16 - 20 Sept 2007Wetland Pollutant Dynamics and Control 1 ARTIFICIAL WETLAND MODELLING FOR PESTICIDES FATE AND TRANSPORT USING A 2D MIXED HYBRID FINITE.

16 - 20 Sept 2007 Wetland Pollutant Dynamics and Control

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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


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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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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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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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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


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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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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ANALYSES

Tests on influents and effluents

will be made at different depths

Tests on sediments


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16 - 20 Sept 2007Wetland Pollutant Dynamics and Control 1 ARTIFICIAL WETLAND MODELLING FOR PESTICIDES FATE AND TRANSPORT USING A 2D MIXED HYBRID FINITE.

Documents

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control case

flux limiter transport

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transport fluxes

different peclet number

transport pecletkd2