The motivation
What comes before upscaling?
Arsenic contamination in the soil

rhizosphere with the new tool?

K. Szegedi, D. Vetterlein, H. Nietfeld, H.-U.-Neue, R. Jahn
krisztian.szegedi@ufz.deArsenic in the plants

As concentration in plants [mg/kg]

Modeling transport and speciation in the15

Bild: Stefan Klotz / UFZ

10500100

200

300

400Threshold foruse as fodder

As concentration in soil (XRF) [mg/kg]

www.bass.ufz.deHelmholtz Centre for Environmental ResearchMartin Luther University Halle-Wittenberg

Department of Soil Physics

Institute of Agricultural and Nutritional Sciences

Vetterlein et al.

Macroscopic approach

But…
No t
thisGradient formation (concentration, pH, etc)

BASS 2005

Root uptake as sink termS(r) is a function of∂ci= v∇ci + DL ∇ 2 ci − S (r )∂troot length density

ePlants se

only thisDistance from root surface!!! Bulk soil ≠ Rhizosphere !!!

concentration in bulk soil
Nietfeld, 2001, Hinsinger 1998

1

Microscopic approach

The arsenic problem
Similar to P→ competes with P

Root geometry is considered

AsV more toxic for plants
less mobile than AsIII

Root uptake is a function ofconcentration at the root surface

AsIII∂ci= −v∇ci + DL ∇ 2 ci∂tRoot uptake as boundary condition

vci + DL ∇ci = J upt , at Ω

more toxic for animals
more mobile than AsVRedox speciation + Complex interactions with other species and phases

A rhizosphere model with chemical speciation is required

Darrah and Roose, 2001

Schmidt et al. J. Appl. Bot. 2003 (77) 17-20.

Microscopic approaches with speciation
PHREEQC
MIN3P• Applied only to special problems

Experimental background*• Not all processes included- Well defined spatial resolution (planar system)- Soil solution sampled weekly• Need experts to use them

- Microtensiometers (water content)- Installed on weighing cells (evapotranspiration)

ORCHESTRA
Doris Vetterlein / UFZ

The codes have to be modified, extended

Nietfeldorapplied as toolboxes of a new approach

Bulk soil

Bulk soil
Vetterlein & Jahn Eur J Soil Sci 2004(55)1*In respect to rhizosphere modelling

Nowack et al. 2006, Nietfeld 2001

Root2

The equations…
∂c∂ 2c∂ci= − v i + DL 2i∂t∂x∂x

The equations…
Transport(+ Ω!!!)

∂c
∂ 2c
∂ci
= − v i + DL 2i
∂t
∂x
∂x

Transport(+ Ω!!!)Option: charge balance

Dicorr =Di zi Ci∂Ckz k Dk∑
2∂r∑ z jC jDj kj+ neutral boundary conditions
Nietfeld, 2001

The equations…

The RhizoMath approach

∂ci
∂c
∂ 2c
= − v i + DL 2i
∂t
∂x
∂x

Transport

K={A}eq ⋅ {B}eq{AB}eqDissociation

K={A}eq ⋅ {HfO _ w}eq
{HfO _ wA}eq

Surface sorption{A}eq ⋅ {HfO _ w}eq
K = PHREEQC{HfO _ wA}eq

Surface sorption

Phase equilibrium

K SP = {A}eq ⋅ {B}eq

Phase equilibrium

K SP = {A}eq ⋅ {B}eq∂ci∂c∂ 2c= MATLAB− v i + DL 2i
∂t
∂x
∂x

Transport{A}eq ⋅ {B}eq{AB}eq

Dissociation

K=

3

Case study – the application of goethite

Case study – Results

432
1
0
0.2
0.1

oxygenironaddition

0.0

As(V)

• Goethite added (0, 1, 4 g/kg soil)

4 g/kg soil

54
422412012244254• Different nutrients added54422412012244254P(V)• Spiked with 5 mg/kg As V
(30% growth depression)

Concentration in soil solution [mmol/l]• Artificial quartz substrate(85 % sand, 10 % silt 5 % clay)

1 g/kg soil

54422412012244254

Goethite
0 g/kg soil

Distance from the centre [mm]BASS 2005

1017
3 Days after planting

Vetterlein et al. 2007

Describing the initial state

Describing the initial state- Substrate and nutrients are mixed- Substrate and nutrients are mixed- No plant is present- No plant is present- Soil solution sampling after one week

BASS 2005

4Describing the initial state

Describing the initial state- Substrate and nutrients are mixed- Substrate and nutrients are mixed- No plant is present- No plant is present- Soil solution sampling after one week

- Soil solution
sampling afterweek relaxation
Understanding
theonesystem
in its initial state is

essential
Gas phase

for a reasonable transport/uptake model !!!Gas phase

Solid phase

Solid phase

What do we have to know?

