Representing radionuclide uptake from soil to plants: key challenges

Jordi Vives i Batlle

SCK.CEN Jordi.vives.i.batlle@sckcen.be

2012 BIOPROTA Workshop Nancy, France 21 – 24 May 2012 Copyright © 2012 SCK•CEN

Introduction

Project framework Radionuclide cycling studies in Chernobyl. Water table measurements in experimental scots pine

forest in the vicinity of Mol (CV, YT). Development of Cl model for forests (YT, CvdH). Currently developing 1D water table model with

biosphere interaction components to couple with Cl. Extensive measurements of Cl (& now Al, Br,Ca, Cl, Cu,

Dy, I, In, Mn and V) in soil (organic/mineral), tree roots, bark, wood, branches, twigs, needles, litter, understory.

New project! we are going to design a decision support tool to analyse risks to Belgian forest ecosystems arising from direct & indirect global change effects - ECORISK.

Partners: University of Antwerp, UCL, KMI, SCK-CEN SCK to develop new module including relative mobility of

pollutants in respect of H20, N & C at GBIZ interface.

Project framework

Groundwater

Porewater

Infiltration_from_soil

Atmosphere

Thoroughfall

Gaining_stream

Water_table_depth [m]

Time_dependent_data T, rainfall, + LAI and Kc

Root_uptake

ET0 Evapotranspiration

rate [m/d]

rs Reference crop

surface resistance [s m-1] Gamma

Psychrometric const [pa/kg]

Radiation Rn - G [W/m2]

Evaporation

Temp Average [K]

Delta_e Pressure differential [Pa]

Delta Vap press slope [Pa/K]

Lv Latent heat of water [J/kg]

Rho_A Dry air density [kg m-3]

Fc_switch Field capacity

Losing_streamRiver Roots

Main_tree (wood + leaves)Washout

Interception

Transpiration

Upward_transfer

Absorption

Leaching

Downward_transferRoot_uptake_rate

Top_soil (organic fraction)

Fall

Decomposition

Needle_loss_rateBioaccumulationCapillarity

ra Aerodynamic

resistance [s/m]

Soil_porosity

Retardation [m]

Plant_cover_index

Evap_leaf

Leaf_surface (external)

Biomass

Tree_density [trees/m2]

Xylem_ascent_rate

Phloem_descent_rate

Water_stress_coefficient

Phloem_viscosity

Some key questions The water table model project has uncovered some

key questions. Is there an agreed way to model the infiltration of

groundwater to soil by capillarity – different modellers do this in different ways.

What is a realistic representation of the rhizosphere, factorising uptake from soil and soil solution by plant roots

Interactions with nutrients and micronutrients – main equations and processes.

Given a model capable of representing the flow of water from the water table to plants via the roots, how do we modify the model to adapt it for transportation of radionuclides e.g. retardation or preferential transport – what are the key equations.

In some cases, we can solve the problem by using simplified approximations of Richard’s equation, with mainly vertical water flow and assuming quasi-steady-state of water (laminar flow).

Approximations: Poiseuille equation, simple infiltration equations for rainfall, the Lucas–Washburn equation (quasi-steady capillary flow), Darcy's law with constant hydraulic conductivity, variable water table height within a single soil compartment.

Such model can be integrated by simple methods: Runge Kutta or Gear solver of the type available in Matlab or ModelMaker.

This is justified for modelling on very long timescales, as the seasonal hydrological cycle can at best be only approximated.

Overall hypothesis

Capillarity

The treatment of capillarity (1) Last meeting we discussed various empirical formulas

that apply only in certain cases (e.g. Phillips’ equation). The capillary transport in the vertical direction can be

described by Newton dynamics' equation for a viscous non-compressible liquid - this seems to be a good starting point:

If the inertial (first) term can be neglected (liquid moves slowly), then we have the following approximation:

( ) 0cos282 =−+

∂∂

+

∂∂

+∂∂

rgz

tzz

rtzz

t ρθγ

ρηλ

z is the vertical coordinate representing the height of capillary rise (m), t the time (s), h the dynamic viscosity (N s m-2), r the density of water (103 kg m-3), r the radius of the capillary (m), g the acceleration of gravity (m s-2), γ the surface tension (N m-1) and θ the contact (wetting) angle of the liquid.

