pe
1.0 0.0 0.1 0.01 0.5 1.0 7.14
a) MHFE without flux limiting b) MHFE with flux limiting, = 1 c) Analytical solution
Iso-concentration lines: second test case
X
Y
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Case 3 : parameters used
Vx(m d-1)
Vy(m d-1)
L
(m2 d-1)
T
(m2 d-1)
Δx(m)
Δy(m)
Pe
1.0 0.0 0.1 0.01 0.5 1.0 7.14
Two-dimensional Transport - Flux limiter effect for different Peclet number
Iso-concentration lines: second third case
a) MHFE without flux limiting b) MHFE with flux limiting, = 1 c) Analytical solution
X
Y
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Adsorption model - Verification K
d KK
Sk
C : the isotherm linear adsorption coefficient
CK is solution concentration of the triangular element K [ML-3],
SK is absorbed concentration of the triangular element K [ML-3].
Test case : Kd = 2.38 l/kg (Atrazine ; Vryzas et al., 2007 )
0
0,2
0,4
0,6
0,8
1
1,2
0 0,05 0,1 0,15 0,2 0,25
Temps (jours)
Con
cent
ratio
n (m
g/l)
Kd =2.38 l/kg, distance 1 cm, EFMH Kd =2.38 l/kg, distance 6 cm, EFMH
Kd =0.00 l/kg, distance 1 cm, EFMH Kd =0.00 l/kg, distance 6 cm, EFMH
Kd =2.38 l/kg, distance 1 cm, HYDRUS Kd =2.38 l/kg, distance 6 cm, HYDRUS
Kd =0.00 l/kg, distance 1 cm, HYDRUS Kd =0.00 l/kg, distance 6 cm, HYDRUS
Time (day)
C(z = 0, t > 0) = 1.0 mg/l
C(z , t = 0) = 0.1 mg/l
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Kinetic models - Verification Simple kinetic models Conditions
2dC
= kdt
mC t =0;z K
1
1 max 0 m
dC= k C
dtavec k X K
mC t =0;z K
2m
2 max 0
dC C- = k
dt K +C
k X
mC t =0;z K
•Zero order
•First order
•Michaelis – Menten
max
C(t = 0, z), the initial concentration, k2 , the dissipation rate, k1, the first order rate constant the maximum reaction rate, Km the Michaelis constant X0 the amount of substrate to produce the initial population density
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Kinetic models – Verification
0
0.2
0.4
0.6
0.8
1
0 0.05 0.1 0.15 0.2 0.25
Temps (jours)
Conc
entra
tion
rela
tive
(-)
z= 1 cm, EFMH z= 6 cm, EFMH
z= 1 cm, HYDRUS z= 6 cm, HYDRUS
0
0.2
0.4
0.6
0.8
1
0 0.05 0.1 0.15 0.2 0.25Temps (jours)
Conc
entra
tion
rela
tive
(-)
z= 1 cm, EFMH z= 6 cm, EFMHz= 1 cm, HYDRUS z= 6 cm, HYDRUS
0
0.2
0.4
0.6
0.8
1
0 0.05 0.1 0.15 0.2 0.25
Temps (jours)
Conc
entra
tion
rela
tive (
-)
z= 1 cm, EFMHz= 6 cm, EFMH
Initial conditions and kinetic parameters of the tested cases
C t =0;z < 0 0.1mg/l
-3C t =0;z < 0 5.10 mg/l -3 -1m max
-30
K =5.10 mg/l ; =1j ;
X = 10 mg/l
-2C t =0;z < 0 5.10 mg/l
Kinetic models Initial concentration Kenitic parameters
Without kinetic --
Michaelis – Menten
Ordre zéro
1er ordre -4C t =0;z < 0 5.10 mg/l
Zero order first order Michaelis - Menten
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Lysimeters : Construction and instrumentation - Model Validation
Aim:to elaborate a pilot-constructed wetland design based on bioaugmentation-phytoremediation coupling in order to study and improve the biological potentialities concerning the pesticides remediation
CONCEPTION AND DIMENSIONS OF THE PILOT-PLANT
•The pilot-plant consists of 12 lysimetersDepth : 1.5m Ø : 3m
•12 storage/collector tanksDepth : 2.55m Ø : 1m
tank
lysimeter
Top view
pipe
•The filtrating media
- Coarse gravel (10/14), 25 cm depth,
- Fine gravel (4/8), 25 cm depth,
- Sediments («80µ), 30 cm depth,
Bottom layer
Top layer
•9 planted bed Phragmites australis, Typha latifolia, Scirpus lacustris
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Lysimeters : Construction and instrumentation - Model Validation
INPUT
-water + pollutant (glyphosate,
diuron, copper)
MATERIAL
-12 Lysimeters
-flexible feeding pipe
-12 collector tanks
ANALYSES
Tests on influents and effluents
will be made at different depths
Tests on sediments
Top view
Cross view
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Lysimeters : Construction and instrumentation - Model Validation
ANALYSES
Tests on influents and effluents
will be made at different depths
Tests on sediments
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