The largest difficulties

Speciation

Which elements
Which reactions

Speciation

Which elements
Which reactions

Equilibrium with minerals

Which minerals

Equilibrium with minerals

Which minerals

Equilibrium with gases

Partial pressures

Equilibrium with gases

Partial pressures

Surface sorption

Specific surface
Surface binding sites

Surface sorption

Specific surface
Surface binding sites

Cation Exchange

Exchange capacity

Cation Exchange

Exchange capacity

5The cause of the largest difficulties

The cause of the largest difficulties

1) The equilibrium constants from literature sources are not consistent1) The equilibrium constants from literature sources are not consistent2) The equilibrium constants of surface reactions are uncertain

2) The equilibrium constants of surface reactions are uncertain

Hfo_wOH + H3AsO3 = Hfo_wH2AsO3s+ H2O

log_k 5.4

Hfo_sOH + H3AsO4 = Hfo_sH2AsO4w+ H2O

log_k 8.67

±60%3) The number of surface binding sites is not clearly definedDzombak and Morel 1990; Parkhurst and Appelo 1999; Tretner 2002

The computer model - RhizoMath
Initial parameters
Measurements(compartment)

Literature(equilibrium const)

Chemicaldatabase

Calibration module(optimization)

PHREEQC(speciation)

Transport and uptake module(solving PDE‘s)

PHREEQC(speciation)

All codes are affected

Hfo_wOH + H3AsO3 = Hfo_wH2AsO3s+ H2O

log_k 5.4

Hfo_sOH + H3AsO3 = Hfo_sH2AsO3w+ H2O

log_k 7.2

±60%3) The number of surface binding sites is not clearly definedDzombak and Morel 1990; Parkhurst and Appelo 1999; Tretner 2002

The initialization module
Automatic… processing of experimental data (.xls)… analysis of the chemical database

Optimizing (simplex method)

MATLAB (numerics)

Transport & Speciation…the uncertain equilibrium constants…the amount of surface binding sites

6Read chemical database

User input

1,0Concentration in soil solution (mmol L-1)

Read measured data

Example: Using the optimized constants

Generate input file for PHREEQC

Calculate speciation

Read PHREEQC output

PHREEQC
Calculate residuals

ChangeLow Enoughthe input parameters
the chemical database

Simplex Method

MATLAB100
As (RhizoMath)
As (measured)
P (RhizoMath)P (measured)
P:As ratio

0,880

0,660

0,4

P:As ratio

Trial and error - Let's optimize!

400,2
200,000

Save values

24681012Goethite (g kg-1)

The transport module

Solving the transport problem

Choice between…

Read chemical database… different transport models (w/o charge balance)

User input… constant / steady state water fluxes… planar / radial geometry
Generate input file for PHREEQC
Plant uptake is…

… a function of plant growth
Chemistry can include…
… no interations

increase time

… different for each species

Read PHREEQC output

PHREEQC
Administrate mineral phases… interactions among solutes

Calculate transport for… multi-phase interactions

one time interval… surface sorption

Calculate speciation

Split operator techniquet = tmax

MATLABPrint output

7

Water flux

Solute uptake parameters

The graphical user interface

Example – pure diffusion
RhizoMath

Surface sorption

Geometry

Phase equilibrium

Diffusion, onlyConstant water content
Constant right boundary
No speciation

Parameters from Schnepf, 2002

Snapshot after 120 days
Main window with message box

Inputs of the Transpot module

Diffusion of K towards a single root, Nowack et al 2006

Example: Competitive sorption of P and AsExample: Competitive sorption of P and As

Without citrate exudation

Without citrate exudation
With citrate exudation

As(V)