−= 2

2cos

41 rg

zr

dtdz ρθγ

η

The treatment of capillarity (2) Considering the soil as a network of N cylindrical tubes

with a radius r and height h, with volume = hπr2 : There is a certain relationship between the porosity ε of

the solid and N:

Also porosity is variable – the more saturated the soil, the less room for the infilling water:

In addition associate sorptivity with γ, θ and η:

−==Φ g

VrNrN

dtdV ρθγπ

ηπ cos28

4

2

22

rSN

SrN

hShrN A

AA πεππε =⇒==

−=

εεε

0

1porosity EffectiveVV

eff

ηθγ

2cosrs =

Do we need to do this?

Comes from comparing with Phillips’ law in the case of a horizontal tube.

The treatment of capillarity (3) For a wetting angle of ~ 0o this gives the non-linear

equation:

It all seems to work: Sorptivity of water in a relatively undisturbed soil = 3.79 ×

10-2 m d-1/2 (Fuentes et al., 2010) vs. 3.29 × 10-2 m d-1/2 if r = 3 × 10-5 m (micropores - Dean, 1967).

Applying this calibration to our model gives an initial capillarity flow of 0.4 mm d-1 stabilising to a 0.25 mm d-1 at equilibrium, whilst real values range from 0.5 to 8 mm day-

1 (Raes and Deproost 2003). If the soil is already too full, the capillarity stops.

Is this a reasonable treatment? (e.g. treating soil as a simple continuous porous medium –macro-porosity?).

−

−

−=

εγηρ

εεε

hSVsg

hSV

VSsS

dtdV

AA

AA 112 2

22

Is this reasonable?

Plant transport

Of special relevance is the transfer from the forest floor and the soil to the roots.

The macroscopic linear root-water uptake model (Prasad, 1988) is the simplest model that can be used:

Next in line is the exponential root water uptake model (Li et al., 2001):

Root uptake (1)

−=

rootrootroot h

hhEThr 12)( 0

where h is the depth of the available water at rooting depth hroot, and ET0 is the evapotranspiration.

( )

( ) hhET

ee

eeee

rrootbh

bh

bhbhbh

bh

root

root

root

root

−−+

+

−+

++

=−

−

−−−

−

0

121

12ln

21

11ln

where b is an empirical extinction coefficient which can be expressed as a function of G10 and G20, the fractions of root length in the top 10% and 20% of the root zone

rootroot hGb

hGb

9047.110

5901.110 8802.13or,6637.24

==

We also need to consider the following processes: Anaerobiosis (plant waterlogging effect):

Upward xylem transport (Poiseuille equation):

Downward phloem transport (osmosis):

Not only water flow matters – speciation affects bioavailability and fixation or radionuclides in roots

Root uptake (2)

( )

≥−−

=−−

<= ε

εε

θθθθ

ε

hfSVfhS

VhShSfV

Ka

a

a

airsat

isat

a

S if 1

if1

Where θsat is the soil water content at saturation (m3/m3), θi is the soil water content in the root zone (m3/m3) with θsat ≤ θi ≤ θair and θair is the soil water content at the anaerobiosis point (m3/m3)

phrr ∆Ψ

=

2

81η

Where r is the pipe radius, h the pipe length, η is the viscosity and ΔΨp the pressure difference

iMRTh

rosm η

π8

4

=Ψ=Φ Where I is the i is the van 't Hoff factor, M the molarity and R the ideal gas constant.

Solute transport

‘Recycling’ the water model We try to use the same model for water transport,

modified for solute transport by: Coupling a solid phase with sorption / ion exchange rates Retarding subsurface transport and root uptake fluxes Changing the units to represent solute concentrations Looking into ways to factorise speciation by adapting HP1

/ PHREEQC approach

Processes Processes that remove species from solution and retard

subsurface migration: ion exchange, sorption and diffusion. Sorption depends on the type of soil, guided by the Kd

(depends on particle size, pH, organic carbon content…). The Kd has two values: Kd1 below the water table (anoxic

conditions) and Kd2 above the capillary fringe (oxic conditions). Ion exchange more important than advection in soils with high

CEC e.g. clay minerals (depends on redox state, water level). Better models must consider root fixation and biomass cycling

(soil-plant-litter) as part of overall mass balance.

Integration of soil-carbon- cycle model (after Battle-Aguilar et al., 2010) Variability of the Kd with pH (Echevarria et al. (2011).

Processes (2)

Kinetic exchange rates

S is the sedimentation rate, dw the typical distance that molecules have to diffuse in water, α the suspended sediment load, D = εDm is the effective diffusion coefficient for a porous medium, ha the thickness of the soil layer, RT the pore water turnover rate, RW the soil reworking rate, θ is the porosity and ρ is the soil dry density.

Now we assume: No suspended load (no sedimentation): RT = α = S = 0 No soil reworking (stable layer): RW = 0 The predominant process is diffusion

( ) ( )

( ) ( )( ) 2

2

2

11

1

1

11

a

aamw

a

aams

hρdK

hρdKWRTRhDr

h

ρhdKWRTRhDdSK

α)dK(wdr

−+

−++=

−+++

+=

θ

θθ

θθθ

θθθ

Kinetic exchange rates (2)

The equations for the transfer rates become then:

All can be calculated if θ, Dm, dw, ha and R are known. R is the retardation factor, defined more generally as:

22 11

;a

m

a

mw

a

ms Rh

D

dρK)(h

Drhwd

Dr =−+

==

θθ

θ

ρ(1- θ) is the dry soil bulk density, with ρ the solid density and θ the porosity. Kd is the solid:liquid distribution coefficient for the solute (m3 kg-1). θV is the soil moisture content, equal to θ for saturated flow.

dρK)(RVθθ−+= 11

Summary

The basic ‘recipe’ Divide all advective flows (in which the solute is physically

transported along with the water) such as infiltration, capillary transport and root uptake, by retardation, e.g.:

Root uptake => multiply by a bioaccumulation factor representing non-selective transfer of radionuclide between soil solution and plant root via water uptake:

The Kd has a different value in the water table (anoxic conditions) compared with above the capillary fringe (oxic conditions), but an average can be taken if data not available.

This is a simplification because nuclide sorption is influenced by geochemical factors including speciation, ionic strength, temperature, trace metals, colloids and organic pollutants.

−+

=

θθρθ

λd

a

L Kh

onInfiltrati)1(1

'

+= BCF

hBM

Rrr

a

UU ρ

1'

Vegetation as a dynamic component. Influence of plant type – forest ecosystems / broadleaf vs. needle leaf.

Lateral transport of sap. Nutrient relocation to perennial

parts before leaves fall. Effectiveness of root

uptake vs. soil water. Bioturbation (< 20 cm). Coupling of plant uptake

with groundwater model Effect of assuming

constant hydraulic conductivity in unsaturated flow vs. Van Genuchten’s model for θ and Hc.

Timescales for combining plant transport and seasonal variations in soil hydrology (avoid parameters estimated from annual water mass balance).

Translocation, fluxes within vegetation – mass balances.

Additional questions

Conclusions We are trying for an integrated modelling approach to

simulate the long-term distribution of a constant influx of groundwater contaminated with long-lived radionuclides into soil.

We should not ignore the selective uptake across root membranes or competition between radionuclides and macronutrients.

We assume invariant climate, but in ECORISK we step beyond radioecology to wider issues (climate change).

Must always aim to balance the computational burden and the model’s ability to represent short-term processes

We aim to use simplified approximations of Richard’s Eq. in a simple system of coupled differential equations.

We develop first a water cycling model and only then we adapt it to solute transport using retardation and bioaccumulation processes. Next step is 36Cl.

References Battle-Aguilar J, Brovelli A, Porporato A, Barry DA (2011) Modelling

soil carbon and nitrogen cycles during land use change: A Review. Agronom. Sust. Dev. 31 (2):251-274.

Dean JA (1967) Lange's Handbook of Chemistry (1967) 10th ed. pp 1661–1665. ISBN 0-07-016190-9 (11th ed.).

Echevarria G, Sheppard MI, Morel J (2001) Effect of pH on the sorption of uranium in soils. J. Environ.l Radioactivity 53 (2):257-264.

Li KY, De Jong R, Boisvert JB (2001) Comparison of root-water-uptake models. In: 10th Int. Soil Conservation Organization Meeting, West Lafayette, pp. 1112–1117.

Prasad R (1988) A linear root water uptake model. Journal of Hydrology 99 (3-4):297-306.

Raes D, Deproost P (2003) Model to assess water movemnet from a shallow water table to the root zone. Agri.l Wat. Man. 62:79-91

Xu, S. L., Worman, A., Dverstorp, B., 2007. Criteria for resolution-scales and parameterisation of compartmental models of hydrological and ecological mass flows. Journal of Hydrology 335 (3-4), 364–373

Thank you for your attention