P(V)
6G-1

0.1050.08

G-4

G-1

40.06

30.04
2G-4

10.02

012

3

40.12

60

12

34

Distance from root surface (cm)Parameters from Meharg & Macnair 1992; Barber 1995; Vetterlein et al 2007;

G-1

0.10

50.08

G-4

G-1

40.06

30.04
2

G-4

10.02

00.00
0As(V)

P(V)
70.12

Concentration in soil solution (mM)Concentration in soil solution (mM)

70.00
012

3

40

1

2

3

4

Distance from root surface (cm)Szegedi et al, submitted

Parameters from Meharg & Macnair 1992; Barber 1995; Vetterlein et al 2007;

Szegedi et al, submitted

8

Example: Competitive sorption of P and As

The crucial points

Without citrate exudation

As(V)

P(V)
0.12

6G-1

0.10

50.08

• Literature data on root uptake• Competition by root uptake• Charge balance by uptake• Water fluxes are not exact

G-4

G-1

4

Th

0.06

hihi

hi fldf h• Choice of the right species

il

3
0.04
2G-4

1

0.02

00.00
01

2

3

40

1

2

3

4

Distance from root surface (cm)Parameters from Meharg & Macnair 1992; Barber 1995; Vetterlein et al 2007;

Szegedi et al, VZJ, in pressExperiments / Nature

Concentration in soil solution (mM)

7

• Reaction kinetics?
Modelling / Theory

With citrate exudation• Root mat development• Sampling „smoothes“ gradients• Each plant species is different
BASS

Micro- vs macroscopic approach
Depends on the question• A. Tretner

which one has to be applied• A. Gergaut & I. Krieg• K. Kaiser & C. Krenkewitz• UFZ, Department of Analytics

We have to understand theThis work is conducted in the framework of theprocesses at the single root

BASS Helmholtz-Hochschul-Nachwuchsgruppe

scale as well before upscalingwww.bass.ufz.de
Helmholtz Centre for Environmental ResearchMartin Luther University Halle-Wittenberg

Department of Soil Physics

Institute of Agricultural and Nutritional Sciences9Required parameters

Comparison of the relative errors

Chemistry:

109• Their relevant stoichiometric equations

8Relative error (%)• Added nutrients• Minerals & Gases• Surface sorption parameters
Transport:

RhizoMathwithout speciation
with6543• Water flux (Darcy)

2• Volumetric water content

10• Diffusion coefficients

00.2

Solute uptake parameters

Water flux (constant in this version)

The graphical user interface

Surface sorption(Δx )2

1

Solute uptake parameters

The graphical user interface

Geometry

3D

Surface sorption

TimeΔt =(Diffusion)

Main window with message box

0.8

Δx: “smallest reasonable”

Phase equilibrium

Δt =

0.6

Water flux (constant in this version)

Δx: “smallest reasonable”

Time

0.4

Distance from root center (cm)• Uptake kinetics (each element)

Geometry

speciation

7

Phase equilibrium

ΔxqΘ−1(Mass flow)

Inputs of the Transpot module

Parkhurst and Appelo 1999

Δt =(Δx )23D(Diffusion)

Main window with message box

Inputs of the Transpot module

Parkhurst and Appelo 1999

10

Nutrient uptake

Transport in the rhizosphere

J iupt = α ⋅ Ci
∂Ci 1 ∂ ⎛∂Ci r0 v0Ci ⎞=+⎜ rDLi
⎟ − RCi∂tr ∂r ⎝∂rb ⎠J iupt = S ⋅ mi ⋅ Ci
⎛ Ci − Ci ,min ⎞⎜⎟J iupt = J iupt, max ⎜⎟⎝ K i + Ci − Ci ,min ⎠Standard deviation

Standard deviation

n(x)

n(x)
μ±σ

μ±σ

The x values are with 95% possibility in this interval.
Could be anywhere…

μxμx11More results I.
AsPa150

100

Trial and Error

b750

Modelled concentrations (μmol·l-1)

More results II.

500

50

25000050

1001500c150

250500750

Trial and Error + Strengite

d750

100

500

50

25000050

100

1500e

150

250

500

750

Optimization + Strengite

f750

100

500
G-0
G-1 250
G-4
1:1

50

0G-0G-1
G-4
1:1

0050

100

150

0250

500

750

Measured concentrations (μmol·l-1)

The graphical user interface

More results III.

12